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Sample records for two-dimensional fourier filter

  1. Three dimensional image reconstruction in the Fourier domain

    International Nuclear Information System (INIS)

    Stearns, C.W.; Chesler, D.A.; Brownell, G.L.

    1987-01-01

    Filtered backprojection reconstruction algorithms are based upon the relationship between the Fourier transform of the imaged object and the Fourier transforms of its projections. A new reconstruction algorithm has been developed which performs the image assembly operation in Fourier space, rather than in image space by backprojection. This represents a significant decrease in the number of operations required to assemble the image. The new Fourier domain algorithm has resolution comparable to the filtered backprojection algorithm, and, after correction by a pointwise multiplication, demonstrates proper recovery throughout image space. Although originally intended for three-dimensional imaging applications, the Fourier domain algorithm can also be developed for two-dimensional imaging applications such as planar positron imaging systems

  2. Design and implementation in VHDL code of the two-dimensional fast Fourier transform for frequency filtering, convolution and correlation operations

    Science.gov (United States)

    Vilardy, Juan M.; Giacometto, F.; Torres, C. O.; Mattos, L.

    2011-01-01

    The two-dimensional Fast Fourier Transform (FFT 2D) is an essential tool in the two-dimensional discrete signals analysis and processing, which allows developing a large number of applications. This article shows the description and synthesis in VHDL code of the FFT 2D with fixed point binary representation using the programming tool Simulink HDL Coder of Matlab; showing a quick and easy way to handle overflow, underflow and the creation registers, adders and multipliers of complex data in VHDL and as well as the generation of test bench for verification of the codes generated in the ModelSim tool. The main objective of development of the hardware architecture of the FFT 2D focuses on the subsequent completion of the following operations applied to images: frequency filtering, convolution and correlation. The description and synthesis of the hardware architecture uses the XC3S1200E family Spartan 3E FPGA from Xilinx Manufacturer.

  3. Two-dimensional fourier transform spectrometer

    Science.gov (United States)

    DeFlores, Lauren; Tokmakoff, Andrei

    2013-09-03

    The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

  4. Two-dimensional filtering of SPECT images using the Metz and Wiener filters

    International Nuclear Information System (INIS)

    King, M.A.; Schwinger, R.B.; Penney, B.C.; Doherty, P.W.

    1984-01-01

    Presently, single photon emission computed tomographic (SPECT) images are usually reconstructed by arbitrarily selecting a one-dimensional ''window'' function for use in reconstruction. A better method would be to automatically choose among a family of two-dimensional image restoration filters in such a way as to produce ''optimum'' image quality. Two-dimensional image processing techniques offer the advantages of a larger statistical sampling of the data for better noise reduction, and two-dimensional image deconvolution to correct for blurring during acquisition. An investigation of two such ''optimal'' digital image restoration techniques (the count-dependent Metz filter and the Wiener filter) was made. They were applied both as two-dimensional ''window'' functions for preprocessing SPECT images, and for filtering reconstructed images. Their performance was compared by measuring image contrast and per cent fractional standard deviation (% FSD) in multiple-acquisitions of the Jaszczak SPECT phantom at two different count levels. A statistically significant increase in image contrast and decrease in % FSD was observed with these techniques when compared to the results of reconstruction with a ramp filter. The adaptability of the techniques was manifested in a lesser % reduction in % FSD at the high count level coupled with a greater enhancement in image contrast. Using an array processor, processing time was 0.2 sec per image for the Metz filter and 3 sec for the Wiener filter. It is concluded that two-dimensional digital image restoration with these techniques can produce a significant increase in SPECT image quality

  5. A high-speed computerized tomography image reconstruction using direct two-dimensional Fourier transform method

    International Nuclear Information System (INIS)

    Niki, Noboru; Mizutani, Toshio; Takahashi, Yoshizo; Inouye, Tamon.

    1983-01-01

    The nescessity for developing real-time computerized tomography (CT) aiming at the dynamic observation of organs such as hearts has lately been advocated. It is necessary for its realization to reconstruct the images which are markedly faster than present CTs. Although various reconstructing methods have been proposed so far, the method practically employed at present is the filtered backprojection (FBP) method only, which can give high quality image reconstruction, but takes much computing time. In the past, the two-dimensional Fourier transform (TFT) method was regarded as unsuitable to practical use because the quality of images obtained was not good, in spite of the promising method for high speed reconstruction because of its less computing time. However, since it was revealed that the image quality by TFT method depended greatly on interpolation accuracy in two-dimensional Fourier space, the authors have developed a high-speed calculation algorithm that can obtain high quality images by pursuing the relationship between the image quality and the interpolation method. In this case, radial data sampling points in Fourier space are increased to β-th power of 2 times, and the linear or spline interpolation is used. Comparison of this method with the present FBP method resulted in the conclusion that the image quality is almost the same in practical image matrix, the computational time by TFT method becomes about 1/10 of FBP method, and the memory capacity also reduces by about 20 %. (Wakatsuki, Y.)

  6. High-speed fan-beam reconstruction using direct two-dimensional Fourier transform method

    International Nuclear Information System (INIS)

    Niki, Noboru; Mizutani, Toshio; Takahashi, Yoshizo; Inouye, Tamon.

    1984-01-01

    Since the first development of X-ray computer tomography (CT), various efforts have been made to obtain high quality of high-speed image. However, the development of high resolution CT and the ultra-high speed CT to be applied to hearts is still desired. The X-ray beam scanning method was already changed from the parallel beam system to the fan-beam system in order to greatly shorten the scanning time. Also, the filtered back projection (DFBP) method has been employed to directly processing fan-beam projection data as reconstruction method. Although the two-dimensional Fourier transform (TFT) method significantly faster than FBP method was proposed, it has not been sufficiently examined for fan-beam projection data. Thus, the ITFT method was investigated, which first executes rebinning algorithm to convert the fan-beam projection data to the parallel beam projection data, thereafter, uses two-dimensional Fourier transform. By this method, although high speed is expected, the reconstructed images might be degraded due to the adoption of rebinning algorithm. Therefore, the effect of the interpolation error of rebinning algorithm on the reconstructed images has been analyzed theoretically, and finally, the result of the employment of spline interpolation which allows the acquisition of high quality images with less errors has been shown by the numerical and visual evaluation based on simulation and actual data. Computation time was reduced to 1/15 for the image matrix of 512 and to 1/30 for doubled matrix. (Wakatsuki, Y.)

  7. The Convergence Acceleration of Two-Dimensional Fourier Interpolation

    Directory of Open Access Journals (Sweden)

    Anry Nersessian

    2008-07-01

    Full Text Available Hereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.

  8. Two-dimensional grating guided-mode resonance tunable filter.

    Science.gov (United States)

    Kuo, Wen-Kai; Hsu, Che-Jung

    2017-11-27

    A two-dimensional (2D) grating guided-mode resonance (GMR) tunable filter is experimentally demonstrated using a low-cost two-step nanoimprinting technology with a one-dimensional (1D) grating polydimethylsiloxane mold. For the first nanoimprinting, we precisely control the UV LED irradiation dosage and demold the device when the UV glue is partially cured and the 1D grating mold is then rotated by three different angles, 30°, 60°, and 90°, for the second nanoimprinting to obtain 2D grating structures with different crossing angles. A high-refractive-index film ZnO is then coated on the surface of the grating structure to form the GMR filter devices. The simulation and experimental results demonstrate that the passband central wavelength of the filter can be tuned by rotating the device to change azimuth angle of the incident light. We compare these three 2D GMR filters with differential crossing angles and find that the filter device with a crossing angle of 60° exhibits the best performance. The tunable range of its central wavelength is 668-742 nm when the azimuth angle varies from 30° to 90°.

  9. Edge Detection from High Resolution Remote Sensing Images using Two-Dimensional log Gabor Filter in Frequency Domain

    International Nuclear Information System (INIS)

    Wang, K; Yu, T; Meng, Q Y; Wang, G K; Li, S P; Liu, S H

    2014-01-01

    Edges are vital features to describe the structural information of images, especially high spatial resolution remote sensing images. Edge features can be used to define the boundaries between different ground objects in high spatial resolution remote sensing images. Thus edge detection is important in the remote sensing image processing. Even though many different edge detection algorithms have been proposed, it is difficult to extract the edge features from high spatial resolution remote sensing image including complex ground objects. This paper introduces a novel method to detect edges from the high spatial resolution remote sensing image based on frequency domain. Firstly, the high spatial resolution remote sensing images are Fourier transformed to obtain the magnitude spectrum image (frequency image) by FFT. Then, the frequency spectrum is analyzed by using the radius and angle sampling. Finally, two-dimensional log Gabor filter with optimal parameters is designed according to the result of spectrum analysis. Finally, dot product between the result of Fourier transform and the log Gabor filter is inverse Fourier transformed to obtain the detections. The experimental result shows that the proposed algorithm can detect edge features from the high resolution remote sensing image commendably

  10. Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Paul, J.; Dey, P.; Karaiskaj, D., E-mail: karaiskaj@usf.edu [Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, Florida 33620 (United States); Tokumoto, T.; Hilton, D. J. [Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 (United States); Reno, J. L. [CINT, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)

    2014-10-07

    The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10{sup 11} cm{sup −2} was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent “rephasing” (S{sub 1}) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S{sub 1} 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The “two-quantum coherence” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.

  11. Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke; Ishibashi, Hideo

    1978-01-01

    A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

  12. Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke

    1975-01-01

    A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

  13. Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

    Science.gov (United States)

    van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

    2015-12-01

    Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

  14. Optimal Padding for the Two-Dimensional Fast Fourier Transform

    Science.gov (United States)

    Dean, Bruce H.; Aronstein, David L.; Smith, Jeffrey S.

    2011-01-01

    One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that

  15. Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals

    International Nuclear Information System (INIS)

    Jiang, Ping; Ding, Chengyuan; Hu, Xiaoyong; Gong, Qihuang

    2007-01-01

    A tunable double-channel filter is presented, which is based on a two-dimensional nonlinear ferroelectric photonic crystal made of cerium doped barium titanate. The filtering properties of the photonic crystal filter can be tuned by adjusting the defect structure or by a pump light. The influences of the structure disorders caused by the perturbations in the radius or the position of air holes on the filtering properties are also analyzed

  16. Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals

    Energy Technology Data Exchange (ETDEWEB)

    Jiang, Ping [State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871 (China); Ding, Chengyuan [State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871 (China); Hu, Xiaoyong [State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871 (China)]. E-mail: xiaoyonghu@pku.edu.cn; Gong, Qihuang [State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871 (China)]. E-mail: qhgong@pku.edu.cn

    2007-04-02

    A tunable double-channel filter is presented, which is based on a two-dimensional nonlinear ferroelectric photonic crystal made of cerium doped barium titanate. The filtering properties of the photonic crystal filter can be tuned by adjusting the defect structure or by a pump light. The influences of the structure disorders caused by the perturbations in the radius or the position of air holes on the filtering properties are also analyzed.

  17. Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

    Science.gov (United States)

    Ma, Q.; Boulet, C.; Tipping, R. H.

    2014-01-01

    The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

  18. Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval

    Science.gov (United States)

    Smith, Jeffrey Scott

    2006-01-01

    Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.

  19. Fourier analysis of cell-wise Block-Jacobi splitting in two-dimensional geometry

    International Nuclear Information System (INIS)

    Rosa, M.; Warsa, J. S.; Kelley, T. M.

    2009-01-01

    A Fourier analysis is conducted in two-dimensional (2D) geometry for the discrete ordinates (S N ) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) using the cell-wise Block-Jacobi (BJ) algorithm. The results of the Fourier analysis show that convergence of cell-wise BJ can degrade, leading to a spectral radius equal to 1, in problems containing optically thin cells. For problems containing cells that are optically thick, instead, the spectral radius tends to 0. Hence, in the optically thick-cell regime, cell-wise BJ is rapidly convergent even for problems that are scattering dominated, with a scattering ratio c close to 1. (authors)

  20. Optical Two Dimensional Fourier Transform Spectroscopy of Layered Metal Dichalcogenides

    Science.gov (United States)

    Dey, P.; Paul, J.; Stevens, C. E.; Kovalyuk, Z. D.; Kudrynskyi, Z. R.; Romero, A. H.; Cantarero, A.; Hilton, D. J.; Shan, J.; Karaiskaj, D.; Z. D. Kovalyuk; Z. R. Kudrynskyi Collaboration; A. H. Romero Collaboration; A. Cantarero Collaboration; D. J. Hilton Collaboration; J. Shan Collaboration

    2015-03-01

    Nonlinear two-dimensional Fourier transform (2DFT) measurements were used to study the mechanism of excitonic dephasing and probe the electronic structure of the excitonic ground state in layered metal dichalcogenides. Temperature-dependent 2DFT measurements were performed to probe exciton-phonon interactions. Excitation density dependent 2DFT measurements reveal exciton-exciton and exciton-carrier scattering, and the lower limit for the homogeneous linewidth of excitons on positively and negatively doped samples. U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0012635.

  1. Design of efficient circularly symmetric two-dimensional variable digital FIR filters.

    Science.gov (United States)

    Bindima, Thayyil; Elias, Elizabeth

    2016-05-01

    Circularly symmetric two-dimensional (2D) finite impulse response (FIR) filters find extensive use in image and medical applications, especially for isotropic filtering. Moreover, the design and implementation of 2D digital filters with variable fractional delay and variable magnitude responses without redesigning the filter has become a crucial topic of interest due to its significance in low-cost applications. Recently the design using fixed word length coefficients has gained importance due to the replacement of multipliers by shifters and adders, which reduces the hardware complexity. Among the various approaches to 2D design, transforming a one-dimensional (1D) filter to 2D by transformation, is reported to be an efficient technique. In this paper, 1D variable digital filters (VDFs) with tunable cut-off frequencies are designed using Farrow structure based interpolation approach, and the sub-filter coefficients in the Farrow structure are made multiplier-less using canonic signed digit (CSD) representation. The resulting performance degradation in the filters is overcome by using artificial bee colony (ABC) optimization. Finally, the optimized 1D VDFs are mapped to 2D using generalized McClellan transformation resulting in low complexity, circularly symmetric 2D VDFs with real-time tunability.

  2. Optical properties of the two-port resonant tunneling filters in two-dimensional photonic crystal slabs

    International Nuclear Information System (INIS)

    Ren Cheng; Cheng Li-Feng; Kang Feng; Gan Lin; Zhang Dao-Zhong; Li Zhi-Yuan

    2012-01-01

    We have designed and fabricated two types of two-port resonant tunneling filters with a triangular air-hole lattice in two-dimensional photonic crystal slabs. In order to improve the filtering efficiency, a feedback method is introduced by closing the waveguide. It is found that the relative position between the closed waveguide boundary and the resonator has an important impact on the dropping efficiency. Based on our analyses, two different types of filters are designed. The transmission spectra and scattering-light far-field patterns are measured, which agree well with theoretical prediction. In addition, the resonant filters are highly sensitive to the size of the resonant cavities, which are useful for practical applications

  3. Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data

    Science.gov (United States)

    Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.

    2017-10-01

    The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.

  4. Electro-optic tunable multi-channel filter in two-dimensional ferroelectric photonic crystals

    International Nuclear Information System (INIS)

    Fu, Yulan; Zhang, Jiaxiang; Hu, Xiaoyong; Gong, Qihuang

    2010-01-01

    An electro-optic tunable multi-channel filter is presented, which is based on a two-dimensional ferroelectric photonic crystal made of barium titanate. The filtering properties of the photonic crystal filter can be tuned by an applied voltage or by adjusting the structural parameters. The channel shifts about 30 nm under excitation of an applied voltage of 54.8 V. The influences of the structural disorders caused by the perturbations in the radius or the position of air holes on the filtering properties are also analyzed

  5. Geometrical bucklings for two-dimensional regular polygonal regions using the finite Fourier transformation

    International Nuclear Information System (INIS)

    Mori, N.; Kobayashi, K.

    1996-01-01

    A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)

  6. A clinical evaluation of the RNCA study using Fourier filtering as a preprocessing method

    Energy Technology Data Exchange (ETDEWEB)

    Robeson, W.; Alcan, K.E.; Graham, M.C.; Palestro, C.; Oliver, F.H.; Benua, R.S.

    1984-06-01

    Forty-one patients (25 male, 16 female) were studied by Radionuclide Cardangiography (RNCA) in our institution. There were 42 rest studies and 24 stress studies (66 studies total). Sixteen patients were normal, 15 had ASHD, seven had a cardiomyopathy, and three had left-sided valvular regurgitation. Each study was preprocessed using both the standard nine-point smoothing method and Fourier filtering. Amplitude and phase images were also generated. Both preprocessing methods were compared with respect to image quality, border definition, reliability and reproducibility of the LVEF, and cine wall motion interpretation. Image quality and border definition were judged superior by the consensus of two independent observers in 65 of 66 studies (98%) using Fourier filtered data. The LVEF differed between the two processes by greater than .05 in 17 of 66 studies (26%) including five studies in which the LVEF could not be determined using nine-point smoothed data. LV wall motion was normal by both techniques in all control patients by cine analysis. However, cine wall motion analysis using Fourier filtered data demonstrated additional abnormalities in 17 of 25 studies (68%) in the ASHD group, including three uninterpretable studies using nine-point smoothed data. In the cardiomyopathy/valvular heart disease group, ten of 18 studies (56%) had additional wall motion abnormalities using Fourier filtered data (including four uninterpretable studies using nine-point smoothed data). We conclude that Fourier filtering is superior to the nine-point smooth preprocessing method now in general use in terms of image quality, border definition, generation of an LVEF, and cine wall motion analysis. The advent of the array processor makes routine preprocessing by Fourier filtering a feasible technologic advance in the development of the RNCA study.

  7. A clinical evaluation of the RNCA study using Fourier filtering as a preprocessing method

    International Nuclear Information System (INIS)

    Robeson, W.; Alcan, K.E.; Graham, M.C.; Palestro, C.; Oliver, F.H.; Benua, R.S.

    1984-01-01

    Forty-one patients (25 male, 16 female) were studied by Radionuclide Cardangiography (RNCA) in our institution. There were 42 rest studies and 24 stress studies (66 studies total). Sixteen patients were normal, 15 had ASHD, seven had a cardiomyopathy, and three had left-sided valvular regurgitation. Each study was preprocessed using both the standard nine-point smoothing method and Fourier filtering. Amplitude and phase images were also generated. Both preprocessing methods were compared with respect to image quality, border definition, reliability and reproducibility of the LVEF, and cine wall motion interpretation. Image quality and border definition were judged superior by the consensus of two independent observers in 65 of 66 studies (98%) using Fourier filtered data. The LVEF differed between the two processes by greater than .05 in 17 of 66 studies (26%) including five studies in which the LVEF could not be determined using nine-point smoothed data. LV wall motion was normal by both techniques in all control patients by cine analysis. However, cine wall motion analysis using Fourier filtered data demonstrated additional abnormalities in 17 of 25 studies (68%) in the ASHD group, including three uninterpretable studies using nine-point smoothed data. In the cardiomyopathy/valvular heart disease group, ten of 18 studies (56%) had additional wall motion abnormalities using Fourier filtered data (including four uninterpretable studies using nine-point smoothed data). We conclude that Fourier filtering is superior to the nine-point smooth preprocessing method now in general use in terms of image quality, border definition, generation of an LVEF, and cine wall motion analysis. The advent of the array processor makes routine preprocessing by Fourier filtering a feasible technologic advance in the development of the RNCA study

  8. Two-Dimensional IIR Filter Design Using Simulated Annealing Based Particle Swarm Optimization

    Directory of Open Access Journals (Sweden)

    Supriya Dhabal

    2014-01-01

    Full Text Available We present a novel hybrid algorithm based on particle swarm optimization (PSO and simulated annealing (SA for the design of two-dimensional recursive digital filters. The proposed method, known as SA-PSO, integrates the global search ability of PSO with the local search ability of SA and offsets the weakness of each other. The acceptance criterion of Metropolis is included in the basic algorithm of PSO to increase the swarm’s diversity by accepting sometimes weaker solutions also. The experimental results reveal that the performance of the optimal filter designed by the proposed SA-PSO method is improved. Further, the convergence behavior as well as optimization accuracy of proposed method has been improved significantly and computational time is also reduced. In addition, the proposed SA-PSO method also produces the best optimal solution with lower mean and variance which indicates that the algorithm can be used more efficiently in realizing two-dimensional digital filters.

  9. Solution of 3-dimensional diffusion equation by finite Fourier transformation

    International Nuclear Information System (INIS)

    Krishnani, P.D.

    1978-01-01

    Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

  10. Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure

    Science.gov (United States)

    Shawkey, Matthew D.; Saranathan, Vinodkumar; Pálsdóttir, Hildur; Crum, John; Ellisman, Mark H.; Auer, Manfred; Prum, Richard O.

    2009-01-01

    Organismal colour can be created by selective absorption of light by pigments or light scattering by photonic nanostructures. Photonic nanostructures may vary in refractive index over one, two or three dimensions and may be periodic over large spatial scales or amorphous with short-range order. Theoretical optical analysis of three-dimensional amorphous nanostructures has been challenging because these structures are difficult to describe accurately from conventional two-dimensional electron microscopy alone. Intermediate voltage electron microscopy (IVEM) with tomographic reconstruction adds three-dimensional data by using a high-power electron beam to penetrate and image sections of material sufficiently thick to contain a significant portion of the structure. Here, we use IVEM tomography to characterize a non-iridescent, three-dimensional biophotonic nanostructure: the spongy medullary layer from eastern bluebird Sialia sialis feather barbs. Tomography and three-dimensional Fourier analysis reveal that it is an amorphous, interconnected bicontinuous matrix that is appropriately ordered at local spatial scales in all three dimensions to coherently scatter light. The predicted reflectance spectra from the three-dimensional Fourier analysis are more precise than those predicted by previous two-dimensional Fourier analysis of transmission electron microscopy sections. These results highlight the usefulness, and obstacles, of tomography in the description and analysis of three-dimensional photonic structures. PMID:19158016

  11. On the Application of the Fourier Series Solution to the Hydromagnetic Buoyant Two-Dimensional Laminar Vertical Jet

    Directory of Open Access Journals (Sweden)

    Marco Rosales-Vera

    2012-01-01

    Full Text Available The problem of a hydromagnetic hot two-dimensional laminar jet issuing vertically into an otherwise quiescent fluid of a lower temperature is studied. We propose solutions to the boundary layer equations using the classical Fourier series. The method is essentiall to transform the boundary layer equations to a coupled set of nonlinear first-order ordinary differential equations through the Fourier series. The accuracy of the results has been tested by the comparison of the velocity distributions obtained by the Fourier series with those calculated by finite difference method. The results show that the present method, based on the Fourier series, is an efficient method, suitable to solve boundary layer equations applied to plane jet flows with high accuracy.

  12. Imaging through scattering media by Fourier filtering and single-pixel detection

    Science.gov (United States)

    Jauregui-Sánchez, Y.; Clemente, P.; Lancis, J.; Tajahuerce, E.

    2018-02-01

    We present a novel imaging system that combines the principles of Fourier spatial filtering and single-pixel imaging in order to recover images of an object hidden behind a turbid medium by transillumination. We compare the performance of our single-pixel imaging setup with that of a conventional system. We conclude that the introduction of Fourier gating improves the contrast of images in both cases. Furthermore, we show that the combination of single-pixel imaging and Fourier spatial filtering techniques is particularly well adapted to provide images of objects transmitted through scattering media.

  13. Measurement of Galactic Logarithmic Spiral Arm Pitch Angle Using Two-Dimensional Fast Fourier Transform Decomposition

    OpenAIRE

    Davis, Benjamin L.; Berrier, Joel C.; Shields, Douglas W.; Kennefick, Julia; Kennefick, Daniel; Seigar, Marc S.; Lacy, Claud H. S.; Puerari, Ivânio

    2012-01-01

    A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quanti...

  14. Two-dimensional Fourier analysis of the spongy medullary keratin of structurally coloured feather barbs

    Science.gov (United States)

    Prum, R. O.; Torres, R.; Williamson, S.; Dyck, J.

    1999-01-01

    We conducted two-dimensional (2D) discrete Fourier analyses of the spatial variation in refractive index of the spongy medullary keratin from four different colours of structurally coloured feather barbs from three species of bird: the rose-faced lovebird, Agapornis roseicollis (Psittacidae), the budgerigar, Melopsittacus undulatus (Psittacidae), and the Gouldian finch, Poephila guttata (Estrildidae). These results indicate that the spongy medullary keratin is a nanostructured tissue that functions as an array of coherent scatterers. The nanostructure of the medullary keratin is nearly uniform in all directions. The largest Fourier components of spatial variation in refractive index in the tissue are of the appropriate size to produce the observed colours by constructive interference alone. The peaks of the predicted reflectance spectra calculated from the 2D Fourier power spectra are congruent with the reflectance spectra measured by using microspectrophotometry. The alternative physical models for the production of these colours, the Rayleigh and Mie theories, hypothesize that medullary keratin is an incoherent array and that scattered waves are independent in phase. This assumption is falsified by the ring-like Fourier power spectra of these feathers, and the spacing of the scattering air vacuoles in the medullary keratin. Structural colours of avian feather barbs are produced by constructive interference of coherently scattered light waves from the optically heterogeneous matrix of keratin and air in the spongy medullary layer.

  15. Solution of the multigroup diffusion equation for two-dimensional triangular regions by finite Fourier transformation

    International Nuclear Information System (INIS)

    Takeshi, Y.; Keisuke, K.

    1983-01-01

    The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method

  16. A fast Gaussian filtering algorithm for three-dimensional surface roughness measurements

    International Nuclear Information System (INIS)

    Yuan, Y B; Piao, W Y; Xu, J B

    2007-01-01

    The two-dimensional (2-D) Gaussian filter can be separated into two one-dimensional (1-D) Gaussian filters. The 1-D Gaussian filter can be implemented approximately by the cascaded Butterworth filters. The approximation accuracy will be improved with the increase of the number of the cascaded filters. A recursive algorithm for Gaussian filtering requires a relatively small number of simple mathematical operations such as addition, subtraction, multiplication, or division, so that it has considerable computational efficiency and it is very useful for three-dimensional (3-D) surface roughness measurements. The zero-phase-filtering technique is used in this algorithm, so there is no phase distortion in the Gaussian filtered mean surface. High-order approximation Gaussian filters are proposed for practical use to assure high accuracy of Gaussian filtering of 3-D surface roughness measurements

  17. A fast Gaussian filtering algorithm for three-dimensional surface roughness measurements

    Science.gov (United States)

    Yuan, Y. B.; Piao, W. Y.; Xu, J. B.

    2007-07-01

    The two-dimensional (2-D) Gaussian filter can be separated into two one-dimensional (1-D) Gaussian filters. The 1-D Gaussian filter can be implemented approximately by the cascaded Butterworth filters. The approximation accuracy will be improved with the increase of the number of the cascaded filters. A recursive algorithm for Gaussian filtering requires a relatively small number of simple mathematical operations such as addition, subtraction, multiplication, or division, so that it has considerable computational efficiency and it is very useful for three-dimensional (3-D) surface roughness measurements. The zero-phase-filtering technique is used in this algorithm, so there is no phase distortion in the Gaussian filtered mean surface. High-order approximation Gaussian filters are proposed for practical use to assure high accuracy of Gaussian filtering of 3-D surface roughness measurements.

  18. Data-parallel tomographic reconstruction : A comparison of filtered backprojection and direct Fourier reconstruction

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.; Westenberg, M.A

    1998-01-01

    We consider the parallelization of two standard 2D reconstruction algorithms, filtered backprojection and direct Fourier reconstruction, using the data-parallel programming style. The algorithms are implemented on a Connection Machine CM-5 with 16 processors and a peak performance of 2 Gflop/s.

  19. Power filtering of nth order in the fractional Fourier domain

    International Nuclear Information System (INIS)

    Alieva, Tatiana; Calvo, Maria Luisa; Bastiaans, Martin J.

    2002-01-01

    The main properties of the power filtering operation in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of linear power filtering for solving the phase retrieval problem from intensity distributions only is proposed. The optical configuration for the experimental realization of the method is discussed. (author)

  20. Power filtering of n-th order in the fractional Fourier domain

    NARCIS (Netherlands)

    Alieva, T.; Calvo, M.L.; Bastiaans, M.J.

    2002-01-01

    The main properties of the power filtering operation in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of linear power filtering for solving the phase retrieval problem from only intensity distributions is proposed. The optical

  1. Two-dimensional restoration of single photon emission computed tomography images using the Kalman filter

    International Nuclear Information System (INIS)

    Boulfelfel, D.; Rangayyan, R.M.; Kuduvalli, G.R.; Hahn, L.J.; Kloiber, R.

    1994-01-01

    The discrete filtered backprojection (DFBP) algorithm used for the reconstruction of single photon emission computed tomography (SPECT) images affects image quality because of the operations of filtering and discretization. The discretization of the filtered backprojection process can cause the modulation transfer function (MTF) of the SPECT imaging system to be anisotropic and nonstationary, especially near the edges of the camera's field of view. The use of shift-invariant restoration techniques fails to restore large images because these techniques do not account for such variations in the MTF. This study presents the application of a two-dimensional (2-D) shift-variant Kalman filter for post-reconstruction restoration of SPECT slices. This filter was applied to SPECT images of a hollow cylinder phantom; a resolution phantom; and a large, truncated cone phantom containing two types of cold spots, a sphere, and a triangular prism. The images were acquired on an ADAC GENESYS camera. A comparison was performed between results obtained by the Kalman filter and those obtained by shift-invariant filters. Quantitative analysis of the restored images performed through measurement of root mean squared errors shows a considerable reduction in error of Kalman-filtered images over images restored using shift-invariant methods

  2. Filtros digitais por transformadas de Fourier aplicados em eletroquímica Digital filters based on Fourier transforms for application in electrochemistry

    Directory of Open Access Journals (Sweden)

    Ricardo Nantes Liang

    2013-01-01

    Full Text Available The electrochemical properties of micro and nano-electrodes are widely investigated due to their low faradaic and capacitive currents, leading to a new generation of smart and implantable devices. However, the current signals obtained in low-dimensional devices are strongly influenced by noise sources. In this paper, we show the evaluation of filters based on Fast Fourier Transform (FFT and their implementation in a graphical user interface (GUI in MATLAB®. As a case study, we evaluated an electrochemical reaction process of charge transfer via outer-sphere. Results showed successful removal of most of the noise in signals, thus proving a promising tool for low-scale measurement.

  3. Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

    Science.gov (United States)

    Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.

    2017-05-01

    The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

  4. A fully three-dimensional reconstruction algorithm with the nonstationary filter for improved single-orbit cone beam SPECT

    International Nuclear Information System (INIS)

    Cao, Z.J.; Tsui, B.M.

    1993-01-01

    Conventional single-orbit cone beam tomography presents special problems. They include incomplete sampling and inadequate three-dimensional (3D) reconstruction algorithm. The commonly used Feldkamp reconstruction algorithm simply extends the two-dimensional (2D) fan beam algorithm to 3D cone beam geometry. A truly 3D reconstruction formulation has been derived for the single-orbit cone beam SPECT based on the 3D Fourier slice theorem. In the formulation, a nonstationary filter which depends on the distance from the central plane of the cone beam was derived. The filter is applied to the 2D projection data in directions along and normal to the axis-of-rotation. The 3D reconstruction algorithm with the nonstationary filter was evaluated using both computer simulation and experimental measurements. Significant improvement in image quality was demonstrated in terms of decreased artifacts and distortions in cone beam reconstructed images. However, compared with the Feldkamp algorithm, a five-fold increase in processing time is required. Further improvement in image quality needs complete sampling in frequency space

  5. [Apply fourier transform infrared spectra coupled with two-dimensional correlation analysis to study the evolution of humic acids during composting].

    Science.gov (United States)

    Bu, Gui-jun; Yu, Jing; Di, Hui-hui; Luo, Shi-jia; Zhou, Da-zhai; Xiao, Qiang

    2015-02-01

    The composition and structure of humic acids formed during composting play an important influence on the quality and mature of compost. In order to explore the composition and evolution mechanism, municipal solid wastes were collected to compost and humic and fulvic acids were obtained from these composted municipal solid wastes. Furthermore, fourier transform infrared spectra and two-dimensional correlation analysis were applied to study the composition and transformation of humic and fulvic acids during composting. The results from fourier transform infrared spectra showed that, the composition of humic acids was complex, and several absorbance peaks were observed at 2917-2924, 2844-2852, 2549, 1662, 1622, 1566, 1454, 1398, 1351, 990-1063, 839 and 711 cm(-1). Compared to humic acids, the composition of fulvci acids was simple, and only three peaks were detected at 1725, 1637 and 990 cm(-1). The appearance of these peaks showed that both humic and fulvic acids comprised the benzene originated from lignin and the polysaccharide. In addition, humic acids comprised a large number of aliphatic and protein which were hardly detected in fulvic acids. Aliphatic, polysaccharide, protein and lignin all were degraded during composting, however, the order of degradation was different between humic and fulvci acids. The result from two-dimensional correlation analysis showed that, organic compounds in humic acids were degraded in the following sequence: aliphatic> protein> polysaccharide and lignin, while that in fulvic acids was as following: protein> polysaccharide and aliphatic. A large number of carboxyl, alcohols and ethers were formed during the degradation process, and the carboxyl was transformed into carbonates. It can be concluded that, fourier transform infrared spectra coupled with two-dimensional correlation analysis not only can analyze the function group composition of humic substances, but also can characterize effectively the degradation sequence of these

  6. Is Fourier analysis performed by the visual system or by the visual investigator.

    Science.gov (United States)

    Ochs, A L

    1979-01-01

    A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.

  7. Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

    Science.gov (United States)

    Moorthi, Shrinivas; Higgins, R. W.

    1993-01-01

    An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

  8. Crustal geomagnetic field - Two-dimensional intermediate-wavelength spatial power spectra

    Science.gov (United States)

    Mcleod, M. G.

    1983-01-01

    Two-dimensional Fourier spatial power spectra of equivalent magnetization values are presented for a region that includes a large portion of the western United States. The magnetization values were determined by inversion of POGO satellite data, assuming a magnetic crust 40 km thick, and were located on an 11 x 10 array with 300 km grid spacing. The spectra appear to be in good agreement with values of the crustal geomagnetic field spatial power spectra given by McLeod and Coleman (1980) and with the crustal field model given by Serson and Hannaford (1957). The spectra show evidence of noise at low frequencies in the direction along the satellite orbital track (N-S). indicating that for this particular data set additional filtering would probably be desirable. These findings illustrate the value of two-dimensional spatial power spectra both for describing the geomagnetic field statistically and as a guide for diagnosing possible noise sources.

  9. A proposal of Fourier-Bessel expansion with optimized ensembles of bases to analyse two dimensional image

    Science.gov (United States)

    Yamasaki, K.; Fujisawa, A.; Nagashima, Y.

    2017-09-01

    It is a critical issue to find the best set of fitting function bases in mode structural analysis of two dimensional images like plasma emission profiles. The paper proposes a method to optimize a set of the bases in the case of Fourier-Bessel function series, using their orthonormal property, for more efficient and precise analysis. The method is applied on a tomography image of plasma emission obtained with the Maximum-likelihood expectation maximization method in a linear cylindrical device. The result demonstrates the excellency of the method that realizes the smaller residual error and minimum Akaike information criterion using smaller number of fitting function bases.

  10. Two-dimensional FIR compaction filter design

    NARCIS (Netherlands)

    Vijayakumar, N.; Prabhu, K.M.M.

    2001-01-01

    The design of signal-adapted multirate filter banks has been an area of research interest. The authors present the design of a 2-D finite impulse response (FIR) compaction filter followed by a 2-D FIR filter bank that packs the maximum energy of the input process into a few subbands. The energy

  11. MEASUREMENT OF GALACTIC LOGARITHMIC SPIRAL ARM PITCH ANGLE USING TWO-DIMENSIONAL FAST FOURIER TRANSFORM DECOMPOSITION

    International Nuclear Information System (INIS)

    Davis, Benjamin L.; Berrier, Joel C.; Shields, Douglas W.; Kennefick, Julia; Kennefick, Daniel; Seigar, Marc S.; Lacy, Claud H. S.; Puerari, Ivânio

    2012-01-01

    A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.

  12. Measurement of Galactic Logarithmic Spiral Arm Pitch Angle Using Two-dimensional Fast Fourier Transform Decomposition

    Science.gov (United States)

    Davis, Benjamin L.; Berrier, Joel C.; Shields, Douglas W.; Kennefick, Julia; Kennefick, Daniel; Seigar, Marc S.; Lacy, Claud H. S.; Puerari, Ivânio

    2012-04-01

    A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.

  13. MEASUREMENT OF GALACTIC LOGARITHMIC SPIRAL ARM PITCH ANGLE USING TWO-DIMENSIONAL FAST FOURIER TRANSFORM DECOMPOSITION

    Energy Technology Data Exchange (ETDEWEB)

    Davis, Benjamin L.; Berrier, Joel C.; Shields, Douglas W.; Kennefick, Julia; Kennefick, Daniel; Seigar, Marc S.; Lacy, Claud H. S. [Arkansas Center for Space and Planetary Sciences, 202 Field House, University of Arkansas, Fayetteville, AR 72701 (United States); Puerari, Ivanio [Instituto Nacional de Astrofisica, Optica y Electronica, Calle Luis Enrique Erro 1, 72840 Santa Maria Tonantzintla, Puebla (Mexico)

    2012-04-01

    A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.

  14. Fourier analysis of parallel block-Jacobi splitting with transport synthetic acceleration in two-dimensional geometry

    International Nuclear Information System (INIS)

    Rosa, M.; Warsa, J. S.; Chang, J. H.

    2007-01-01

    A Fourier analysis is conducted in two-dimensional (2D) Cartesian geometry for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. The results for the un-accelerated algorithm show that convergence of PBJ can degrade, leading in particular to stagnation of GMRES(m) in problems containing optically thin sub-domains. The results for the accelerated algorithm indicate that TSA can be used to efficiently precondition an iterative method in the optically thin case when implemented in the 'modified' version MTSA, in which only the scattering in the low order equations is reduced by some non-negative factor β<1. (authors)

  15. Two-dimensional 220 MHz Fourier transform EPR imaging

    International Nuclear Information System (INIS)

    Placidi, Giuseppe; Brivati, John A.; Alecci, Marcello; Testa, Luca; Sotgiu, Antonello

    1998-01-01

    In the last decade radiofrequency continuous-wave EPR spectrometers have been developed to detect and localize free radicals in vivo. Only recently, pulsed radiofrequency EPR spectrometers have been described for imaging applications with small samples. In the present work, we show the first two-dimensional image obtained at 220 MHz on a large phantom (40 ml) that simulates typical conditions of in vivo EPR imaging. This pulsed EPR apparatus has the potential to make the time required for three-dimensional imaging compatible with the biological half-life of normally used paramagnetic probes. (author)

  16. Utilização de filtro de transformada de fourier para a minimização de ruídos em sinais analíticos Utilization of fourier transform filter for noise minimization in analytical signals

    Directory of Open Access Journals (Sweden)

    Eduardo O. Cerqueira

    2000-10-01

    Full Text Available Instrumental data always present some noise. The analytical data information and instrumental noise generally has different frequencies. Thus is possible to remove the noise using a digital filter based on Fourier transform and inverse Fourier transform. This procedure enhance the signal/noise ratio and consecutively increase the detection limits on instrumental analysis. The basic principle of Fourier transform filter with modifications implemented to improve its performance is presented. A numerical example, as well as a real voltammetric example are showed to demonstrate the Fourier transform filter implementation. The programs to perform the Fourier transform filter, in Matlab and Visual Basic languages, are included as appendices

  17. Analysis of moiré fringes by Wiener filtering: An extension to the Fourier method

    International Nuclear Information System (INIS)

    Harasse, Sébastien; Yashiro, Wataru; Momose, Atsushi

    2012-01-01

    In X-ray Talbot interferometry, tilting the phase grating with respect to the absorption grating results in the formation of spatial fringes. The analysis of this moiré pattern, classically performed by the Fourier method, allows the extraction of the sample phase shift information from a single image. In this context, an extension to the Fourier method is proposed. The filter used to extract the fringe information is chosen optimally in the least-squares sense, given models for the zeroth and first order modes, noise and the modulation transfer function. The latter is obtained by measuring the detector response to moiré fringes with increasing frequencies. The obtained Wiener filter allows a better reconstruction of the phase information at all fringe frequencies, compared to the usual box or gaussian filters. This is demonstrated quantitatively by experiments using synchrotron radiation.

  18. Two-Dimensional Planar Lightwave Circuit Integrated Spatial Filter Array and Method of Use Thereof

    Science.gov (United States)

    Ai, Jun (Inventor); Dimov, Fedor (Inventor)

    2015-01-01

    A large coherent two-dimensional (2D) spatial filter array (SFA), 30 by 30 or larger, is produced by coupling a 2D planar lightwave circuit (PLC) array with a pair of lenslet arrays at the input and output side. The 2D PLC array is produced by stacking a plurality of chips, each chip with a plural number of straight PLC waveguides. A pupil array is coated onto the focal plane of the lenslet array. The PLC waveguides are produced by deposition of a plural number of silica layers on the silicon wafer, followed by photolithography and reactive ion etching (RIE) processes. A plural number of mode filters are included in the silica-on-silicon waveguide such that the PLC waveguide is transparent to the fundamental mode but higher order modes are attenuated by 40 dB or more.

  19. Experimental demonstration of an OFDM receiver based on a silicon-nanophot onic discrete Fourier transform filter

    DEFF Research Database (Denmark)

    Da Ros, Francesco; Nolle, Markus; Meuer, C.

    2014-01-01

    We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit.......We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit....

  20. High-resolution and high-throughput multichannel Fourier transform spectrometer with two-dimensional interferogram warping compensation

    Science.gov (United States)

    Watanabe, A.; Furukawa, H.

    2018-04-01

    The resolution of multichannel Fourier transform (McFT) spectroscopy is insufficient for many applications despite its extreme advantage of high throughput. We propose an improved configuration to realise both performance using a two-dimensional area sensor. For the spectral resolution, we obtained the interferogram of a larger optical path difference by shifting the area sensor without altering any optical components. The non-linear phase error of the interferometer was successfully corrected using a phase-compensation calculation. Warping compensation was also applied to realise a higher throughput to accumulate the signal between vertical pixels. Our approach significantly improved the resolution and signal-to-noise ratio by factors of 1.7 and 34, respectively. This high-resolution and high-sensitivity McFT spectrometer will be useful for detecting weak light signals such as those in non-invasive diagnosis.

  1. A bias-tunable electron-spin filter based on a two-dimensional electron gas modulated by ferromagnetic-Schottky metal stripes

    Energy Technology Data Exchange (ETDEWEB)

    Lu Jianduo, E-mail: l_j316@163.co [Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081 (China); Li Yunbao; Yun Meijuan [Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081 (China); Zheng Wei [Key Laboratory of Dynamic Geodesy, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077 (China)

    2011-03-28

    We investigate the effect of the bias in an electron-spin filter based on a two-dimensional electron gas modulated by ferromagnetic-Schottky metal stripes. The numerical results show that the electron transmission and the conductance as well as the spin polarization are strongly dependent on the bias applied to the device. - Research highlights: We propose a bias-tunable electron-spin filter. The transmission and the conductance depend on the bias and the electron energy. The spin polarization depends on the bias and the electron energy. The results are helpful for making new types of bias-tunable spin filters.

  2. Three-dimensional reconstruction from cone-beam data using an efficient Fourier technique combined with a special interpolation filter

    International Nuclear Information System (INIS)

    Magnusson Seger, Maria

    1998-01-01

    We here present LINCON FAST which is an exact method for 3D reconstruction from cone-beam projection data. The new method is compared to the LINCON method which is known to be fast and to give good image quality. Both methods have O(N 3 log N) complexity and are based on Grangeat's result which states that the derivative of the Radon transform of the object function can be obtained from cone-beam projections. One disadvantage with LINCON is that the rather computationally intensive chirp z-transform is frequently used. In LINCON FAST , FFT and interpolation in the Fourier domain are used instead, which are less computationally demanding. The computation tools involved in LINCON FAST are solely FFT, 1D eight-point interpolation, multiplicative weighting and tri-linear interpolation. We estimate that LINCON FAST will be 2-2.5 times faster than LINCON. The interpolation filter belongs to a special class of filters developed by us. It turns out that the filter must be very carefully designed to keep a good image quality. Visual inspection of experimental results shows that the image quality is almost the same for LINCON and the new method LINCON FAST . However, it should be remembered that LINCON FAST can never give better image quality than LINCON, since LINCON FAST is designed to approximate LINCON as well as possible. (author)

  3. Blended particle filters for large-dimensional chaotic dynamical systems

    Science.gov (United States)

    Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

    2014-01-01

    A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

  4. Deconvolution of Doppler-broadened positron annihilation lineshapes by fast Fourier transformation using a simple automatic filtering technique

    International Nuclear Information System (INIS)

    Britton, D.T.; Bentvelsen, P.; Vries, J. de; Veen, A. van

    1988-01-01

    A deconvolution scheme for digital lineshapes using fast Fourier transforms and a filter based on background subtraction in Fourier space has been developed. In tests on synthetic data this has been shown to give optimum deconvolution without prior inspection of the Fourier spectrum. Although offering significant improvements on the raw data, deconvolution is shown to be limited. The contribution of the resolution function is substantially reduced but not eliminated completely and unphysical oscillations are introduced into the lineshape. The method is further tested on measurements of the lineshape for positron annihilation in single crystal copper at the relatively poor resolution of 1.7 keV at 512 keV. A two-component fit is possible yielding component widths in agreement with previous measurements. (orig.)

  5. Digital, realizable Wiener filtering in two-dimensions

    International Nuclear Information System (INIS)

    Ekstrom, M.P.

    1979-01-01

    The extension of Wiener's classical mean-square filtering theory to the estimation of two-dimensional (2-D), discrete random fields is discussed. In analogy with the 1-D case, the optimal realizable filter is derived by solution of a 2-D discrete Wiener--Hopf equation using a spectral factorization procedure. Computational algorithms for performing the required calculations are discussed. 3 figures

  6. Dual curved photonic crystal ring resonator based channel drop filter using two-dimensional photonic crystal structure

    Energy Technology Data Exchange (ETDEWEB)

    Chhipa, Mayur Kumar, E-mail: mayurchhipa1@gmail.com [Deptt. of Electronics and Communication Engineering, Government Engineering College Ajmer Rajasthan INDIA (India); Dusad, Lalit Kumar [Rajasthan Technical University Kota, Rajasthan (India)

    2016-05-06

    In this paper channel drop filter (CDF) is designed using dual curved photonic crystal ring resonator (PCRR). The photonic band gap (PBG) is calculated by plane wave expansion (PWE) method and the photonic crystal (PhC) based on two dimensional (2D) square lattice periodic arrays of silicon (Si) rods in air structure have been investigated using finite difference time domain (FDTD) method. The number of rods in Z and X directions is 21 and 20 respectively with lattice constant 0.540 nm and rod radius r = 0.1 µm. The channel drop filter has been optimized for telecommunication wavelengths λ = 1.591 µm with refractive indices 3.533. In the designed structure further analysis is also done by changing whole rods refractive index and it has been observed that this filter may be used for filtering several other channels also. The designed structure is useful for CWDM systems. This device may serve as a key component in photonic integrated circuits. The device is ultra compact with the overall size around 123 µm{sup 2}.

  7. A Novel Medical Image Watermarking in Three-dimensional Fourier Compressed Domain

    Directory of Open Access Journals (Sweden)

    Baoru Han

    2015-09-01

    Full Text Available Digital watermarking is a research hotspot in the field of image security, which is protected digital image copyright. In order to ensure medical image information security, a novel medical image digital watermarking algorithm in three-dimensional Fourier compressed domain is proposed. The novel medical image digital watermarking algorithm takes advantage of three-dimensional Fourier compressed domain characteristics, Legendre chaotic neural network encryption features and robust characteristics of differences hashing, which is a robust zero-watermarking algorithm. On one hand, the original watermarking image is encrypted in order to enhance security. It makes use of Legendre chaotic neural network implementation. On the other hand, the construction of zero-watermarking adopts differences hashing in three-dimensional Fourier compressed domain. The novel watermarking algorithm does not need to select a region of interest, can solve the problem of medical image content affected. The specific implementation of the algorithm and the experimental results are given in the paper. The simulation results testify that the novel algorithm possesses a desirable robustness to common attack and geometric attack.

  8. Fourier transform and its application to 1D and 2D NMR

    International Nuclear Information System (INIS)

    Canet, D.

    1988-01-01

    In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr

  9. Selection of unstable patterns and control of optical turbulence by Fourier plane filtering

    DEFF Research Database (Denmark)

    Mamaev, A.V.; Saffman, M.

    1998-01-01

    We report on selection and stabilization of transverse optical patterns in a feedback mirror experiment. Amplitude filtering in the Fourier plane is used to select otherwise unstable spatial patterns. Optical turbulence observed for nonlinearities far above the pattern formation threshold...

  10. Distributed Kalman filtering compared to Fourier domain preconditioned conjugate gradient for laser guide star tomography on extremely large telescopes.

    Science.gov (United States)

    Gilles, Luc; Massioni, Paolo; Kulcsár, Caroline; Raynaud, Henri-François; Ellerbroek, Brent

    2013-05-01

    This paper discusses the performance and cost of two computationally efficient Fourier-based tomographic wavefront reconstruction algorithms for wide-field laser guide star (LGS) adaptive optics (AO). The first algorithm is the iterative Fourier domain preconditioned conjugate gradient (FDPCG) algorithm developed by Yang et al. [Appl. Opt.45, 5281 (2006)], combined with pseudo-open-loop control (POLC). FDPCG's computational cost is proportional to N log(N), where N denotes the dimensionality of the tomography problem. The second algorithm is the distributed Kalman filter (DKF) developed by Massioni et al. [J. Opt. Soc. Am. A28, 2298 (2011)], which is a noniterative spatially invariant controller. When implemented in the Fourier domain, DKF's cost is also proportional to N log(N). Both algorithms are capable of estimating spatial frequency components of the residual phase beyond the wavefront sensor (WFS) cutoff frequency thanks to regularization, thereby reducing WFS spatial aliasing at the expense of more computations. We present performance and cost analyses for the LGS multiconjugate AO system under design for the Thirty Meter Telescope, as well as DKF's sensitivity to uncertainties in wind profile prior information. We found that, provided the wind profile is known to better than 10% wind speed accuracy and 20 deg wind direction accuracy, DKF, despite its spatial invariance assumptions, delivers a significantly reduced wavefront error compared to the static FDPCG minimum variance estimator combined with POLC. Due to its nonsequential nature and high degree of parallelism, DKF is particularly well suited for real-time implementation on inexpensive off-the-shelf graphics processing units.

  11. Solution of the two-dimensional spectral factorization problem

    Science.gov (United States)

    Lawton, W. M.

    1985-01-01

    An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.

  12. Hiding objects and creating illusions above a carpet filter using a Fourier optics approach.

    Science.gov (United States)

    Wu, Kedi; Wang, Guo Ping

    2010-09-13

    Invisibility carpet cloaks are usually used to hide an object beneath carpet. In this paper we propose and demonstrate a carpet filter to hide objects and create illusions above the filter by using a Fourier optics method. Instead of using transformation optics, we get electromagnetic parameters of the filter by optical transfer functions, which play the role of modulating the propagation of the scattering angular spectrum directly from an object above the filter. By further adding a functional layer onto the filter, we can even camouflage the object so that it appears to be a different object. The analytical results are confirmed by numerical simulations. Our method is completely different from the current coordinate transfer method and may provide another point of view to more clearly understand the mechanism of invisibility cloaks.

  13. Spherical harmonics solutions of multi-dimensional neutron transport equation by finite Fourier transformation

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke

    1977-01-01

    A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)

  14. Rotor-System Log-Decrement Identification Using Short-Time Fourier-Transform Filter

    OpenAIRE

    Li, Qihang; Wang, Weimin; Chen, Lifang; Sun, Dan

    2015-01-01

    With the increase of the centrifugal compressor capability, such as large scale LNG and CO2 reinjection, the stability margin evaluation is crucial to assure the compressor work in the designed operating conditions in field. Improving the precision of parameter identification of stability is essential and necessary as well. Based on the time-varying characteristics of response vibration during the sine-swept process, a short-time Fourier transform (STFT) filter was introduced to increase the ...

  15. Fourier-based magnetic induction tomography for mapping resistivity

    International Nuclear Information System (INIS)

    Puwal, Steffan; Roth, Bradley J.

    2011-01-01

    Magnetic induction tomography is used as an experimental tool for mapping the passive electromagnetic properties of conductors, with the potential for imaging biological tissues. Our numerical approach to solving the inverse problem is to obtain a Fourier expansion of the resistivity and the stream functions of the magnetic fields and eddy current density. Thus, we are able to solve the inverse problem of determining the resistivity from the applied and measured magnetic fields for a two-dimensional conducting plane. When we add noise to the measured magnetic field, we find the fidelity of the measured to the true resistivity is quite robust for increasing levels of noise and increasing distances of the applied and measured field coils from the conducting plane, when properly filtered. We conclude that Fourier methods provide a reliable alternative for solving the inverse problem.

  16. Estimation of three-dimensional radar tracking using modified extended kalman filter

    Science.gov (United States)

    Aditya, Prima; Apriliani, Erna; Khusnul Arif, Didik; Baihaqi, Komar

    2018-03-01

    Kalman filter is an estimation method by combining data and mathematical models then developed be extended Kalman filter to handle nonlinear systems. Three-dimensional radar tracking is one of example of nonlinear system. In this paper developed a modification method of extended Kalman filter from the direct decline of the three-dimensional radar tracking case. The development of this filter algorithm can solve the three-dimensional radar measurements in the case proposed in this case the target measured by radar with distance r, azimuth angle θ, and the elevation angle ϕ. Artificial covariance and mean adjusted directly on the three-dimensional radar system. Simulations result show that the proposed formulation is effective in the calculation of nonlinear measurement compared with extended Kalman filter with the value error at 0.77% until 1.15%.

  17. Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

    Science.gov (United States)

    Liang, Zhichun; Crepeau, Richard H; Freed, Jack H

    2005-12-01

    Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

  18. Infrared maritime target detection using the high order statistic filtering in fractional Fourier domain

    Science.gov (United States)

    Zhou, Anran; Xie, Weixin; Pei, Jihong

    2018-06-01

    Accurate detection of maritime targets in infrared imagery under various sea clutter conditions is always a challenging task. The fractional Fourier transform (FRFT) is the extension of the Fourier transform in the fractional order, and has richer spatial-frequency information. By combining it with the high order statistic filtering, a new ship detection method is proposed. First, the proper range of angle parameter is determined to make it easier for the ship components and background to be separated. Second, a new high order statistic curve (HOSC) at each fractional frequency point is designed. It is proved that maximal peak interval in HOSC reflects the target information, while the points outside the interval reflect the background. And the value of HOSC relative to the ship is much bigger than that to the sea clutter. Then, search the curve's maximal target peak interval and extract the interval by bandpass filtering in fractional Fourier domain. The value outside the peak interval of HOSC decreases rapidly to 0, so the background is effectively suppressed. Finally, the detection result is obtained by the double threshold segmenting and the target region selection method. The results show the proposed method is excellent for maritime targets detection with high clutters.

  19. App. 1. Fourier series and Fourier transform

    International Nuclear Information System (INIS)

    Anon.

    1977-01-01

    Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr

  20. Two-dimensional signal processing using a morphological filter for holographic memory

    Science.gov (United States)

    Kondo, Yo; Shigaki, Yusuke; Yamamoto, Manabu

    2012-03-01

    Today, along with the wider use of high-speed information networks and multimedia, it is increasingly necessary to have higher-density and higher-transfer-rate storage devices. Therefore, research and development into holographic memories with three-dimensional storage areas is being carried out to realize next-generation large-capacity memories. However, in holographic memories, interference between bits, which affect the detection characteristics, occurs as a result of aberrations such as the deviation of a wavefront in an optical system. In this study, we pay particular attention to the nonlinear factors that cause bit errors, where filters with a Volterra equalizer and the morphologies are investigated as a means of signal processing.

  1. Fourier two-level analysis for higher dimensional discontinuous Galerkin discretisation

    NARCIS (Netherlands)

    P.W. Hemker (Piet); M.H. van Raalte (Marc)

    2002-01-01

    textabstractIn this paper we study the convergence of a multigrid method for the solution of a two-dimensional linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods. For the Baumann-Oden and for the symmetric DG method, we give a detailed analysis of the

  2. Multi-dimensional medical images compressed and filtered with wavelets

    International Nuclear Information System (INIS)

    Boyen, H.; Reeth, F. van; Flerackers, E.

    2002-01-01

    Full text: Using the standard wavelet decomposition methods, multi-dimensional medical images can be compressed and filtered by repeating the wavelet-algorithm on 1D-signals in an extra loop per extra dimension. In the non-standard decomposition for multi-dimensional images the areas that must be zero-filled in case of band- or notch-filters are more complex than geometric areas such as rectangles or cubes. Adding an additional dimension in this algorithm until 4D (e.g. a 3D beating heart) increases the geometric complexity of those areas even more. The aim of our study was to calculate the boundaries of the formed complex geometric areas, so we can use the faster non-standard decomposition to compress and filter multi-dimensional medical images. Because a lot of 3D medical images taken by PET- or SPECT-cameras have only a few layers in the Z-dimension and compressing images in a dimension with a few voxels is usually not worthwhile, we provided a solution in which one can choose which dimensions will be compressed or filtered. With the proposal of non-standard decomposition on Daubechies' wavelets D2 to D20 by Steven Gollmer in 1992, 1D data can be compressed and filtered. Each additional level works only on the smoothed data, so the transformation-time halves per extra level. Zero-filling a well-defined area alter the wavelet-transform and then performing the inverse transform will do the filtering. To be capable to compress and filter up to 4D-Images with the faster non-standard wavelet decomposition method, we have investigated a new method for calculating the boundaries of the areas which must be zero-filled in case of filtering. This is especially true for band- and notch filtering. Contrary to the standard decomposition method, the areas are no longer rectangles in 2D or cubes in 3D or a row of cubes in 4D: they are rectangles expanded with a half-sized rectangle in the other direction for 2D, cubes expanded with half cubes in one and quarter cubes in the

  3. Fast Fourier single-pixel imaging via binary illumination.

    Science.gov (United States)

    Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang

    2017-09-20

    Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.

  4. Discrimination of different red wine by Fourier-transform infrared and two-dimensional infrared correlation spectroscopy

    Science.gov (United States)

    Zhang, Yan-ling; Chen, Jian-bo; Lei, Yu; Zhou, Qun; Sun, Su-qin; Noda, Isao

    2010-06-01

    Fourier-transform infrared spectroscopy (FT-IR) and two-dimensional infrared (2D IR) correlation spectroscopy were applied to analyze main components of liquid red wine with different sugar contents and volatilization residues of dry red wine from different manufactures. The infrared spectra, second derivative spectra of dry red wine show the typical peaks of alcohol, while the spectra of sweet wine are composed of the peaks of both alcohol and sugar, and the contribution of sugar enhanced as the increase of sugar content. Using principal component analysis (PCA) method, dry and sweet wine can be readily classified. Analysis of the infrared spectra of the volatilization residues of dry red wine samples from five different manufactures indicates that dry red wine may be composed of glycerol, carboxylic acids or esters and carboxyl ate, at the same time, different dry red wine show different characteristic peaks in the second derivative spectra and 2D IR correlation spectra, which can be used to discriminate the different manufactures and evaluate the quality of wine samples. The results suggested that infrared spectroscopy is a direct and effective method for the analysis of principle components of different red wines and discrimination of different red wines.

  5. Rotor-System Log-Decrement Identification Using Short-Time Fourier-Transform Filter

    Directory of Open Access Journals (Sweden)

    Qihang Li

    2015-01-01

    Full Text Available With the increase of the centrifugal compressor capability, such as large scale LNG and CO2 reinjection, the stability margin evaluation is crucial to assure the compressor work in the designed operating conditions in field. Improving the precision of parameter identification of stability is essential and necessary as well. Based on the time-varying characteristics of response vibration during the sine-swept process, a short-time Fourier transform (STFT filter was introduced to increase the signal-noise ratio and improve the accuracy of the estimated stability parameters. A finite element model was established to simulate the sine-swept process, and the simulated vibration signals were used to study the filtering effect and demonstrate the feasibility to identify the stability parameters by using Multiple-Input and Multiple-Output system identification method that combines the prediction error method and instrumental variable method. Simulation results show that the identification method with STFT filter improves the estimated accuracy much well and makes the curves of frequency response function clearer. Experiment was carried out on a test rig as well, which indicates the identification method is feasible in stability identification, and the results of experiment indicate that STFT filter works very well.

  6. Automated Processing of Two-Dimensional Correlation Spectra

    Science.gov (United States)

    Sengstschmid; Sterk; Freeman

    1998-04-01

    An automated scheme is described which locates the centers of cross peaks in two-dimensional correlation spectra, even under conditions of severe overlap. Double-quantum-filtered correlation (DQ-COSY) spectra have been investigated, but the method is also applicable to TOCSY and NOESY spectra. The search criterion is the intrinsic symmetry (or antisymmetry) of cross-peak multiplets. An initial global search provides the preliminary information to build up a two-dimensional "chemical shift grid." All genuine cross peaks must be centered at intersections of this grid, a fact that reduces the extent of the subsequent search program enormously. The program recognizes cross peaks by examining the symmetry of signals in a test zone centered at a grid intersection. This "symmetry filter" employs a "lowest value algorithm" to discriminate against overlapping responses from adjacent multiplets. A progressive multiplet subtraction scheme provides further suppression of overlap effects. The processed two-dimensional correlation spectrum represents cross peaks as points at the chemical shift coordinates, with some indication of their relative intensities. Alternatively, the information is presented in the form of a correlation table. The authenticity of a given cross peak is judged by a set of "confidence criteria" expressed as numerical parameters. Experimental results are presented for the 400-MHz double-quantum-filtered COSY spectrum of 4-androsten-3,17-dione, a case where there is severe overlap. Copyright 1998 Academic Press.

  7. Mathematical principles of signal processing Fourier and wavelet analysis

    CERN Document Server

    Brémaud, Pierre

    2002-01-01

    Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...

  8. Post-processing of EPR spectrum from dosimetric substances through filtering of Discrete Fourier Transform

    International Nuclear Information System (INIS)

    Vieira, Fabio P.B.; Bevilacqua, Joyce S.

    2014-01-01

    The use of electron paramagnetic resonance spectrometers - EPR - in radiation dosimetry is known for more than four decades. It is an important tool in the retrospective determination of doses absorbed. To estimate the dose absorbed by the sample, it is necessary to know the amplitude of the peak to peak signature of the substance in its EPR spectrum. This information can be compromised by the presence of spurious information: noise - of random and low intensity nature; and the behavior of the baseline - coming from the coupling between the resonator tube and the sample analyzed. Due to the intrinsic characteristics of the three main components of the signal, i.e. signature, noise, and baseline - the analysis in the frequency domain allows, through post-processing techniques to filter spurious information. In this work, an algorithm that retrieves the signature of a substance has been implemented. The Discrete Fourier Transform is applied to the signal and without user intervention, the noise is filtered. From the filtered signal, recovers the signature by Inverse Discrete Fourier Transform. The peak to peak amplitude, and the absorbed dose is calculated with an error of less than 1% for signals wherein the base line is linearized. Some more general cases are under investigation and with little user intervention, you can get the same error

  9. FPGA Implementation of one-dimensional and two-dimensional cellular automata

    International Nuclear Information System (INIS)

    D'Antone, I.

    1999-01-01

    This report describes the hardware implementation of one-dimensional and two-dimensional cellular automata (CAs). After a general introduction to the cellular automata, we consider a one-dimensional CA used to implement pseudo-random techniques in built-in self test for VLSI. Due to the increase in digital ASIC complexity, testing is becoming one of the major costs in the VLSI production. The high electronics complexity, used in particle physics experiments, demands higher reliability than in the past time. General criterions are given to evaluate the feasibility of the circuit used for testing and some quantitative parameters are underlined to optimize the architecture of the cellular automaton. Furthermore, we propose a two-dimensional CA that performs a peak finding algorithm in a matrix of cells mapping a sub-region of a calorimeter. As in a two-dimensional filtering process, the peaks of the energy clusters are found in one evolution step. This CA belongs to Wolfram class II cellular automata. Some quantitative parameters are given to optimize the architecture of the cellular automaton implemented in a commercial field programmable gate array (FPGA)

  10. Two-dimensional modelling of internal arc effects in an enclosed MV cell provided with a protection porous filter

    International Nuclear Information System (INIS)

    Rochette, D; Clain, S; Andre, P; Bussiere, W; Gentils, F

    2007-01-01

    Medium voltage (MV) cells have to respect standards (for example IEC ones (IEC TC 17C 2003 IEC 62271-200 High Voltage Switchgear and Controlgear-Part 200 1st edn)) that define security levels against internal arc faults such as an accidental electrical arc occurring in the apparatus. New protection filters based on porous materials are developed to provide better energy absorption properties and a higher protection level for people. To study the filter behaviour during a major electrical accident, a two-dimensional model is proposed. The main point is the use of a dedicated numerical scheme for a non-conservative hyperbolic problem. We present a numerical simulation of the process during the first 0.2 s when the safety valve bursts and we compare the numerical results with tests carried out in a high power test laboratory on real electrical apparatus

  11. Two-dimensional modelling of internal arc effects in an enclosed MV cell provided with a protection porous filter

    Science.gov (United States)

    Rochette, D.; Clain, S.; André, P.; Bussière, W.; Gentils, F.

    2007-05-01

    Medium voltage (MV) cells have to respect standards (for example IEC ones (IEC TC 17C 2003 IEC 62271-200 High Voltage Switchgear and Controlgear—Part 200 1st edn)) that define security levels against internal arc faults such as an accidental electrical arc occurring in the apparatus. New protection filters based on porous materials are developed to provide better energy absorption properties and a higher protection level for people. To study the filter behaviour during a major electrical accident, a two-dimensional model is proposed. The main point is the use of a dedicated numerical scheme for a non-conservative hyperbolic problem. We present a numerical simulation of the process during the first 0.2 s when the safety valve bursts and we compare the numerical results with tests carried out in a high power test laboratory on real electrical apparatus.

  12. Two-dimensional modelling of internal arc effects in an enclosed MV cell provided with a protection porous filter

    Energy Technology Data Exchange (ETDEWEB)

    Rochette, D [Laboratoire Arc Electrique et Plasmas Thermiques, CNRS UMR 6069, Universite Blaise Pascal, IUT de Montlucon, Avenue Aristide Briand, BP 2235, 03101 Montlucon Cedex (France); Clain, S [Laboratoire de Mathematiques pour l' Industrie et la Physique, CNRS UMR 5640, Universite Paul Sabatier Toulouse 3, 118 route de Narbonne, 31062 Toulouse Cedex 4 (France); Andre, P [Laboratoire Arc Electrique et Plasmas Thermiques, CNRS UMR 6069, Universite Blaise Pascal, IUT de Montlucon, Avenue Aristide Briand, BP 2235, 03101 Montlucon Cedex (France); Bussiere, W [Laboratoire Arc Electrique et Plasmas Thermiques, CNRS UMR 6069, Universite Blaise Pascal, IUT de Montlucon, Avenue Aristide Briand, BP 2235, 03101 Montlucon Cedex (France); Gentils, F [Schneider Electric-Science and Technology Division-Research Center A2, 38050 Grenoble Cedex 9 (France)

    2007-05-21

    Medium voltage (MV) cells have to respect standards (for example IEC ones (IEC TC 17C 2003 IEC 62271-200 High Voltage Switchgear and Controlgear-Part 200 1st edn)) that define security levels against internal arc faults such as an accidental electrical arc occurring in the apparatus. New protection filters based on porous materials are developed to provide better energy absorption properties and a higher protection level for people. To study the filter behaviour during a major electrical accident, a two-dimensional model is proposed. The main point is the use of a dedicated numerical scheme for a non-conservative hyperbolic problem. We present a numerical simulation of the process during the first 0.2 s when the safety valve bursts and we compare the numerical results with tests carried out in a high power test laboratory on real electrical apparatus.

  13. Orthonormal mode sets for the two-dimensional fractional Fourier transformation

    NARCIS (Netherlands)

    Alieva, T.; Bastiaans, M.J.

    2007-01-01

    A family of orthonormal mode sets arises when Hermite–Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an

  14. Three-dimensional imaging using computer-generated holograms synthesized from 3-D Fourier spectra

    International Nuclear Information System (INIS)

    Yatagai, Toyohiko; Miura, Ken-ichi; Sando, Yusuke; Itoh, Masahide

    2008-01-01

    Computer-generated holograms(CGHs) synthesized from projection images of real existing objects are considered. A series of projection images are recorded both vertically and horizontally with an incoherent light source and a color CCD. According to the principles of computer tomography(CT), the 3-D Fourier spectrum is calculated from several projection images of objects and the Fresnel CGH is synthesized using a part of the 3-D Fourier spectrum. This method has following advantages. At first, no-blur reconstructed images in any direction are obtained owing to two-dimensionally scanning in recording. Secondarily, since not interference fringes but simple projection images of objects are recorded, a coherent light source is not necessary. Moreover, when a color CCD is used in recording, it is easily possible to record and reconstruct colorful objects. Finally, we demonstrate reconstruction of biological objects.

  15. Three-dimensional imaging using computer-generated holograms synthesized from 3-D Fourier spectra

    Energy Technology Data Exchange (ETDEWEB)

    Yatagai, Toyohiko; Miura, Ken-ichi; Sando, Yusuke; Itoh, Masahide [University of Tsukba, Institute of Applied Physics, Tennoudai 1-1-1, Tsukuba, Ibaraki 305-8571 (Japan)], E-mail: yatagai@cc.utsunomiya-u.ac.jp

    2008-11-01

    Computer-generated holograms(CGHs) synthesized from projection images of real existing objects are considered. A series of projection images are recorded both vertically and horizontally with an incoherent light source and a color CCD. According to the principles of computer tomography(CT), the 3-D Fourier spectrum is calculated from several projection images of objects and the Fresnel CGH is synthesized using a part of the 3-D Fourier spectrum. This method has following advantages. At first, no-blur reconstructed images in any direction are obtained owing to two-dimensionally scanning in recording. Secondarily, since not interference fringes but simple projection images of objects are recorded, a coherent light source is not necessary. Moreover, when a color CCD is used in recording, it is easily possible to record and reconstruct colorful objects. Finally, we demonstrate reconstruction of biological objects.

  16. Wave field restoration using three-dimensional Fourier filtering method.

    Science.gov (United States)

    Kawasaki, T; Takai, Y; Ikuta, T; Shimizu, R

    2001-11-01

    A wave field restoration method in transmission electron microscopy (TEM) was mathematically derived based on a three-dimensional (3D) image formation theory. Wave field restoration using this method together with spherical aberration correction was experimentally confirmed in through-focus images of amorphous tungsten thin film, and the resolution of the reconstructed phase image was successfully improved from the Scherzer resolution limit to the information limit. In an application of this method to a crystalline sample, the surface structure of Au(110) was observed in a profile-imaging mode. The processed phase image showed quantitatively the atomic relaxation of the topmost layer.

  17. Two dimensional nonlinear spectral estimation techniques for breast cancer localization

    International Nuclear Information System (INIS)

    Stathaki, P.T.; Constantinides, A.G.

    1994-01-01

    In this paper the problem of image texture analysis in the presence of noise is examined from a higher-order statistical perspective. The approach taken involves the use of two dimensional second order Volterra filters where the filter weights are derived from third order cumulants of the two dimensional signal. The specific application contained in this contribution is in mammography, an area in which it is difficult to discern the appropriate features. The paper describes the fundamental issues of the various components of the approach. The results of the entire texture modelling, classification and segmentation scheme contained in this paper are very encouraging

  18. Study on Angelica and its different extracts by Fourier transform infrared spectroscopy and two-dimensional correlation IR spectroscopy

    Science.gov (United States)

    Liu, Hong-xia; Sun, Su-qin; Lv, Guang-hua; Chan, Kelvin K. C.

    2006-05-01

    In order to develop a rapid and effective analysis method for studying integrally the main constituents in the medicinal materials and their extracts, discriminating the extracts from different extraction process, comparing the categories of chemical constituents in the different extracts and monitoring the qualities of medicinal materials, we applied Fourier transform infrared spectroscopy (FT-IR) associated with second derivative infrared spectroscopy and two-dimensional correlation infrared spectroscopy (2D-IR) to study the main constituents in traditional Chinese medicine Angelica and its different extracts (extracted by petroleum ether, ethanol and water in turn). The findings indicated that FT-IR spectrum can provide many holistic variation rules of chemical constituents. Use of the macroscopical fingerprint characters of FT-IR and 2D-IR spectrum can not only identify the main chemical constituents in medicinal materials and their different extracts, but also compare the components differences among the similar samples. This analytical method is highly rapid, effective, visual and accurate for pharmaceutical research.

  19. Tunable fractional-order Fourier transformer

    International Nuclear Information System (INIS)

    Malyutin, A A

    2006-01-01

    A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

  20. Anticipatory synchronization via low-dimensional filters

    International Nuclear Information System (INIS)

    Pyragiene, T.; Pyragas, K.

    2017-01-01

    An anticipatory chaotic synchronization scheme based on a low-order all-pass filter is proposed. The filter is designed as a Padé approximation to the transfer function of an ideal delay line, which is used in a standard Voss scheme. We show that despite its simplicity, the filter works in an anticipatory scheme as well as an ideal delay line. It provides extremely small synchronization error in the whole interval of anticipation time where the anticipatory manifold is stable. The efficacy of our scheme is explained by an analytically solvable model of unidirectionally coupled unstable spirals and confirmed numerically by an example of unidirectionally coupled chaotic Rössler systems. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of a drive system coupled to a low-dimensional filter. • Long-term anticipation is achieved without using time-delay terms. • An analytical treatment estimates the maximum anticipation time. • The method is verified for the Rössler system.

  1. Anticipatory synchronization via low-dimensional filters

    Energy Technology Data Exchange (ETDEWEB)

    Pyragiene, T., E-mail: tatjana.pyragiene@ftmc.lt; Pyragas, K.

    2017-06-15

    An anticipatory chaotic synchronization scheme based on a low-order all-pass filter is proposed. The filter is designed as a Padé approximation to the transfer function of an ideal delay line, which is used in a standard Voss scheme. We show that despite its simplicity, the filter works in an anticipatory scheme as well as an ideal delay line. It provides extremely small synchronization error in the whole interval of anticipation time where the anticipatory manifold is stable. The efficacy of our scheme is explained by an analytically solvable model of unidirectionally coupled unstable spirals and confirmed numerically by an example of unidirectionally coupled chaotic Rössler systems. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of a drive system coupled to a low-dimensional filter. • Long-term anticipation is achieved without using time-delay terms. • An analytical treatment estimates the maximum anticipation time. • The method is verified for the Rössler system.

  2. Verification of Ganoderma (lingzhi) commercial products by Fourier Transform infrared spectroscopy and two-dimensional IR correlation spectroscopy

    Science.gov (United States)

    Choong, Yew-Keong; Sun, Su-Qin; Zhou, Qun; Lan, Jin; Lee, Han-Lim; Chen, Xiang-Dong

    2014-07-01

    Ganoderma commercial products are typically based on two sources, raw material (powder form and/or spores) and extract (water and/or solvent). This study compared three types of Ganoderma commercial products using 1 Dimensional Fourier Transform infrared and second derivative spectroscopy. The analyzed spectra of Ganoderma raw material products were compared with spectra of cultivated Ganoderma raw material powder from different mushroom farms in Malaysia. The Ganoderma extract product was also compared with three types of cultivated Ganoderma extracts. Other medicinal Ganoderma contents in commercial extract product that included glucan and triterpenoid were analyzed by using FTIR and 2DIR. The results showed that water extract of cultivated Ganoderma possessed comparable spectra with that of Ganoderma product water extract. By comparing the content of Ganoderma commercial products using FTIR and 2DIR, product content profiles could be detected. In addition, the geographical origin of the Ganoderma products could be verified by comparing their spectra with Ganoderma products from known areas. This study demonstrated the possibility of developing verification tool to validate the purity of commercial medicinal herbal and mushroom products.

  3. Two-dimensional analysis of trapped-ion eigenmodes

    International Nuclear Information System (INIS)

    Marchand, R.; Tang, W.M.; Rewoldt, G.

    1979-11-01

    A fully two-dimensional eigenmode analysis of the trapped-ion instability in axisymmetric toroidal geometry is presented. The calculations also takes into account the basic dynamics associated with other low frequency modes such as the trapped-electron instability and the ion-temperature-gradient instability. The poloidal structure of the mode is taken into account by Fourier expanding the perturbed electrostatic potential, PHI, in theta

  4. Partial Fourier analysis of time-harmonic Maxwell's equations in axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-01-01

    We analyze the Fourier method for treating time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with non-axisymmetric data. The Fourier method reduces the three-dimensional boundary value problem to a system of decoupled two-dimensional boundary value problems on the plane meridian domain of the axisymmetric domain. The reduction process is fully described and suitable weighted spaces are introduced on the meridian domain to characterize the two-dimensional solutions. In particular, existence and uniqueness of solutions of the two-dimensional problems is proved and a priori estimates for the solutions are given. (author)

  5. Application of Savitzky-Golay differentiation filters and Fourier functions to simultaneous determination of cefepime and the co-administered drug, levofloxacin, in spiked human plasma

    Science.gov (United States)

    Abdel-Aziz, Omar; Abdel-Ghany, Maha F.; Nagi, Reham; Abdel-Fattah, Laila

    2015-03-01

    The present work is concerned with simultaneous determination of cefepime (CEF) and the co-administered drug, levofloxacin (LEV), in spiked human plasma by applying a new approach, Savitzky-Golay differentiation filters, and combined trigonometric Fourier functions to their ratio spectra. The different parameters associated with the calculation of Savitzky-Golay and Fourier coefficients were optimized. The proposed methods were validated and applied for determination of the two drugs in laboratory prepared mixtures and spiked human plasma. The results were statistically compared with reported HPLC methods and were found accurate and precise.

  6. Biomedical applications of two- and three-dimensional deterministic radiation transport methods

    International Nuclear Information System (INIS)

    Nigg, D.W.

    1992-01-01

    Multidimensional deterministic radiation transport methods are routinely used in support of the Boron Neutron Capture Therapy (BNCT) Program at the Idaho National Engineering Laboratory (INEL). Typical applications of two-dimensional discrete-ordinates methods include neutron filter design, as well as phantom dosimetry. The epithermal-neutron filter for BNCT that is currently available at the Brookhaven Medical Research Reactor (BMRR) was designed using such methods. Good agreement between calculated and measured neutron fluxes was observed for this filter. Three-dimensional discrete-ordinates calculations are used routinely for dose-distribution calculations in three-dimensional phantoms placed in the BMRR beam, as well as for treatment planning verification for live canine subjects. Again, good agreement between calculated and measured neutron fluxes and dose levels is obtained

  7. Filter's importance in nuclear cardiology imaging

    International Nuclear Information System (INIS)

    Jesus, Maria C. de; Lima, Ana L.S.; Santos, Joyra A. dos; Megueriam, Berdj A.

    2008-01-01

    Full text: Nuclear Medicine is a medical speciality which employs tomography procedures for the diagnosis, treatment and prevention of diseases. One of the most commonly used apparatus is the Single Photon Emission Computed Tomography (SPECT). To perform exams, a very small amount of a radiopharmaceutical must be given to the patient. Then, a gamma camera is placed in convenient positions to perform the photon counting, which is used to reconstruct a full 3 dimensional distribution of the radionuclide inside the body or organ. This reconstruction provides a 3-dimensional image in spatial coordinates, of the body or organ under study, allowing the physician to give the diagnostic. Image reconstruction is usually worked in the frequency domain, due to a great simplification introduced by the Fourier decomposition of image spectra. After the reconstruction, an inverse Fourier transform must be applied to trace back the image into spatial coordinates. To optimize this reconstruction procedure, digital filters are used to remove undesirable components of frequency, which can 'shadow' relevant physical signatures of diseases. Unfortunately, the efficiency of the applied filter is strongly dependent on its own mathematical parameters. In this work we demonstrate how filters interfere on image quality in cardiology examinations with SPECT, concerning perfusion and myocardial viability and the importance of the medical physicist in the choice of the right filters avoiding some serious problems that could occur in the inadequate processing of an image damaging the medical diagnosis. (author)

  8. Two dimensional nonlinear spectral estimation techniques for breast cancer localization

    Energy Technology Data Exchange (ETDEWEB)

    Stathaki, P T; Constantinides, A G [Signal Processing Section, Department of Electrical and Electronic Engineering, Imperial College, Exhibition Road, London SW7 2BT, UK (United Kingdom)

    1994-12-31

    In this paper the problem of image texture analysis in the presence of noise is examined from a higher-order statistical perspective. The approach taken involves the use of two dimensional second order Volterra filters where the filter weights are derived from third order cumulants of the two dimensional signal. The specific application contained in this contribution is in mammography, an area in which it is difficult to discern the appropriate features. The paper describes the fundamental issues of the various components of the approach. The results of the entire texture modelling, classification and segmentation scheme contained in this paper are very encouraging. 7 refs, 2 figs.

  9. A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing

    International Nuclear Information System (INIS)

    Pang Chaoyang; Hu Benqiong

    2008-01-01

    The discrete Fourier transform (DFT) is the base of modern signal processing. 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N 2 log N) respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, ID and 2D QDFT have time complexity O(√N) and O (N) respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible. (general)

  10. Fourier transformation for engineering and natural science

    International Nuclear Information System (INIS)

    Klingen, B.

    2001-01-01

    The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)

  11. Predicting respiratory tumor motion with multi-dimensional adaptive filters and support vector regression

    International Nuclear Information System (INIS)

    Riaz, Nadeem; Wiersma, Rodney; Mao Weihua; Xing Lei; Shanker, Piyush; Gudmundsson, Olafur; Widrow, Bernard

    2009-01-01

    Intra-fraction tumor tracking methods can improve radiation delivery during radiotherapy sessions. Image acquisition for tumor tracking and subsequent adjustment of the treatment beam with gating or beam tracking introduces time latency and necessitates predicting the future position of the tumor. This study evaluates the use of multi-dimensional linear adaptive filters and support vector regression to predict the motion of lung tumors tracked at 30 Hz. We expand on the prior work of other groups who have looked at adaptive filters by using a general framework of a multiple-input single-output (MISO) adaptive system that uses multiple correlated signals to predict the motion of a tumor. We compare the performance of these two novel methods to conventional methods like linear regression and single-input, single-output adaptive filters. At 400 ms latency the average root-mean-square-errors (RMSEs) for the 14 treatment sessions studied using no prediction, linear regression, single-output adaptive filter, MISO and support vector regression are 2.58, 1.60, 1.58, 1.71 and 1.26 mm, respectively. At 1 s, the RMSEs are 4.40, 2.61, 3.34, 2.66 and 1.93 mm, respectively. We find that support vector regression most accurately predicts the future tumor position of the methods studied and can provide a RMSE of less than 2 mm at 1 s latency. Also, a multi-dimensional adaptive filter framework provides improved performance over single-dimension adaptive filters. Work is underway to combine these two frameworks to improve performance.

  12. Application of the one-dimensional Fourier transform for tracking moving objects in noisy environments

    Science.gov (United States)

    Rajala, S. A.; Riddle, A. N.; Snyder, W. E.

    1983-01-01

    In Riddle and Rajala (1981), an algorithm was presented which operates on an image sequence to identify all sets of pixels having the same velocity. The algorithm operates by performing a transformation in which all pixels with the same two-dimensional velocity map to a peak in a transform space. The transform can be decomposed into applications of the one-dimensional Fourier transform and therefore can gain from the computational advantages of the FFT. The aim of this paper is the concern with the fundamental limitations of that algorithm, particularly as relates to its sensitivity to image-disturbing parameters as noise, jitter, and clutter. A modification to the algorithm is then proposed which increases its robustness in the presence of these disturbances.

  13. Fan beam image reconstruction with generalized Fourier slice theorem.

    Science.gov (United States)

    Zhao, Shuangren; Yang, Kang; Yang, Kevin

    2014-01-01

    For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.

  14. Application of Savitzky-Golay differentiation filters and Fourier functions to simultaneous determination of cefepime and the co-administered drug, levofloxacin, in spiked human plasma.

    Science.gov (United States)

    Abdel-Aziz, Omar; Abdel-Ghany, Maha F; Nagi, Reham; Abdel-Fattah, Laila

    2015-03-15

    The present work is concerned with simultaneous determination of cefepime (CEF) and the co-administered drug, levofloxacin (LEV), in spiked human plasma by applying a new approach, Savitzky-Golay differentiation filters, and combined trigonometric Fourier functions to their ratio spectra. The different parameters associated with the calculation of Savitzky-Golay and Fourier coefficients were optimized. The proposed methods were validated and applied for determination of the two drugs in laboratory prepared mixtures and spiked human plasma. The results were statistically compared with reported HPLC methods and were found accurate and precise. Copyright © 2014 Elsevier B.V. All rights reserved.

  15. Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction

    Science.gov (United States)

    Chen, Liang-Chia; Ho, Hsuan-Wei; Nguyen, Xuan-Loc

    2010-02-01

    This article presents a novel band-pass filter for Fourier transform profilometry (FTP) for accurate 3-D surface reconstruction. FTP can be employed to obtain 3-D surface profiles by one-shot images to achieve high-speed measurement. However, its measurement accuracy has been significantly influenced by the spectrum filtering process required to extract the phase information representing various surface heights. Using the commonly applied 2-D Hanning filter, the measurement errors could be up to 5-10% of the overall measuring height and it is unacceptable to various industrial application. To resolve this issue, the article proposes an elliptical band-pass filter for extracting the spectral region possessing essential phase information for reconstructing accurate 3-D surface profiles. The elliptical band-pass filter was developed and optimized to reconstruct 3-D surface models with improved measurement accuracy. Some experimental results verify that the accuracy can be effectively enhanced by using the elliptical filter. The accuracy improvement of 44.1% and 30.4% can be achieved in 3-D and sphericity measurement, respectively, when the elliptical filter replaces the traditional filter as the band-pass filtering method. Employing the developed method, the maximum measured error can be kept within 3.3% of the overall measuring range.

  16. High-dimensional change-point estimation: Combining filtering with convex optimization

    OpenAIRE

    Soh, Yong Sheng; Chandrasekaran, Venkat

    2017-01-01

    We consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they have undesirable scaling behavior in the high-dimensional setting. However, many high-dimensional signals encountered in practice frequently possess latent low-dimensional structure. Motivated by this observation, we propose a technique for high-dimensional...

  17. Nonlinear spatio-temporal filtering of dynamic PET data using a four-dimensional Gaussian filter and expectation-maximization deconvolution

    International Nuclear Information System (INIS)

    Floberg, J M; Holden, J E

    2013-01-01

    We introduce a method for denoising dynamic PET data, spatio-temporal expectation-maximization (STEM) filtering, that combines four-dimensional Gaussian filtering with EM deconvolution. The initial Gaussian filter suppresses noise at a broad range of spatial and temporal frequencies and EM deconvolution quickly restores the frequencies most important to the signal. We aim to demonstrate that STEM filtering can improve variance in both individual time frames and in parametric images without introducing significant bias. We evaluate STEM filtering with a dynamic phantom study, and with simulated and human dynamic PET studies of a tracer with reversible binding behaviour, [C-11]raclopride, and a tracer with irreversible binding behaviour, [F-18]FDOPA. STEM filtering is compared to a number of established three and four-dimensional denoising methods. STEM filtering provides substantial improvements in variance in both individual time frames and in parametric images generated with a number of kinetic analysis techniques while introducing little bias. STEM filtering does bias early frames, but this does not affect quantitative parameter estimates. STEM filtering is shown to be superior to the other simple denoising methods studied. STEM filtering is a simple and effective denoising method that could be valuable for a wide range of dynamic PET applications. (paper)

  18. An Exact Method to Determine the Photonic Resonances of Quasicrystals Based on Discrete Fourier Harmonics of Higher-Dimensional Atomic Surfaces

    Directory of Open Access Journals (Sweden)

    Farhad A. Namin

    2016-08-01

    Full Text Available A rigorous method for obtaining the diffraction patterns of quasicrystals is presented. Diffraction patterns are an essential analytical tool in the study of quasicrystals, since they can be used to determine their photonic resonances. Previous methods for approximating the diffraction patterns of quasicrystals have relied on evaluating the Fourier transform of finite-sized super-lattices. Our approach, on the other hand, is exact in the sense that it is based on a technique that embeds quasicrystals into higher dimensional periodic hyper-lattices, thereby completely capturing the properties of the infinite structure. The periodicity of the unit cell in the higher dimensional space can be exploited to obtain the Fourier series expansion in closed-form of the corresponding atomic surfaces. The utility of the method is demonstrated by applying it to one-dimensional Fibonacci and two-dimensional Penrose quasicrystals. The results are verified by comparing them to those obtained by using the conventional super-lattice method. It is shown that the conventional super-cell approach can lead to inaccurate results due to the continuous nature of the Fourier transform, since quasicrystals have a discrete spectrum, whereas the approach introduced in this paper generates discrete Fourier harmonics. Furthermore, the conventional approach requires very large super-cells and high-resolution sampling of the reciprocal space in order to produce accurate results leading to a very large computational burden, whereas the proposed method generates accurate results with a relatively small number of terms. Finally, we propose how this approach can be generalized from the vertex model, which assumes identical particles at all vertices, to a more realistic case where the quasicrystal is composed of different atoms.

  19. Review of tomography technique for 3-dimensional fission product distribution determination in irradiated fuel

    Energy Technology Data Exchange (ETDEWEB)

    Pakr, D G; Hong, K P; Joo, Y S; Lee, H K

    2006-04-15

    Tomography algorithm is reviewed in order to determine radial 2-dimensional fission product distribution of irradiated fuel rod and to reconstruct it's image using computer. Main contents are Radon transformation, Fourier central slice theorem, inverse Fourier transform, accompanied FBP(Filtered Back Projection) and BPB(Back Projection Filtering). In addition, another tomography reconstruction algorithm, namely, ART(Algebraic Reconstruction Technique) is reviewed briefly. According to reviewed results, we devise equipment for determining of 2-dimensional distribution of irradiated nuclear fuel using existing gamma scanning apparatus. On results of review, It is necessary to develop computer program of reconstruction algorithm for determining of object function and image reconstruction.

  20. Review of tomography technique for 3-dimensional fission product distribution determination in irradiated fuel

    International Nuclear Information System (INIS)

    Pakr, D. G.; Hong, K. P.; Joo, Y. S.; Lee, H. K.

    2006-04-01

    Tomography algorithm is reviewed in order to determine radial 2-dimensional fission product distribution of irradiated fuel rod and to reconstruct it's image using computer. Main contents are Radon transformation, Fourier central slice theorem, inverse Fourier transform, accompanied FBP(Filtered Back Projection) and BPB(Back Projection Filtering). In addition, another tomography reconstruction algorithm, namely, ART(Algebraic Reconstruction Technique) is reviewed briefly. According to reviewed results, we devise equipment for determining of 2-dimensional distribution of irradiated nuclear fuel using existing gamma scanning apparatus. On results of review, It is necessary to develop computer program of reconstruction algorithm for determining of object function and image reconstruction

  1. High Time-Resolution 640-Gb/s Clock Recovery Using Time-Domain Optical Fourier Transformation and Narrowband Optical Filter

    DEFF Research Database (Denmark)

    Guan, P.; Mulvad, Hans Christian Hansen; Kasai, K.

    2010-01-01

    We present a novel scheme for subharmonic clock recovery from an optical time-division-multiplexing signal using time-domain optical Fourier transformation and a narrowband optical filter. High-resolution 640-Gb/s clock recovery is successfully demonstrated with no pattern dependence. The clock...

  2. Chemical Source Inversion using Assimilated Constituent Observations in an Idealized Two-dimensional System

    Science.gov (United States)

    Tangborn, Andrew; Cooper, Robert; Pawson, Steven; Sun, Zhibin

    2009-01-01

    We present a source inversion technique for chemical constituents that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier-Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green's function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral spectral model, but differs by an unbiased Gaussian model error, and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out by either direct use of synthetically generated observations with added noise, or by first assimilating the observations and using the analyses to extract observations. We have conducted 20 identical twin experiments for each set of source and observation configurations, and find that in the limiting cases of a very few localized observations, or an extremely large observation network there is little advantage to carrying out assimilation first. However, in intermediate observation densities, there decreases in source inversion error standard deviation using the Kalman filter algorithm followed by Green's function inversion by 50% to 95%.

  3. Engineering two-photon high-dimensional states through quantum interference

    Science.gov (United States)

    Zhang, Yingwen; Roux, Filippus S.; Konrad, Thomas; Agnew, Megan; Leach, Jonathan; Forbes, Andrew

    2016-01-01

    Many protocols in quantum science, for example, linear optical quantum computing, require access to large-scale entangled quantum states. Such systems can be realized through many-particle qubits, but this approach often suffers from scalability problems. An alternative strategy is to consider a lesser number of particles that exist in high-dimensional states. The spatial modes of light are one such candidate that provides access to high-dimensional quantum states, and thus they increase the storage and processing potential of quantum information systems. We demonstrate the controlled engineering of two-photon high-dimensional states entangled in their orbital angular momentum through Hong-Ou-Mandel interference. We prepare a large range of high-dimensional entangled states and implement precise quantum state filtering. We characterize the full quantum state before and after the filter, and are thus able to determine that only the antisymmetric component of the initial state remains. This work paves the way for high-dimensional processing and communication of multiphoton quantum states, for example, in teleportation beyond qubits. PMID:26933685

  4. A variational Bayesian multiple particle filtering scheme for large-dimensional systems

    KAUST Repository

    Ait-El-Fquih, Boujemaa

    2016-06-14

    This paper considers the Bayesian filtering problem in high-dimensional nonlinear state-space systems. In such systems, classical particle filters (PFs) are impractical due to the prohibitive number of required particles to obtain reasonable performances. One approach that has been introduced to overcome this problem is the concept of multiple PFs (MPFs), where the state-space is split into low-dimensional subspaces and then a separate PF is applied to each subspace. Remarkable performances of MPF-like filters motivated our investigation here into a new strategy that combines the variational Bayesian approach to split the state-space with random sampling techniques, to derive a new computationally efficient MPF. The propagation of each particle in the prediction step of the resulting filter requires generating only a single particle in contrast with standard MPFs, for which a set of (children) particles is required. We present simulation results to evaluate the behavior of the proposed filter and compare its performances against standard PF and a MPF.

  5. A variational Bayesian multiple particle filtering scheme for large-dimensional systems

    KAUST Repository

    Ait-El-Fquih, Boujemaa; Hoteit, Ibrahim

    2016-01-01

    This paper considers the Bayesian filtering problem in high-dimensional nonlinear state-space systems. In such systems, classical particle filters (PFs) are impractical due to the prohibitive number of required particles to obtain reasonable performances. One approach that has been introduced to overcome this problem is the concept of multiple PFs (MPFs), where the state-space is split into low-dimensional subspaces and then a separate PF is applied to each subspace. Remarkable performances of MPF-like filters motivated our investigation here into a new strategy that combines the variational Bayesian approach to split the state-space with random sampling techniques, to derive a new computationally efficient MPF. The propagation of each particle in the prediction step of the resulting filter requires generating only a single particle in contrast with standard MPFs, for which a set of (children) particles is required. We present simulation results to evaluate the behavior of the proposed filter and compare its performances against standard PF and a MPF.

  6. Biomedical signal and image processing

    CERN Document Server

    Najarian, Kayvan

    2012-01-01

    INTRODUCTION TO DIGITAL SIGNAL AND IMAGE PROCESSINGSignals and Biomedical Signal ProcessingIntroduction and OverviewWhat is a ""Signal""?Analog, Discrete, and Digital SignalsProcessing and Transformation of SignalsSignal Processing for Feature ExtractionSome Characteristics of Digital ImagesSummaryProblemsFourier TransformIntroduction and OverviewOne-Dimensional Continuous Fourier TransformSampling and NYQUIST RateOne-Dimensional Discrete Fourier TransformTwo-Dimensional Discrete Fourier TransformFilter DesignSummaryProblemsImage Filtering, Enhancement, and RestorationIntroduction and Overview

  7. One-dimensional, non-local, first-order, stationary mean-field games with congestion: a Fourier approach

    KAUST Repository

    Nurbekyan, Levon

    2017-01-01

    Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric polynomials. Our technique is based on Fourier expansion methods.

  8. One-dimensional, non-local, first-order, stationary mean-field games with congestion: a Fourier approach

    KAUST Repository

    Nurbekyan, Levon

    2017-03-11

    Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric polynomials. Our technique is based on Fourier expansion methods.

  9. Two-dimensional real-time imaging system for subtraction angiography using an iodine filter

    Science.gov (United States)

    Umetani, Keiji; Ueda, Ken; Takeda, Tohoru; Anno, Izumi; Itai, Yuji; Akisada, Masayoshi; Nakajima, Teiichi

    1992-01-01

    A new type of subtraction imaging system was developed using an iodine filter and a single-energy broad bandwidth monochromatized x ray. The x-ray images of coronary arteries made after intravenous injection of a contrast agent are enhanced by an energy-subtraction technique. Filter chopping of the x-ray beam switches energies rapidly, so that a nearly simultaneous pair of filtered and nonfiltered images can be made. By using a high-speed video camera, a pair of two 512 × 512 pixel images can be obtained within 9 ms. Three hundred eighty-four images (raw data) are stored in a 144-Mbyte frame memory. After phantom studies, in vivo subtracted images of coronary arteries in dogs were obtained at a rate of 15 images/s.

  10. One-Dimensional Tunable Photonic-Crystal IR Filter, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — MetroLaser proposes to design and develop an innovative narrowband tunable IR filter based on the properties of a one-dimensional photonic crystal structure with a...

  11. One-Dimensional Tunable Photonic-Crystal IR Filter, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — MetroLaser proposes to design and develop an innovative narrowband tunable IR filter based on the properties of a one-dimensional photonic crystal structure with a...

  12. Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

    International Nuclear Information System (INIS)

    Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P

    2011-01-01

    According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.

  13. Efficient design of two-dimensional recursive digital filters. Final report

    International Nuclear Information System (INIS)

    Twogood, R.E.; Mitra, S.K.

    1980-01-01

    This report outlines the research progress during the period August 1978 to July 1979. This work can be divided into seven basic project areas. Project 1 deals with a comparative study of 2-D recursive and nonrecursive digital filters. The second project addresses a new design technique for 2-D half-plane recursive filters, and Projects 3 thru 5 deal with implementation issues. The sixth project presents our recent study of the applicability of array processors to 2-D digital signal processing. The final project involves our investigation into techniques for incorporating symmetry constraints on 2-D recursive filters in order to yield more efficient implementations

  14. Impact of bowtie filter and object position on the two-dimensional noise power spectrum of a clinical MDCT system

    Energy Technology Data Exchange (ETDEWEB)

    Gomez-Cardona, Daniel; Cruz-Bastida, Juan Pablo [Department of Medical Physics, University of Wisconsin-Madison School of Medicine and Public Health, 1111 Highland Avenue, Madison, Wisconsin 53705 (United States); Li, Ke; Chen, Guang-Hong, E-mail: gchen7@wisc.edu [Department of Medical Physics, University of Wisconsin-Madison School of Medicine and Public Health, 1111 Highland Avenue, Madison, Wisconsin 53705 and Department of Radiology, University of Wisconsin-Madison School of Medicine and Public Health, 600 Highland Avenue, Madison, Wisconsin 53792 (United States); Budde, Adam; Hsieh, Jiang [Department of Medical Physics, University of Wisconsin-Madison School of Medicine and Public Health, 1111 Highland Avenue, Madison, Wisconsin 53705 and GE Healthcare, 3000 N Grandview Boulevard, Waukesha, Wisconsin 53188 (United States)

    2016-08-15

    Purpose: Noise characteristics of clinical multidetector CT (MDCT) systems can be quantified by the noise power spectrum (NPS). Although the NPS of CT has been extensively studied in the past few decades, the joint impact of the bowtie filter and object position on the NPS has not been systematically investigated. This work studies the interplay of these two factors on the two dimensional (2D) local NPS of a clinical CT system that uses the filtered backprojection algorithm for image reconstruction. Methods: A generalized NPS model was developed to account for the impact of the bowtie filter and image object location in the scan field-of-view (SFOV). For a given bowtie filter, image object, and its location in the SFOV, the shape and rotational symmetries of the 2D local NPS were directly computed from the NPS model without going through the image reconstruction process. The obtained NPS was then compared with the measured NPSs from the reconstructed noise-only CT images in both numerical phantom simulation studies and experimental phantom studies using a clinical MDCT scanner. The shape and the associated symmetry of the 2D NPS were classified by borrowing the well-known atomic spectral symbols s, p, and d, which correspond to circular, dumbbell, and cloverleaf symmetries, respectively, of the wave function of electrons in an atom. Finally, simulated bar patterns were embedded into experimentally acquired noise backgrounds to demonstrate the impact of different NPS symmetries on the visual perception of the object. Results: (1) For a central region in a centered cylindrical object, an s-wave symmetry was always present in the NPS, no matter whether the bowtie filter was present or not. In contrast, for a peripheral region in a centered object, the symmetry of its NPS was highly dependent on the bowtie filter, and both p-wave symmetry and d-wave symmetry were observed in the NPS. (2) For a centered region-ofinterest (ROI) in an off-centered object, the symmetry of

  15. Impact of bowtie filter and object position on the two-dimensional noise power spectrum of a clinical MDCT system

    International Nuclear Information System (INIS)

    Gomez-Cardona, Daniel; Cruz-Bastida, Juan Pablo; Li, Ke; Chen, Guang-Hong; Budde, Adam; Hsieh, Jiang

    2016-01-01

    Purpose: Noise characteristics of clinical multidetector CT (MDCT) systems can be quantified by the noise power spectrum (NPS). Although the NPS of CT has been extensively studied in the past few decades, the joint impact of the bowtie filter and object position on the NPS has not been systematically investigated. This work studies the interplay of these two factors on the two dimensional (2D) local NPS of a clinical CT system that uses the filtered backprojection algorithm for image reconstruction. Methods: A generalized NPS model was developed to account for the impact of the bowtie filter and image object location in the scan field-of-view (SFOV). For a given bowtie filter, image object, and its location in the SFOV, the shape and rotational symmetries of the 2D local NPS were directly computed from the NPS model without going through the image reconstruction process. The obtained NPS was then compared with the measured NPSs from the reconstructed noise-only CT images in both numerical phantom simulation studies and experimental phantom studies using a clinical MDCT scanner. The shape and the associated symmetry of the 2D NPS were classified by borrowing the well-known atomic spectral symbols s, p, and d, which correspond to circular, dumbbell, and cloverleaf symmetries, respectively, of the wave function of electrons in an atom. Finally, simulated bar patterns were embedded into experimentally acquired noise backgrounds to demonstrate the impact of different NPS symmetries on the visual perception of the object. Results: (1) For a central region in a centered cylindrical object, an s-wave symmetry was always present in the NPS, no matter whether the bowtie filter was present or not. In contrast, for a peripheral region in a centered object, the symmetry of its NPS was highly dependent on the bowtie filter, and both p-wave symmetry and d-wave symmetry were observed in the NPS. (2) For a centered region-ofinterest (ROI) in an off-centered object, the symmetry of

  16. The noise analysis and optimum filtering techniques for a two-dimensional position sensitive orthogonal strip gamma ray detector employing resistive charge division

    International Nuclear Information System (INIS)

    Gerber, M.S.; Muller, D.W.

    1976-01-01

    The analysis of an orthogonal strip, two-dimensional position sensitive high purity germanium gamma ray detector is discussed. Position sensitivity is obtained by connecting each electrode strip on the detector to a resistor network. Charge, entering the network, divides in relation to the resistance between its entry point and the virtual earth points of the charge sensitive preamplifiers located at the end of each resistor network. The difference of the voltage pulses at the output of each preamplifier is proportional to the position at which the charge entered the resistor network and the sum of the pulse is proportional to the energy of the detected gamma ray. The analysis and spatial noise resolution is presented for this type of position sensitive detector. The results of the analysis show that the position resolution is proportional to the square root of the filter amplifier's output pulse time constant and that for energy measurement the resolution is maximized at the filter amplifier's noise corner time constant. The design of the electronic noise filtering system for the prototype gamma ray camera was based on the mathematical energy and spatial resolution equations. For the spatial channel a Gaussian trapezoidal filtering system was developed. Gaussian filtering was used for the energy channel. The detector noise model was verified by taking rms noise measurements of the filtered energy and spatial pulses from resistive readout charge dividing detectors. These measurements were within 10% of theory. (Auth.)

  17. [Continuum based fast Fourier transform processing of infrared spectrum].

    Science.gov (United States)

    Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai

    2009-12-01

    To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.

  18. Low-dimensional recurrent neural network-based Kalman filter for speech enhancement.

    Science.gov (United States)

    Xia, Youshen; Wang, Jun

    2015-07-01

    This paper proposes a new recurrent neural network-based Kalman filter for speech enhancement, based on a noise-constrained least squares estimate. The parameters of speech signal modeled as autoregressive process are first estimated by using the proposed recurrent neural network and the speech signal is then recovered from Kalman filtering. The proposed recurrent neural network is globally asymptomatically stable to the noise-constrained estimate. Because the noise-constrained estimate has a robust performance against non-Gaussian noise, the proposed recurrent neural network-based speech enhancement algorithm can minimize the estimation error of Kalman filter parameters in non-Gaussian noise. Furthermore, having a low-dimensional model feature, the proposed neural network-based speech enhancement algorithm has a much faster speed than two existing recurrent neural networks-based speech enhancement algorithms. Simulation results show that the proposed recurrent neural network-based speech enhancement algorithm can produce a good performance with fast computation and noise reduction. Copyright © 2015 Elsevier Ltd. All rights reserved.

  19. Discrete Fourier transform in nanostructures using scattering

    International Nuclear Information System (INIS)

    Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.

    2004-01-01

    In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed

  20. Fourier method for three-dimensional partial differential equations in periodic geometry. Application: HELIAC

    International Nuclear Information System (INIS)

    Shestakov, A.I.; Mirin, A.A.

    1984-01-01

    A numerical method based on Fourier expansions and finite differences is presented. The method is demonstrated by solving a scalar, three-dimensional elliptic equation arising in MFE research, but has applicability to a wider class of problems. The scheme solves equations whose solutions are expected to be periodic in one or more of the independent variables

  1. Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots

    Energy Technology Data Exchange (ETDEWEB)

    Cundiff, Steven T. [Univ. of Colorado, Boulder, CO (United States)

    2016-05-03

    This final report describes the activities undertaken under grant "Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots". The goal of this program was to implement optical 2-dimensional Fourier transform spectroscopy and apply it to electronic excitations, including excitons, in semiconductors. Specifically of interest are quantum wells that exhibit disorder due to well width fluctuations and quantum dots. In both cases, 2-D spectroscopy will provide information regarding coupling among excitonic localization sites.

  2. Fourier spectral simulations for wake fields in conducting cavities

    International Nuclear Information System (INIS)

    Min, M.; Chin, Y.-H.; Fischer, P.F.; Chae, Y.-Chul; Kim, K.-J.

    2007-01-01

    We investigate Fourier spectral time-domain simulations applied to wake field calculations in two-dimensional cylindrical structures. The scheme involves second-order explicit leap-frogging in time and Fourier spectral approximation in space, which is obtained from simply replacing the spatial differentiation operator of the YEE scheme by the Fourier differentiation operator on nonstaggered grids. This is a first step toward investigating high-order computational techniques with the Fourier spectral method, which is relatively simple to implement.

  3. Two-stage nonlinear filter for processing of scintigrams

    International Nuclear Information System (INIS)

    Pistor, P.; Hoener, J.; Walch, G.

    1973-01-01

    Linear filters which have been successfully used to process scintigrams can be modified in a meaningful manner by a preceding non-linear point operator, the Anscombe-transform. The advantages are: The scintigraphic noise becomes quasi-stationary and thus independent of the image. By these means the noise can be readily allowed for in the design of the convolutional operators. Transformed images with a stationary signal-to-noise ratio and a non-constant background t correspond to untransformed images with a signal-to-noise ratio that varies in certain limits. The filter chain automatically adapts to these changes. Our filter has the advantage over the majority of space-varying filters of being realizable by Fast Fourier Transform techniques. These advantages have to be paid for by reduced signal amplitude to background ratios. If the background is known, this shortcoming can be easily by-passed by processing trendfree scintigrams. If not, the filter chain should be completed by a third operator which reverses the Anscombe-transform. The Anscombe-transform influences the signal-to-noise ratio of cold spots and of hot spots in a different way. It remains an open question if this fact can be utilized to directly influence the detectability of the different kinds of spots

  4. Study on Senna alata and its different extracts by Fourier transform infrared spectroscopy and two-dimensional correlation infrared spectroscopy

    Science.gov (United States)

    Adiana, M. A.; Mazura, M. P.

    2011-04-01

    Senna alata L. commonly known as candle bush belongs to the family of Fabaceae and the plant has been reported to possess anti-inflammatory, analgesic, laxative and antiplatelet-aggregating activity. In order to develop a rapid and effective analysis method for studying integrally the main constituents in the medicinal materials and their extracts, discriminating the extracts from different extraction process, comparing the categories of chemical constituents in the different extracts and monitoring the qualities of medicinal materials, we applied Fourier transform infrared spectroscopy (FT-IR) associated with second derivative infrared spectroscopy and two-dimensional infrared correlation spectroscopy (2D-IR) to study the main constituents of S. alata and its different extracts (extracted by hexane, dichloromethane, ethyl acetate and methanol in turn). The findings indicated that FT-IR and 2D-IR can provide many holistic variation rules of chemical constituents. Use of the macroscopical fingerprint characters of FT-IR and 2D-IR spectrum can identify the main chemical constituents in medicinal materials and their extracts, but also compare the components differences among similar samples. In a conclusion, FT-IR spectroscopy combined with 2D correlation analysis provides a powerful method for the quality control of traditional medicines.

  5. Direct fourier methods in 3D-reconstruction from cone-beam data

    International Nuclear Information System (INIS)

    Axelsson, C.

    1994-01-01

    The problem of 3D-reconstruction is encountered in both medical and industrial applications of X-ray tomography. A method able to utilize a complete set of projections complying with Tuys condition was proposed by Grangeat. His method is mathematically exact and consists of two distinct phases. In phase 1 cone-beam projection data are used to produce the derivative of the radon transform. In phase 2, after interpolation, the radon transform data are used to reconstruct the three-dimensional object function. To a large extent our method is an extension of the Grangeat method. Our aim is to reduce the computational complexity, i.e. to produce a faster method. The most taxing procedure during phase 1 is computation of line-integrals in the detector plane. By applying the direct Fourier method in reverse for this computation, we reduce the complexity of phase 1 from O(N 4 ) to O(N 3 logN). Phase 2 can be performed either as a straight 3D-reconstruction or as a sequence of two 2D-reconstructions in vertical and horizontal planes, respectively. Direct Fourier methods can be applied for the 2D- and for the 3D-reconstruction, which reduces the complexity of phase 2 from O(N 4 ) to O(N 3 logN) as well. In both cases, linogram techniques are applied. For 3D-reconstruction the inversion formula contains the second derivative filter instead of the well-known ramp-filter employed in the 2D-case. The derivative filter is more well-behaved than the 2D ramp-filter. This implies that less zeropadding is necessary which brings about a further reduction of the computational efforts. The method has been verified by experiments on simulated data. The image quality is satisfactory and independent of cone-beam angles. For a 512 3 volume we estimate that our method is ten times faster than Grangeats method

  6. Fast multiview three-dimensional reconstruction method using cost volume filtering

    Science.gov (United States)

    Lee, Seung Joo; Park, Min Ki; Jang, In Yeop; Lee, Kwan H.

    2014-03-01

    As the number of customers who want to record three-dimensional (3-D) information using a mobile electronic device increases, it becomes more and more important to develop a method which quickly reconstructs a 3-D model from multiview images. A fast multiview-based 3-D reconstruction method is presented, which is suitable for the mobile environment by constructing a cost volume of the 3-D height field. This method consists of two steps: the construction of a reliable base surface and the recovery of shape details. In each step, the cost volume is constructed using photoconsistency and then it is filtered according to the multiscale. The multiscale-based cost volume filtering allows the 3-D reconstruction to maintain the overall shape and to preserve the shape details. We demonstrate the strength of the proposed method in terms of computation time, accuracy, and unconstrained acquisition environment.

  7. Iterative Two- and One-Dimensional Methods for Three-Dimensional Neutron Diffusion Calculations

    International Nuclear Information System (INIS)

    Lee, Hyun Chul; Lee, Deokjung; Downar, Thomas J.

    2005-01-01

    Two methods are proposed for solving the three-dimensional neutron diffusion equation by iterating between solutions of the two-dimensional (2-D) radial and one-dimensional (1-D) axial solutions. In the first method, the 2-D/1-D equations are coupled using a current correction factor (CCF) with the average fluxes of the lower and upper planes and the axial net currents at the plane interfaces. In the second method, an analytic expression for the axial net currents at the interface of the planes is used for planar coupling. A comparison of the new methods is made with two previously proposed methods, which use interface net currents and partial currents for planar coupling. A Fourier convergence analysis of the four methods was performed, and results indicate that the two new methods have at least three advantages over the previous methods. First, the new methods are unconditionally stable, whereas the net current method diverges for small axial mesh size. Second, the new methods provide better convergence performance than the other methods in the range of practical mesh sizes. Third, the spectral radii of the new methods asymptotically approach zero as the mesh size increases, while the spectral radius of the partial current method approaches a nonzero value as the mesh size increases. Of the two new methods proposed here, the analytic method provides a smaller spectral radius than the CCF method, but the CCF method has several advantages over the analytic method in practical applications

  8. Push-Broom-Type Very High-Resolution Satellite Sensor Data Correction Using Combined Wavelet-Fourier and Multiscale Non-Local Means Filtering

    Science.gov (United States)

    Kang, Wonseok; Yu, Soohwan; Seo, Doochun; Jeong, Jaeheon; Paik, Joonki

    2015-01-01

    In very high-resolution (VHR) push-broom-type satellite sensor data, both destriping and denoising methods have become chronic problems and attracted major research advances in the remote sensing fields. Since the estimation of the original image from a noisy input is an ill-posed problem, a simple noise removal algorithm cannot preserve the radiometric integrity of satellite data. To solve these problems, we present a novel method to correct VHR data acquired by a push-broom-type sensor by combining wavelet-Fourier and multiscale non-local means (NLM) filters. After the wavelet-Fourier filter separates the stripe noise from the mixed noise in the wavelet low- and selected high-frequency sub-bands, random noise is removed using the multiscale NLM filter in both low- and high-frequency sub-bands without loss of image detail. The performance of the proposed method is compared to various existing methods on a set of push-broom-type sensor data acquired by Korean Multi-Purpose Satellite 3 (KOMPSAT-3) with severe stripe and random noise, and the results of the proposed method show significantly improved enhancement results over existing state-of-the-art methods in terms of both qualitative and quantitative assessments. PMID:26378532

  9. Anomalous phase behavior and apparent anharmonicity of the pump-probe signal in a two-dimensional harmonic potential system

    International Nuclear Information System (INIS)

    Taneichi, T.; Kobayashi, T.

    2007-01-01

    Discussion on wavelength dependent 'anharmonic' effects in a pump-probe signal for a system of wavepacket on one- and two-dimensional harmonic potentials was given. The Fourier power spectrum of the signal, calculated for a model composed of a three-state electronic system coupled to a set of displaced harmonic oscillators, depends on the pulse duration. Condition under which the wavepacket motion in the harmonic potential substantially deviates from that of the classical point mass is derived. The Fourier power spectrum has enhanced components with frequencies of harmonics even in a system composed of ideally harmonic potentials. Utility of the Fourier analysis of the spectrum for clarification of the squeezed molecular vibrational state is discussed. Calculated oscillatory behavior in phase of a pump-probe signal, as a function of probe frequency, was discussed in terms of a two-dimensional effect on a pump-probe signal

  10. Application of Fourier analysis to multispectral/spatial recognition

    Science.gov (United States)

    Hornung, R. J.; Smith, J. A.

    1973-01-01

    One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.

  11. MR image reconstruction via guided filter.

    Science.gov (United States)

    Huang, Heyan; Yang, Hang; Wang, Kang

    2018-04-01

    Magnetic resonance imaging (MRI) reconstruction from the smallest possible set of Fourier samples has been a difficult problem in medical imaging field. In our paper, we present a new approach based on a guided filter for efficient MRI recovery algorithm. The guided filter is an edge-preserving smoothing operator and has better behaviors near edges than the bilateral filter. Our reconstruction method is consist of two steps. First, we propose two cost functions which could be computed efficiently and thus obtain two different images. Second, the guided filter is used with these two obtained images for efficient edge-preserving filtering, and one image is used as the guidance image, the other one is used as a filtered image in the guided filter. In our reconstruction algorithm, we can obtain more details by introducing guided filter. We compare our reconstruction algorithm with some competitive MRI reconstruction techniques in terms of PSNR and visual quality. Simulation results are given to show the performance of our new method.

  12. Analysis of Chuanxiong Rhizoma and its active components by Fourier transform infrared spectroscopy combined with two-dimensional correlation infrared spectroscopy.

    Science.gov (United States)

    Guo, Yizhen; Lv, Beiran; Wang, Jingjuan; Liu, Yang; Sun, Suqin; Xiao, Yao; Lu, Lina; Xiang, Li; Yang, Yanfang; Qu, Lei; Meng, Qinghong

    2016-01-15

    As complicated mixture systems, active components of Chuanxiong Rhizoma are very difficult to identify and discriminate. In this paper, the macroscopic IR fingerprint method including Fourier transform infrared spectroscopy (FT-IR), the second derivative infrared spectroscopy (SD-IR) and two-dimensional correlation infrared spectroscopy (2DCOS-IR), was applied to study and identify Chuanxiong raw materials and its different segmented production of HPD-100 macroporous resin. Chuanxiong Rhizoma is rich in sucrose. In the FT-IR spectra, water eluate is more similar to sucrose than the powder and the decoction. Their second derivative spectra amplified the differences and revealed the potentially characteristic IR absorption bands and combined with the correlation coefficient, concluding that 50% ethanol eluate had more ligustilide than other eluates. Finally, it can be found from 2DCOS-IR spectra that proteins were extracted by ethanol from Chuanxiong decoction by HPD-100 macroporous resin. It was demonstrated that the above three-step infrared spectroscopy could be applicable for quick, non-destructive and effective analysis and identification of very complicated and similar mixture systems of traditional Chinese medicines. Copyright © 2015 Elsevier B.V. All rights reserved.

  13. Geometric Representations for Discrete Fourier Transforms

    Science.gov (United States)

    Cambell, C. W.

    1986-01-01

    Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

  14. A filtering approach to image reconstruction in 3D SPECT

    International Nuclear Information System (INIS)

    Bronnikov, Andrei V.

    2000-01-01

    We present a new approach to three-dimensional (3D) image reconstruction using analytical inversion of the exponential divergent beam transform, which can serve as a mathematical model for cone-beam 3D SPECT imaging. We apply a circular cone-beam scan and assume constant attenuation inside a convex area with a known boundary, which is satisfactory in brain imaging. The reconstruction problem is reduced to an image restoration problem characterized by a shift-variant point spread function which is given analytically. The method requires two computation steps: backprojection and filtering. The modulation transfer function (MTF) of the filter is derived by means of an original methodology using the 2D Laplace transform. The filter is implemented in the frequency domain and requires 2D Fourier transform of transverse slices. In order to obtain a shift-invariant cone-beam projection-backprojection operator we resort to an approximation, assuming that the collimator has a relatively large focal length. Nevertheless, numerical experiments demonstrate surprisingly good results for detectors with relatively short focal lengths. The use of a wavelet-based filtering algorithm greatly improves the stability to Poisson noise. (author)

  15. A Fourier Optical Model for the Laser Doppler Velocimeter

    DEFF Research Database (Denmark)

    Lading, Lars

    1972-01-01

    The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. ldquodifferential moderdquo and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions. The particles are represented...... filtering ability vanishes as the aperture size converges towards zero. The results based on fourier optics are compared with the rough estimates obtainable by using the "antenna formular" for heterodyning (ArΩr≈λ2)....

  16. Fourier transform nuclear magnetic resonance

    International Nuclear Information System (INIS)

    Geick, R.

    1981-01-01

    This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)

  17. Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism ( S-quantization)

    Science.gov (United States)

    Ivanov, K. A.; Nikolaev, V. V.; Gubaydullin, A. R.; Kaliteevski, M. A.

    2017-10-01

    Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures ( S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate

  18. The gridding method for image reconstruction by Fourier transformation

    International Nuclear Information System (INIS)

    Schomberg, H.; Timmer, J.

    1995-01-01

    This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f. The method involves a window function w and proceeds in three steps. First, the convolution g = w * f is computed numerically on a Cartesian grid, using the available samples of f. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w * f is much less error prone than merely interpolating f. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform

  19. Eleven-dimensional supergravity from filtered subdeformations of the Poincaré superalgebra

    International Nuclear Information System (INIS)

    Figueroa-O’Farrill, José; Santi, Andrea

    2016-01-01

    We summarise recent results concerning the classification of filtered deformations of graded subalgebras of the Poincaré superalgebra in eleven dimensions, highlighting what could be considered a novel Lie-algebraic derivation of eleven-dimensional supergravity. (paper)

  20. Tunable ultra-wideband terahertz filter based on three-dimensional arrays of H-shaped plasmonic crystals

    International Nuclear Information System (INIS)

    Yuan Cai; Xu Shi-Lin; Yao Jian-Quan; Zhao Xiao-Lei; Cao Xiao-Long; Wu Liang

    2014-01-01

    A face-to-face system of double-layer three-dimensional arrays of H-shaped plasmonic crystals is proposed, and its transmission and filtering properties are investigated in the terahertz regime. Simulation results show that our design has excellent filtering properties. It has an ultra-wide bandgap and passband with steep band-edges, and the transmittance of the passband and the forbidden band are very close to 1 and 0, respectively. As the distance between the two face-to-face plates increases, the resonance frequency exhibits a gradual blueshift from 0.88 THz to 1.30 THz. Therefore, we can dynamically control the bandwidths of bandgap and passband by adding a piezoelectric ceramic plate between the two crystal plates. Furthermore, the dispersion relations of modes and electric field distributions are presented to analyze the generation mechanisms of bandgaps and to explain the location of bandgaps and the frequency shift phenomenon. Due to the fact that our design can provide many resonant modes, the bandwidth of the bandgaps can be greatly broadened. This paper can serve as a valuable reference for the design of terahertz functional devices and three-dimensional terahertz metamaterials. (interdisciplinary physics and related areas of science and technology)

  1. Hybrid three-dimensional variation and particle filtering for nonlinear systems

    International Nuclear Information System (INIS)

    Leng Hong-Ze; Song Jun-Qiang

    2013-01-01

    This work addresses the problem of estimating the states of nonlinear dynamic systems with sparse observations. We present a hybrid three-dimensional variation (3DVar) and particle piltering (PF) method, which combines the advantages of 3DVar and particle-based filters. By minimizing the cost function, this approach will produce a better proposal distribution of the state. Afterwards the stochastic resampling step in standard PF can be avoided through a deterministic scheme. The simulation results show that the performance of the new method is superior to the traditional ensemble Kalman filtering (EnKF) and the standard PF, especially in highly nonlinear systems

  2. Measurement of the presampled two-dimensional modulation transfer function of digital imaging systems

    International Nuclear Information System (INIS)

    Fetterly, Kenneth A.; Hangiandreou, Nicholas J.; Schueler, Beth A.; Ritenour, E. Russell

    2002-01-01

    The purpose of this work was to develop methods to measure the presampled two-dimensional modulation transfer function (2D MTF) of digital imaging systems. A custom x-ray 'point source' phantom was created by machining 256 holes with diameter 0.107 mm through a 0.5-mm-thick copper plate. The phantom was imaged several times, resulting in many images of individual x-ray 'spots'. The center of each spot (with respect to the pixel matrix) was determined to subpixel accuracy by fitting each spot to a 2D Gaussian function. The subpixel spot center locations were used to create a 5x oversampled system point spread function (PSF), which characterizes the optical and electrical properties of the system and is independent of the pixel sampling of the original image. The modulus of the Fourier transform of the PSF was calculated. Next, the Fourier function was normalized to the zero frequency value. Finally, the Fourier transform function was divided by the first-order Bessel function that defined the frequency content of the holes, resulting in the presampled 2D MTF. The presampled 2D MTF of a 0.1 mm pixel pitch computed radiography system and 0.2 mm pixel pitch flat panel digital imaging system that utilized a cesium iodide scintillator was measured. Comparison of the axial components of the 2D MTF to one-dimensional MTF measurements acquired using an edge device method demonstrated that the two methods produced consistent results

  3. A theoretical study on the performances of thermoelectric heat engine and refrigerator with two-dimensional electron reservoirs

    International Nuclear Information System (INIS)

    Luo, Xiaoguang; Long, Kailin; Wang, Jun; Qiu, Teng; He, Jizhou; Liu, Nian

    2014-01-01

    Theoretical thermoelectric nanophysics models of low-dimensional electronic heat engine and refrigerator devices, comprising two-dimensional hot and cold reservoirs and an interconnecting filtered electron transport mechanism have been established. The models were used to numerically simulate and evaluate the thermoelectric performance and energy conversion efficiencies of these low-dimensional devices, based on three different types of electron transport momentum-dependent filters, referred to herein as k x , k y , and k r filters. Assuming the Fermi-Dirac distribution of electrons, expressions for key thermoelectric performance parameters were derived for the resonant transport processes, in which the transmission of electrons has been approximated as a Lorentzian resonance function. Optimizations were carried out and the corresponding optimized design parameters have been determined, including but not limited to the universal theoretical upper bound of the efficiency at maximum power for heat engines, and the maximum coefficient of performance for refrigerators. From the results, it was determined that k r filter delivers the best thermoelectric performance, followed by the k x filter, and then the k y filter. For refrigerators with any one of three filters, an optimum range for the full width at half maximum of the transport resonance was found to be B T.

  4. Double Fourier analysis for Emotion Identification in Voiced Speech

    International Nuclear Information System (INIS)

    Sierra-Sosa, D.; Bastidas, M.; Ortiz P, D.; Quintero, O.L.

    2016-01-01

    We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented. (paper)

  5. Solution of the two dimensional diffusion and transport equations in a rectangular lattice with an elliptical fuel element using Fourier transform methods: One and two group cases

    International Nuclear Information System (INIS)

    Williams, M.M.R.; Hall, S.K.; Eaton, M.D.

    2014-01-01

    Highlights: • A rectangular reactor cell with an elliptical fuel element. • Solution of transport and diffusion equations by Fourier expansion. • Numerical examples showing convergence. • Two group cell problems. - Abstract: A method for solving the diffusion and transport equations in a rectangular lattice cell with an elliptical fuel element has been developed using a Fourier expansion of the neutron flux. The method is applied to a one group model with a source in the moderator. The cell flux is obtained and also the associated disadvantage factor. In addition to the one speed case, we also consider the two group equations in the cell which now become an eigenvalue problem for the lattice multiplication factor. The method of solution relies upon an efficient procedure to solve a large set of simultaneous linear equations and for this we use the IMSL library routines. Our method is compared with the results from a finite element code. The main drawback of the problem arises from the very large number of terms required in the Fourier series which taxes the storage and speed of the computer. Nevertheless, useful solutions are obtained in geometries that would normally require the use of finite element or analogous methods, for this reason the Fourier method is useful for comparison with that type of numerical approach. Extension of the method to more intricate fuel shapes, such as stars and cruciforms as well as superpositions of these, is possible

  6. Some applications of Fourier's great discovery for beginners

    International Nuclear Information System (INIS)

    Kraftmakher, Yaakov

    2012-01-01

    Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency ω = 2π/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students should be familiar with this subject. A suitable device for demonstrating spectra of electrical signals is a digital storage oscilloscope. Spectra of various waveforms and of AM and FM signals are demonstrated, as well as AM signals from a broadcasting station. Changes in the signals filtered by frequency-selective circuits are seen by comparing the spectra of the input and output voltages. All the experiments are suitable for undergraduate laboratories and usable as classroom demonstrations. (paper)

  7. Regularization of DT-MRI Using 3D Median Filtering Methods

    Directory of Open Access Journals (Sweden)

    Soondong Kwon

    2014-01-01

    Full Text Available DT-MRI (diffusion tensor magnetic resonance imaging tractography is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvectors obtained from tensor matrix, which is different from the conventional isotropic MRI. Tractography based on DT-MRI is known to need many computations and is highly sensitive to noise. Hence, adequate regularization methods, such as image processing techniques, are in demand. Among many regularization methods we are interested in the median filtering method. In this paper, we extended two-dimensional median filters already developed to three-dimensional median filters. We compared four median filtering methods which are two-dimensional simple median method (SM2D, two-dimensional successive Fermat method (SF2D, three-dimensional simple median method (SM3D, and three-dimensional successive Fermat method (SF3D. Three kinds of synthetic data with different altitude angles from axial slices and one kind of human data from MR scanner are considered for numerical implementation by the four filtering methods.

  8. High Performance, Three-Dimensional Bilateral Filtering

    International Nuclear Information System (INIS)

    Bethel, E. Wes

    2008-01-01

    Image smoothing is a fundamental operation in computer vision and image processing. This work has two main thrusts: (1) implementation of a bilateral filter suitable for use in smoothing, or denoising, 3D volumetric data; (2) implementation of the 3D bilateral filter in three different parallelization models, along with parallel performance studies on two modern HPC architectures. Our bilateral filter formulation is based upon the work of Tomasi [11], but extended to 3D for use on volumetric data. Our three parallel implementations use POSIX threads, the Message Passing Interface (MPI), and Unified Parallel C (UPC), a Partitioned Global Address Space (PGAS) language. Our parallel performance studies, which were conducted on a Cray XT4 supercomputer and aquad-socket, quad-core Opteron workstation, show our algorithm to have near-perfect scalability up to 120 processors. Parallel algorithms, such as the one we present here, will have an increasingly important role for use in production visual analysis systems as the underlying computational platforms transition from single- to multi-core architectures in the future.

  9. High Performance, Three-Dimensional Bilateral Filtering

    Energy Technology Data Exchange (ETDEWEB)

    Bethel, E. Wes

    2008-06-05

    Image smoothing is a fundamental operation in computer vision and image processing. This work has two main thrusts: (1) implementation of a bilateral filter suitable for use in smoothing, or denoising, 3D volumetric data; (2) implementation of the 3D bilateral filter in three different parallelization models, along with parallel performance studies on two modern HPC architectures. Our bilateral filter formulation is based upon the work of Tomasi [11], but extended to 3D for use on volumetric data. Our three parallel implementations use POSIX threads, the Message Passing Interface (MPI), and Unified Parallel C (UPC), a Partitioned Global Address Space (PGAS) language. Our parallel performance studies, which were conducted on a Cray XT4 supercomputer and aquad-socket, quad-core Opteron workstation, show our algorithm to have near-perfect scalability up to 120 processors. Parallel algorithms, such as the one we present here, will have an increasingly important role for use in production visual analysis systems as the underlying computational platforms transition from single- to multi-core architectures in the future.

  10. Detection of Point Sources on Two-Dimensional Images Based on Peaks

    Directory of Open Access Journals (Sweden)

    R. B. Barreiro

    2005-09-01

    Full Text Available This paper considers the detection of point sources in two-dimensional astronomical images. The detection scheme we propose is based on peak statistics. We discuss the example of the detection of far galaxies in cosmic microwave background experiments throughout the paper, although the method we present is totally general and can be used in many other fields of data analysis. We consider sources with a Gaussian profile—that is, a fair approximation of the profile of a point source convolved with the detector beam in microwave experiments—on a background modeled by a homogeneous and isotropic Gaussian random field characterized by a scale-free power spectrum. Point sources are enhanced with respect to the background by means of linear filters. After filtering, we identify local maxima and apply our detection scheme, a Neyman-Pearson detector that defines our region of acceptance based on the a priori pdf of the sources and the ratio of number densities. We study the different performances of some linear filters that have been used in this context in the literature: the Mexican hat wavelet, the matched filter, and the scale-adaptive filter. We consider as well an extension to two dimensions of the biparametric scale-adaptive filter (BSAF. The BSAF depends on two parameters which are determined by maximizing the number density of real detections while fixing the number density of spurious detections. For our detection criterion the BSAF outperforms the other filters in the interesting case of white noise.

  11. Fourier transform wavefront control with adaptive prediction of the atmosphere.

    Science.gov (United States)

    Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre

    2007-09-01

    Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

  12. Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation

    Science.gov (United States)

    Pagán Muñoz, Raúl; Hornikx, Maarten

    2017-11-01

    The Fourier Pseudospectral time-domain (Fourier PSTD) method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. This paper presents a hybrid approach to solve the LEE, coupling Fourier PSTD with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of DG at the boundaries, while keeping the efficient Fourier PSTD in the bulk of the domain. The hybridization approach is based on conformal meshes to avoid spatial interpolation of the DG solutions when transferring values from DG to Fourier PSTD, while the data transfer from Fourier PSTD to DG is done utilizing spectral interpolation of the Fourier PSTD solutions. The accuracy of the hybrid approach is presented for one- and two-dimensional acoustic problems and the main sources of error are investigated. It is concluded that the hybrid methodology does not introduce significant errors compared to the Fourier PSTD stand-alone solver. An example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach. Finally, no instabilities were found during long-time calculation using the current hybrid methodology on a two-dimensional domain.

  13. Flat microwave photonic filter based on hybrid of two filters

    International Nuclear Information System (INIS)

    Qi, Chunhui; Pei, Li; Ning, Tigang; Li, Jing; Gao, Song

    2010-01-01

    A new microwave photonic filter (MPF) hybrid of two filters that can realize both multiple taps and a flat bandpass or bandstop response is presented. Based on the phase character of a Mach–Zehnder modulator (MZM), a two taps finite impulse response (FIR) filter is obtained as the first part. The second part is obtained by taking full advantage of the wavelength selectivity of the fiber Bragg grating (FBG) and the gain of a erbium-doped fiber (EDF). Combining the two filters, the flat bandpass or bandstop response is realized by changing the coupler's factor k, the reflectivity of FBG1 R 1 or the gain of the EDF g. Optimizing the system parameters, a flat bandpass response with amplitude depth of more than 45 dB is obtained at k = 0.5, R 1 = 0.33, g = 10, and a flat bandstop response is also obtained at k = 0.4, R 1 = 0.5, g = 2. In addition, the free-spectral range (FSR) can be controlled by changing the length of the EDF and the length difference between two MZMs. The method is proved feasible by some experiments. Such a method offers realistic solutions to support future radio-frequency (RF) optical communication systems

  14. Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method

    Science.gov (United States)

    Kodera, Masako; Wang, Qinghua; Ri, Shien; Tsuda, Hiroshi; Yoshioka, Akira; Sugiyama, Toru; Hamamoto, Takeshi; Miyashita, Naoto

    2018-04-01

    Recently, we have developed a two-dimensional (2D) fast-Fourier-transform (FFT) sampling Moiré technique to visually and quantitatively determine the locations of minute defects in a transmission electron microscopy (TEM) image. We applied this technique for defect detection with GaN high electron mobility transistor (HEMT) devices, and successfully and clearly visualized atom-size defects in AlGaN/GaN crystalline structures. The defect density obtained in the AlGaN/GaN structures is ∼1013 counts/cm2. In addition, we have successfully confirmed that the distribution and number of defects closely depend on the process conditions. Thus, this technique is quite useful for a device development. Moreover, the strain fields in an AlGaN/GaN crystal were effectively calculated with nm-scale resolution using this method. We also demonstrated that this sampling Moiré technique is applicable to silicon devices, which have principal directions different from those of AlGaN/GaN crystals. As a result, we believe that the 2D FFT sampling Moiré method has great potential applications to the discovery of new as yet unknown phenomena occurring between the characteristics of a crystalline material and device performance.

  15. Evaluation of chondromalacia in the knee joint using three dimensional Fourier transformation constructive interference in steady state (CISS)

    International Nuclear Information System (INIS)

    Yoon, Sam Hyun; Ha, Doo Hoe; Kwak, Jin Young; Lee, Young Soo

    2000-01-01

    To assess the usefulness of three-dimensional Fourier transformation constructive interference in steady state (CISS) for the evaluation of chondromalacia. In 110 knee joints which underwent both MR imaging and arthroscopy, the findings were retrospectively reviewed. MR imaging sequences included two-dimensional dual-echo turbo spin-echo imaging along the sagittal and coronal planes, two-dimensional fast low-angle shot (FLASH) with magnetization transfer along the axial plane, and three-dimensional CISS along the sagittal plane. After the cartilage surfaces of each joint were divided into eight areas (each medial and lateral area of patellar facets, trochlear surfaces, femoral condyles, and tibial plateaux), a total of 880 areas were assessed. Using both combined two-dimensional (2-D turbo spin-echo and FLASH) and CISS imaging during different sessions, each chondromalacia case was assigned one of five grades. Arthroscopy revealed the presence of chondromalacia in 162 areas. This was first grade in 77 areas, second grade in 38, third grade in 21, and fourth grade in 26. The sensitivity, specificity, and accuracy of 2-D and CISS imaging were 48.1%, 93.7% and 85.3%, and 45.7%, 95.3% and 86.1%, respectively. Agreement between MR and arthroscopic staging occurred in 81.48% of 2-D imaging procedures and 82.16% of CISS procedures. If a difference of one grade was accepted, these proportions rose to 84.32% and 85.22%, respectively, though this increase was statistically insignificant. Though CISS imaging was less sensitive than 2-D imaging in the grading of chondromalacia, additional CISS imaging can help improve the accuracy of this grading

  16. Evaluation of chondromalacia in the knee joint using three dimensional Fourier transformation constructive interference in steady state (CISS)

    Energy Technology Data Exchange (ETDEWEB)

    Yoon, Sam Hyun; Ha, Doo Hoe; Kwak, Jin Young [College of Medicine, Pochon CHA University, Sungnam (Korea, Republic of); Lee, Young Soo [Pundang CHA General Hospital, College of Medicine, Pochon CHA University, Seoul (Korea, Republic of)

    2000-10-01

    To assess the usefulness of three-dimensional Fourier transformation constructive interference in steady state (CISS) for the evaluation of chondromalacia. In 110 knee joints which underwent both MR imaging and arthroscopy, the findings were retrospectively reviewed. MR imaging sequences included two-dimensional dual-echo turbo spin-echo imaging along the sagittal and coronal planes, two-dimensional fast low-angle shot (FLASH) with magnetization transfer along the axial plane, and three-dimensional CISS along the sagittal plane. After the cartilage surfaces of each joint were divided into eight areas (each medial and lateral area of patellar facets, trochlear surfaces, femoral condyles, and tibial plateaux), a total of 880 areas were assessed. Using both combined two-dimensional (2-D turbo spin-echo and FLASH) and CISS imaging during different sessions, each chondromalacia case was assigned one of five grades. Arthroscopy revealed the presence of chondromalacia in 162 areas. This was first grade in 77 areas, second grade in 38, third grade in 21, and fourth grade in 26. The sensitivity, specificity, and accuracy of 2-D and CISS imaging were 48.1%, 93.7% and 85.3%, and 45.7%, 95.3% and 86.1%, respectively. Agreement between MR and arthroscopic staging occurred in 81.48% of 2-D imaging procedures and 82.16% of CISS procedures. If a difference of one grade was accepted, these proportions rose to 84.32% and 85.22%, respectively, though this increase was statistically insignificant. Though CISS imaging was less sensitive than 2-D imaging in the grading of chondromalacia, additional CISS imaging can help improve the accuracy of this grading.

  17. A vector Wiener filter for dual-radionuclide imaging

    International Nuclear Information System (INIS)

    Links, J.M.; Prince, J.L.; Gupta, S.N.

    1996-01-01

    The routine use of a single radionuclide for patient imaging in nuclear medicine can be complemented by studies employing two tracers to examine two different processes in a single organ, most frequently by simultaneous imaging of both radionuclides in two different energy windows. In addition, simultaneous transmission/emission imaging with dual-radionuclides has been described, with one radionuclide used for the transmission study and a second for the emission study. There is thus currently considerable interest in dual-radionuclide imaging. A major problem with all dual-radionuclide imaging is the crosstalk between the two radionuclides. Such crosstalk frequently occurs, because scattered radiation from the higher energy radionuclide is detected in the lower energy window, and because the lower energy radionuclide may have higher energy emissions which are detected in the higher energy window. The authors have previously described the use of Fourier-based restoration filtering in single photon emission computed tomography (SPECT) and positron emission tomography (PET) to improve quantitative accuracy by designing a Wiener or other Fourier filter to partially restore the loss of contrast due to scatter and finite spatial resolution effects. The authors describe here the derivation and initial validation of an extension of such filtering for dual-radionuclide imaging that simultaneously (1) improves contrast in each radionuclide's direct image, (2) reduces image noise, and (3) reduces the crosstalk contribution from the other radionuclide. This filter is based on a vector version of the Wiener filter, which is shown to be superior [in the minimum mean square error (MMSE) sense] to the sequential application of separate crosstalk and restoration filters

  18. Fourier rebinning and consistency equations for time-of-flight PET planograms.

    Science.gov (United States)

    Li, Yusheng; Defrise, Michel; Matej, Samuel; Metzler, Scott D

    2016-01-01

    Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms

  19. Filter and Filter Bank Design for Image Texture Recognition

    Energy Technology Data Exchange (ETDEWEB)

    Randen, Trygve

    1997-12-31

    The relevance of this thesis to energy and environment lies in its application to remote sensing such as for instance sea floor mapping and seismic pattern recognition. The focus is on the design of two-dimensional filters for feature extraction, segmentation, and classification of digital images with textural content. The features are extracted by filtering with a linear filter and estimating the local energy in the filter response. The thesis gives a review covering broadly most previous approaches to texture feature extraction and continues with proposals of some new techniques. 143 refs., 59 figs., 7 tabs.

  20. Stress wave calculations in composite plates using the fast Fourier transform.

    Science.gov (United States)

    Moon, F. C.

    1973-01-01

    The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

  1. Application of finite Fourier transformation for the solution of the diffusion equation

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke

    1991-01-01

    The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)

  2. Projection multiplex recording of computer-synthesised one-dimensional Fourier holograms for holographic memory systems: mathematical and experimental modelling

    Energy Technology Data Exchange (ETDEWEB)

    Betin, A Yu; Bobrinev, V I; Verenikina, N M; Donchenko, S S; Odinokov, S B [Research Institute ' Radiotronics and Laser Engineering' , Bauman Moscow State Technical University, Moscow (Russian Federation); Evtikhiev, N N; Zlokazov, E Yu; Starikov, S N; Starikov, R S [National Reseach Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation)

    2015-08-31

    A multiplex method of recording computer-synthesised one-dimensional Fourier holograms intended for holographic memory devices is proposed. The method potentially allows increasing the recording density in the previously proposed holographic memory system based on the computer synthesis and projection recording of data page holograms. (holographic memory)

  3. Two-dimensional errors

    International Nuclear Information System (INIS)

    Anon.

    1991-01-01

    This chapter addresses the extension of previous work in one-dimensional (linear) error theory to two-dimensional error analysis. The topics of the chapter include the definition of two-dimensional error, the probability ellipse, the probability circle, elliptical (circular) error evaluation, the application to position accuracy, and the use of control systems (points) in measurements

  4. Fourier transform methods for calculating action variables and semiclassical eigenvalues for coupled oscillator systems

    International Nuclear Information System (INIS)

    Eaker, C.W.; Schatz, G.C.; De Leon, N.; Heller, E.J.

    1984-01-01

    Two methods for calculating the good action variables and semiclassical eigenvalues for coupled oscillator systems are presented, both of which relate the actions to the coefficients appearing in the Fourier representation of the normal coordinates and momenta. The two methods differ in that one is based on the exact expression for the actions together with the EBK semiclassical quantization condition while the other is derived from the Sorbie--Handy (SH) approximation to the actions. However, they are also very similar in that the actions in both methods are related to the same set of Fourier coefficients and both require determining the perturbed frequencies in calculating actions. These frequencies are also determined from the Fourier representations, which means that the actions in both methods are determined from information entirely contained in the Fourier expansion of the coordinates and momenta. We show how these expansions can very conveniently be obtained from fast Fourier transform (FFT) methods and that numerical filtering methods can be used to remove spurious Fourier components associated with the finite trajectory integration duration. In the case of the SH based method, we find that the use of filtering enables us to relax the usual periodicity requirement on the calculated trajectory. Application to two standard Henon--Heiles models is considered and both are shown to give semiclassical eigenvalues in good agreement with previous calculations for nondegenerate and 1:1 resonant systems. In comparing the two methods, we find that although the exact method is quite general in its ability to be used for systems exhibiting complex resonant behavior, it converges more slowly with increasing trajectory integration duration and is more sensitive to the algorithm for choosing perturbed frequencies than the SH based method

  5. Maximum-entropy data restoration using both real- and Fourier-space analysis

    International Nuclear Information System (INIS)

    Anderson, D.M.; Martin, D.C.; Thomas, E.L.

    1989-01-01

    An extension of the maximum-entropy (ME) data-restoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-noise ratio for periodic information in Fourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier filtering. This procedure incorporates concepts underlying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introduced that speeds convergence of the ME computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases improvement can be obtained from two to four stages of iteration. It is shown that in traditional Fourier filtering spurious features can be induced by selection or elimination of Fourier components without regard to their statistical significance. With the present approach there is no such freedom for the user to exert personal bias, so that features present in the final image and power spectrum are those which have survived the tests of statistical significance in both real and Fourier space. However, it is still possible for periodicities to 'bleed' across sharp boundaries. An 'uncertainty' relation is derived describing the inverse relationship between the resolution of these boundaries and the level of noise that can be eliminated. (orig./BHO)

  6. Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

    Energy Technology Data Exchange (ETDEWEB)

    Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.

    2006-01-01

    Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.

  7. Clifford Fourier transform on vector fields.

    Science.gov (United States)

    Ebling, Julia; Scheuermann, Gerik

    2005-01-01

    Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.

  8. Fourier imaging of non-linear structure formation

    Energy Technology Data Exchange (ETDEWEB)

    Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)

    2017-04-01

    We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

  9. Fourier imaging of non-linear structure formation

    International Nuclear Information System (INIS)

    Brandbyge, Jacob; Hannestad, Steen

    2017-01-01

    We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

  10. Fourier domain optical coherence tomography achieves full range complex imaging in vivo by introducing a carrier frequency during scanning

    International Nuclear Information System (INIS)

    Wang, Ruikang K

    2007-01-01

    The author describes a Fourier domain optical coherence tomography (FDOCT) system that is capable of full range complex imaging in vivo. This is achieved by introducing a constant carrier frequency into the OCT spectral interferograms at the time when imaging is performed. The complex functions of the spatial interferograms formed by each single wavelength are constructed before performing the Fourier transformation to localize the scatters within a sample. Two algorithms, based on Fourier filtering and Hilbert transformation, respectively, are described to achieve the full range complex FDOCT imaging. It is shown that the Hilbert transformation approach delivers better performance than the Fourier filtering method does in terms of tolerating the sample movement in vivo. The author finally demonstrates experimentally the system and algorithms for true in vivo imaging at a rate of 20 000 axial scans per second

  11. ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES

    Directory of Open Access Journals (Sweden)

    Nikola Stefanović

    2007-06-01

    Full Text Available In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic leadership style, leadership theory researchers use two dimensional matrices. The two-dimensional matrices define leadership styles on the basis of different parameters. By using these parameters, one can identify two-dimensional styles.

  12. Fourier series, Fourier transform and their applications to mathematical physics

    CERN Document Server

    Serov, Valery

    2017-01-01

    This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.  Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing.  The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations.  The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...

  13. Effects of statistical quality, sampling rate and temporal filtering techniques on the extraction of functional parameters from the left ventricular time-activity curves

    Energy Technology Data Exchange (ETDEWEB)

    Guignard, P.A.; Chan, W. (Royal Melbourne Hospital, Parkville (Australia). Dept. of Nuclear Medicine)

    1984-09-01

    Several techniques for the processing of a series of curves derived from two left ventricular time-activity curves acquired at rest and during exercise with a nuclear stethoscope were evaluated. They were three and five point time smoothing. Fourier filtering preserving one to four harmonics (H), truncated curve Fourier filtering, and third degree polynomial curve fitting. Each filter's ability to recover, with fidelity, systolic and diastolic function parameters was evaluated under increasingly 'noisy' conditions and at several sampling rates. Third degree polynomial curve fittings and truncated Fourier filters exhibited very high sensitivity to noise. Three and five point time smoothing had moderate sensitivity to noise, but were highly affected by sampling rate. Fourier filtering preserving 2H or 3H produced the best compromise with high resilience to noise and independence of sampling rate as far as the recovery of these functional parameters is concerned.

  14. Effects of statistical quality, sampling rate and temporal filtering techniques on the extraction of functional parameters from the left ventricular time-activity curves

    International Nuclear Information System (INIS)

    Guignard, P.A.; Chan, W.

    1984-01-01

    Several techniques for the processing of a series of curves derived from two left ventricular time-activity curves acquired at rest and during exercise with a nuclear stethoscope were evaluated. They were three and five point time smoothing. Fourier filtering preserving one to four harmonics (H), truncated curve Fourier filtering, and third degree polynomial curve fitting. Each filter's ability to recover, with fidelity, systolic and diastolic function parameters was evaluated under increasingly 'noisy' conditions and at several sampling rates. Third degree polynomial curve fittings and truncated Fourier filters exhibited very high sensitivity to noise. Three and five point time smoothing had moderate sensitivity to noise, but were highly affected by sampling rate. Fourier filtering preserving 2H or 3H produced the best compromise with high resilience to noise and independence of sampling rate as far as the recovery of these functional parameters is concerned. (author)

  15. Two-stage nonrecursive filter/decimator

    International Nuclear Information System (INIS)

    Yoder, J.R.; Richard, B.D.

    1980-08-01

    A two-stage digital filter/decimator has been designed and implemented to reduce the sampling rate associated with the long-term computer storage of certain digital waveforms. This report describes the design selection and implementation process and serves as documentation for the system actually installed. A filter design with finite-impulse response (nonrecursive) was chosen for implementation via direct convolution. A newly-developed system-test statistic validates the system under different computer-operating environments

  16. Generalized Fourier slice theorem for cone-beam image reconstruction.

    Science.gov (United States)

    Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

    2015-01-01

    The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

  17. A filtering technique for solving the advection equation in two-phase flow problems

    International Nuclear Information System (INIS)

    Devals, C.; Heniche, M.; Bertrand, F.; Tanguy, P.A.; Hayes, R.E.

    2004-01-01

    The aim of this work is to develop a numerical strategy for the simulation of two-phase flow in the context of chemical engineering applications. The finite element method has been chosen because of its flexibility to deal with complex geometries. One of the key points of two-phase flow simulation is to determine precisely the position of the interface between the two phases, which is an unknown of the problem. In this case, the interface can be tracked by the advection of the so-called color function. It is well known that the solution of the advection equation by most numerical schemes, including the Streamline Upwind Petrov-Galerkin (SUPG) method, may exhibit spurious oscillations. This work proposes an approach to filter out these oscillations by means of a change of variable that is efficient for both steady state and transient cases. First, the filtering technique will be presented in detail. Then, it will be applied to two-dimensional benchmark problems, namely, the advection skew to the mesh and the Zalesak's problems. (author)

  18. Two-dimensional NMR spectrometry

    International Nuclear Information System (INIS)

    Farrar, T.C.

    1987-01-01

    This article is the second in a two-part series. In part one (ANALYTICAL CHEMISTRY, May 15) the authors discussed one-dimensional nuclear magnetic resonance (NMR) spectra and some relatively advanced nuclear spin gymnastics experiments that provide a capability for selective sensitivity enhancements. In this article and overview and some applications of two-dimensional NMR experiments are presented. These powerful experiments are important complements to the one-dimensional experiments. As in the more sophisticated one-dimensional experiments, the two-dimensional experiments involve three distinct time periods: a preparation period, t 0 ; an evolution period, t 1 ; and a detection period, t 2

  19. Fourier coefficientes computation in two variables, a distributional version

    OpenAIRE

    Carlos Manuel Ulate R.

    2015-01-01

    The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.

  20. Fourier descriptor classification of differential eddy current probe impedance plane trajectories

    International Nuclear Information System (INIS)

    Lord, W.; Satish, S.R.

    1984-01-01

    This chapter describes the use of a parametric model for representing the two-dimensional eddy current impedance plane trajectory. The main advantage of this approach is the ability to reconstruct the trajectory from the model coefficients. Fourier descriptors are used to facilitate defect classification. The Fourier descriptors are obtained by expanding the complex contour function in a Fourier series. Functions of Fourier coefficients which are invariant under transformation of the trajectory are derived and incorporated into a feature vector. Defect classification is obtained by using the K-Means algorithm to cluster the feature vectors. It is demonstrated that the Fourier descriptor approach represents a powerful tool which have several advantages over nonparametric approaches including its insensitivity to drift in the eddy current instrument as well as variations in the probe speed

  1. Digital filtering techniques applied to electric power systems protection; Tecnicas de filtragem digital aplicadas a protecao de sistemas eletricos de potencia

    Energy Technology Data Exchange (ETDEWEB)

    Brito, Helio Glauco Ferreira

    1996-12-31

    This work introduces an analysis and a comparative study of some of the techniques for digital filtering of the voltage and current waveforms from faulted transmission lines. This study is of fundamental importance for the development of algorithms applied to digital protection of electric power systems. The techniques studied are based on the Discrete Fourier Transform theory, the Walsh functions and the Kalman filter theory. Two aspects were emphasized in this study: Firstly, the non-recursive techniques were analysed with the implementation of filters based on Fourier theory and the Walsh functions. Secondly, recursive techniques were analyzed, with the implementation of the filters based on the Kalman theory and once more on the Fourier theory. (author) 56 refs., 25 figs., 16 tabs.

  2. Two-dimensional unwrapped phase inversion with damping and a Gaussian filter

    KAUST Repository

    Choi, Yun Seok; Alkhalifah, Tariq Ali

    2014-01-01

    Phase wrapping is one of main causes of the local minima problem in waveform inversion. However, the unwrapping process for 2D phase maps that includes singular points (residues) is complicated and does not guarantee unique solutions. We employ an exponential damping to eliminate the residues in the 2D phase maps, which makes the 2D phase unwrapping process easy and produce a unique solution. A recursive inversion process using the damped unwrapped phase provides an opportunity to invert for smooth background updates first, and higher resolution updates later as we reduce the damping. We also apply a Gaussian filter to the gradient to mitigate the edge artifacts resulting from the narrow shape of the sensitivity kernels at high damping. Numerical examples demonstrate that our unwrapped phase inversion with damping and a Gaussian filter produces good convergent results even for a 3Hz single frequency of Marmousi dataset and with a starting model far from the true model.

  3. Separation of complex fringe patterns using two-dimensional continuous wavelet transform.

    Science.gov (United States)

    Pokorski, Krzysztof; Patorski, Krzysztof

    2012-12-10

    A method for processing fringe patterns containing additively superimposed multiple fringe sets is presented. It enables to analyze different fringe families present in a single image separately. The proposed method is based on a two-dimensional continuous wavelet transform. A robust ridge extraction algorithm for a single fringe set extraction is presented. The method is fully automatic and requires no user interference. Spectral separation of fringe families is not required. Simulations are presented to verify performance and advantage of the proposed method over the Fourier transform based technique. Method validity has been confirmed using experimental images.

  4. Fourier coefficientes computation in two variables, a distributional version

    Directory of Open Access Journals (Sweden)

    Carlos Manuel Ulate R.

    2015-01-01

    Full Text Available The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.

  5. Image registration under translation and rotation in two-dimensional planes using Fourier slice theorem.

    Science.gov (United States)

    Pohit, M; Sharma, J

    2015-05-10

    Image recognition in the presence of both rotation and translation is a longstanding problem in correlation pattern recognition. Use of log polar transform gives a solution to this problem, but at a cost of losing the vital phase information from the image. The main objective of this paper is to develop an algorithm based on Fourier slice theorem for measuring the simultaneous rotation and translation of an object in a 2D plane. The algorithm is applicable for any arbitrary object shift for full 180° rotation.

  6. The Fourier U(2 Group and Separation of Discrete Variables

    Directory of Open Access Journals (Sweden)

    Kurt Bernardo Wolf

    2011-06-01

    Full Text Available The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R, whose maximal compact subgroup is the Fourier group U(2_F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4. Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle coordinates, thus realizing one case of separation in two discrete coordinates. The N^2-vectors in this space are digital (pixellated images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.

  7. Evaluating Assessment Using N-Dimensional Filtering.

    Science.gov (United States)

    Dron, Jon; Boyne, Chris; Mitchell, Richard

    This paper describes the use of the CoFIND (Collaborative Filter in N Dimensions) system to evaluate two assessment styles. CoFIND is a resource database that organizes itself around its users' needs. Learners enter resources, categorize, then rate them using "qualities," aspects of resources which learners find worthwhile, the n…

  8. Fourier rebinning and consistency equations for time-of-flight PET planograms

    International Nuclear Information System (INIS)

    Li, Yusheng; Matej, Samuel; Metzler, Scott D; Defrise, Michel

    2016-01-01

    Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John’s equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations (FCEs) and the Fourier–John equation (FJE), which are the duals of the consistency equations and John’s equation, respectively. We then solve the FCEs and FJE using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give

  9. An Efficient State–Parameter Filtering Scheme Combining Ensemble Kalman and Particle Filters

    KAUST Repository

    Ait-El-Fquih, Boujemaa

    2017-12-11

    This work addresses the state-parameter filtering problem for dynamical systems with relatively large-dimensional state and low-dimensional parameters\\' vector. A Bayesian filtering algorithm combining the strengths of the particle filter (PF) and the ensemble Kalman filter (EnKF) is proposed. At each assimilation cycle of the proposed EnKF-PF, the PF is first used to sample the parameters\\' ensemble followed by the EnKF to compute the state ensemble conditional on the resulting parameters\\' ensemble. The proposed scheme is expected to be more efficient than the traditional state augmentation techniques, which suffer from the curse of dimensionality and inconsistency that is particularly pronounced when the state is a strongly nonlinear function of the parameters. In the new scheme, the EnKF and PF interact via their ensembles\\' members, in contrast with the recently introduced two-stage EnKF-PF (TS-EnKF-PF), which exchanges point estimates between EnKF and PF while requiring almost double the computational load. Numerical experiments are conducted with the Lorenz-96 model to assess the behavior of the proposed filter and to evaluate its performances against the joint PF, joint EnKF, and TS-EnKF-PF. Numerical results suggest that the EnKF-PF performs best in all tested scenarios. It was further found to be more robust, successfully estimating both state and parameters in different sensitivity experiments.

  10. An Efficient State–Parameter Filtering Scheme Combining Ensemble Kalman and Particle Filters

    KAUST Repository

    Ait-El-Fquih, Boujemaa; Hoteit, Ibrahim

    2017-01-01

    This work addresses the state-parameter filtering problem for dynamical systems with relatively large-dimensional state and low-dimensional parameters' vector. A Bayesian filtering algorithm combining the strengths of the particle filter (PF) and the ensemble Kalman filter (EnKF) is proposed. At each assimilation cycle of the proposed EnKF-PF, the PF is first used to sample the parameters' ensemble followed by the EnKF to compute the state ensemble conditional on the resulting parameters' ensemble. The proposed scheme is expected to be more efficient than the traditional state augmentation techniques, which suffer from the curse of dimensionality and inconsistency that is particularly pronounced when the state is a strongly nonlinear function of the parameters. In the new scheme, the EnKF and PF interact via their ensembles' members, in contrast with the recently introduced two-stage EnKF-PF (TS-EnKF-PF), which exchanges point estimates between EnKF and PF while requiring almost double the computational load. Numerical experiments are conducted with the Lorenz-96 model to assess the behavior of the proposed filter and to evaluate its performances against the joint PF, joint EnKF, and TS-EnKF-PF. Numerical results suggest that the EnKF-PF performs best in all tested scenarios. It was further found to be more robust, successfully estimating both state and parameters in different sensitivity experiments.

  11. Morphology of bipolar planetary nebulae. I. Two-dimensional spectrophotometry

    International Nuclear Information System (INIS)

    Pascoli, G.

    1990-01-01

    Two-dimensional spectrophotometric observations of bipolar planetary nebulae were performed by using a CCD detector mounted at the Cassegrain focus of either 1.54 m Danish Telescope or 2.2 m German Telescope at La Silla (ESO) in Chile. Emission lines have been selected with the help of narrow band-pass interference filters (Δλ∼ 10 - 20 A). Isophotal maps in various lines Hα, [NII] λ 6584, [OIII] λ 5007 and [SII] λλ 6717-6731 are presented. Particular attention has been given to scrutinize the symmetries inside a few bipolar planetary nebulae, in order to subsequently investigate their space structure

  12. Two-dimensional simulation of broad-band ferrite electromagnetic wave absorbers by using the FDTD method

    Energy Technology Data Exchange (ETDEWEB)

    Yoon, Hyun Jin; Kim, Dong Il [Korea Maritime University, Busan (Korea, Republic of)

    2004-10-15

    The purpose of this simulation study is to design and fabricate an electromagnetic (EM) wave absorber in order to develop a wide-band absorber. We have proposed and modeled a bird-eye-type and cutting-cone-type EM wave absorber by using the equivalent material constants method (EMCM), and we simulated them by using a finite-difference time-domain (FDTD) method. A two or a three-dimensional simulation would be desirable to analyze the EM wave absorber characteristics and to develop new structures. The two-dimensional FDTD simulation requires less computer resources than a three-dimensional simulation to consider the structural effects of the EM wave absorbers. The numerical simulation by using the FDTD method shows propagating EM waves in various types of periodic structure EM wave absorbers. Simultaneously, a Fourier analysis is used to characterize the input pulse and the reflected EM waves for ferrite absorbers with various structures. The results have a wide-band reflection-reducing characteristic. The validity of the proposed model was confirmed by comparing the two-dimensional simulation with the experimental results. The simulations were carried out in the frequency band from 30 MHz to 10 GHz.

  13. Two-dimensional simulation of broad-band ferrite electromagnetic wave absorbers by using the FDTD method

    International Nuclear Information System (INIS)

    Yoon, Hyun Jin; Kim, Dong Il

    2004-01-01

    The purpose of this simulation study is to design and fabricate an electromagnetic (EM) wave absorber in order to develop a wide-band absorber. We have proposed and modeled a bird-eye-type and cutting-cone-type EM wave absorber by using the equivalent material constants method (EMCM), and we simulated them by using a finite-difference time-domain (FDTD) method. A two or a three-dimensional simulation would be desirable to analyze the EM wave absorber characteristics and to develop new structures. The two-dimensional FDTD simulation requires less computer resources than a three-dimensional simulation to consider the structural effects of the EM wave absorbers. The numerical simulation by using the FDTD method shows propagating EM waves in various types of periodic structure EM wave absorbers. Simultaneously, a Fourier analysis is used to characterize the input pulse and the reflected EM waves for ferrite absorbers with various structures. The results have a wide-band reflection-reducing characteristic. The validity of the proposed model was confirmed by comparing the two-dimensional simulation with the experimental results. The simulations were carried out in the frequency band from 30 MHz to 10 GHz.

  14. Two-dimensional linear and nonlinear Talbot effect from rogue waves.

    Science.gov (United States)

    Zhang, Yiqi; Belić, Milivoj R; Petrović, Milan S; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Lu, Keqing; Zhang, Yanpeng

    2015-03-01

    We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.

  15. Integrable systems with quadratic nonlinearity in Fourier space

    International Nuclear Information System (INIS)

    Marikhin, V.G.

    2003-01-01

    The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed

  16. Extremely compact formulas for the Fourier transform of a product of two-centre Slater-type orbitals

    International Nuclear Information System (INIS)

    Vukovic, T; Dmitrovic, S

    2010-01-01

    A compact formula for the Fourier transform of a product of Slater-type orbitals on different centres is derived. The integral is reduced to a finite one-dimensional integration over non-oscillatory hypergeometric functions of type 1 F 2 (x;y;z). The formula is valid for all quantum numbers and does not involve the reduced Bessel functions that are usually used to evaluate these integrals. Reduced formulas are calculated for some special directions in the reciprocal space. Also, some useful identities for the Fourier transforms of a product of Slater-type orbitals with correlated sets of parameters are obtained. In order to illustrate simple and efficient use of the presented results, we have applied them to graphene.

  17. Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

    Science.gov (United States)

    Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

    2010-01-01

    We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

  18. An improved analytic solution for analysis of particle trajectories in fibrous, two-dimensional filters

    International Nuclear Information System (INIS)

    Marshall, H.; Sahraoui, M.; Kaviany, M.

    1994-01-01

    The Kuwabara solution for creeping fluid flow through periodic arrangement of cylinders is widely used in analytic and numerical studies of fibrous filters. Numerical solutions have shown that the Kuwabara solution has systematic errors, and when used for the particle trajectories in filters it results in some error in the predicted filter efficiency. The numerical solutions, although accurate, preclude further analytic treatments, and are not as compact and convenient to use as the Kuwabara solution. By reexamining the outer boundary conditions of the Kuwabara solution, a correction term to the Kuwabara solution has been derived to obtain an extended solution that is more accurate and improves prediction of the filter efficiency. By comparison with the numerical solutions, it is shown that the Kuwabara solution is the high porosity asymptote, and that the extended solution has an improved porosity dependence. A rectification is explained that can make particle collection less efficient for periodic, in-line arrangements of fibers with particle diffusion or body force. This rectification also results in the alignment of particles with inertia (i.e., high Stokes number particles)

  19. Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations

    Directory of Open Access Journals (Sweden)

    Liping Gao

    2017-01-01

    Full Text Available In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell’s equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.

  20. Teaching stable two-mirror resonators through the fractional Fourier transform

    International Nuclear Information System (INIS)

    Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

    2010-01-01

    We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects.

  1. Discrete Fourier and wavelet transforms an introduction through linear algebra with applications to signal processing

    CERN Document Server

    Goodman, Roe W

    2016-01-01

    This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

  2. Flexible time-varying filter banks

    Science.gov (United States)

    Tuncer, Temel E.; Nguyen, Truong Q.

    1993-09-01

    Linear phase maximally flat FIR Butterworth filter approximations are discussed and a new filter design method is introduced. This variable cutoff filter design method uses the cosine modulated versions of a prototype filter. The design procedure is simple and different variants of this procedure can be used to obtain close to optimum linear phase filters. Using this method, flexible time-varying filter banks with good reconstruction error are introduced. These types of oversampled filter banks have small magnitude error which can be easily controlled by the appropriate choice of modulation frequency. This error can be further decreased by magnitude equalization without increasing the computational complexity considerably. Two dimensional design examples are also given.

  3. Topological Valley Transport in Two-dimensional Honeycomb Photonic Crystals.

    Science.gov (United States)

    Yang, Yuting; Jiang, Hua; Hang, Zhi Hong

    2018-01-25

    Two-dimensional photonic crystals, in analogy to AB/BA stacking bilayer graphene in electronic system, are studied. Inequivalent valleys in the momentum space for photons can be manipulated by simply engineering diameters of cylinders in a honeycomb lattice. The inequivalent valleys in photonic crystal are selectively excited by a designed optical chiral source and bulk valley polarizations are visualized. Unidirectional valley interface states are proved to exist on a domain wall connecting two photonic crystals with different valley Chern numbers. With the similar optical vortex index, interface states can couple with bulk valley polarizations and thus valley filter and valley coupler can be designed. Our simple dielectric PC scheme can help to exploit the valley degree of freedom for future optical devices.

  4. Study of the characteristics of forced homogeneous turbulence using band-pass Fourier filtering

    Energy Technology Data Exchange (ETDEWEB)

    Kareem, Waleed Abdel [Suez Canal University, Suez (Egypt)

    2012-03-15

    Simulations of forced homogeneous isotropic turbulence with resolutions of 128{sup 3} and 256{sup 3} using the Lattice Boltzmann method are carried out. The multi-scale vortical structures are identified using the band-pass Fourier cutoff filtering. Three fields at each simulation are extracted and their characteristics are studied. The vortical structures are visualized using the Q-identification method. A new lattice segmentation scheme to identify the central axes of the vortical structures is introduced. The central points of each vortex are identified and they are connected using the direction cosines technique. Results show that the Q-spectrum of the fine scale field survives at low and high wave-numbers. However, the large and intermediate Q-spectra survives till wave-numbers less than or equal to twice the used velocity cutoff wave-numbers. It is found that the extracted central axes clearly resemble the corresponding vortical structures at each scale. Using the central axes scheme, the radii and lengths of the vortical structures at each scale are determined and compared. It is also found that the radii of the identified vortical structures at each scale in both simulations are of the order of several times the Kolmogorov microscales.

  5. Novel Control Strategy for VSI and CSI Active Filters and Comparing These Two Types of Filters

    Directory of Open Access Journals (Sweden)

    Gholam Reza Arab

    2014-10-01

    Full Text Available Recently to eliminate the harmonics and improve the power factor of the power networks, much attention has been attracted to active filters. The advantages of these filters are lower volume and their better compensating characteristics than the passive filters. In conventional sliding mode controllers, the source current waveform is fluctuated in near to zero values. In this paper, using a new sliding technique, lower Total Harmonic Distortion (THD in source current is obtained and the current waveform is improved. As well as, two novel control strategies for two types of active filters, VSI and CSI is proposed and then these two types of filters are compared to reduce THD value of source current.The proposed controlled strategies are simulated by MATLAB/Simulink. The Simulation results confirm that the proposed strategies reduce the THD of source current more than other strategies, and active filter based on CSI has a better performance than active filter based on VSI with a dead time area (for avoiding short circuit of the source in high powers.

  6. Novel properties of the Fourier decomposition of the sinogram

    International Nuclear Information System (INIS)

    Edholm, P.R.; Lewitt, R.M.; Lindholm, B.

    1986-01-01

    The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency ω (continuous) and angular harmonic number n (discrete). For absolute value of ω large, the Fourier coefficients on the line n=kω of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed

  7. Generalized multi-dimensional adaptive filtering for conventional and spiral single-slice, multi-slice, and cone-beam CT

    International Nuclear Information System (INIS)

    Kachelriess, Marc; Watzke, Oliver; Kalender, Willi A.

    2001-01-01

    In modern computed tomography (CT) there is a strong desire to reduce patient dose and/or to improve image quality by increasing spatial resolution and decreasing image noise. These are conflicting demands since increasing resolution at a constant noise level or decreasing noise at a constant resolution level implies a higher demand on x-ray power and an increase of patient dose. X-ray tube power is limited due to technical reasons. We therefore developed a generalized multi-dimensional adaptive filtering approach that applies nonlinear filters in up to three dimensions in the raw data domain. This new method differs from approaches in the literature since our nonlinear filters are applied not only in the detector row direction but also in the view and in the z-direction. This true three-dimensional filtering improves the quantum statistics of a measured projection value proportional to the third power of the filter size. Resolution tradeoffs are shared among these three dimensions and thus are considerably smaller as compared to one-dimensional smoothing approaches. Patient data of spiral and sequential single- and multi-slice CT scans as well as simulated spiral cone-beam data were processed to evaluate these new approaches. Image quality was assessed by evaluation of difference images, by measuring the image noise and the noise reduction, and by calculating the image resolution using point spread functions. The use of generalized adaptive filters helps to reduce image noise or, alternatively, patient dose. Image noise structures, typically along the direction of the highest attenuation, are effectively reduced. Noise reduction values of typically 30%-60% can be achieved in noncylindrical body regions like the shoulder. The loss in image resolution remains below 5% for all cases. In addition, the new method has a great potential to reduce metal artifacts, e.g., in the hip region

  8. On the moments of the Wigner distribution and the fractional Fourier transform

    NARCIS (Netherlands)

    Alieva, T.; Bastiaans, M.J.; Veen, J.P.

    2000-01-01

    A Fourier transformation maps a one-dimensional time signal into a one-dimensional frequency function, the signal spectrum. Although the Fourier transform provides the signal's spectral content, it fails to indicate the time location of the spectral components, which is important, for example, when

  9. Bias aware Kalman filters

    DEFF Research Database (Denmark)

    Drecourt, J.-P.; Madsen, H.; Rosbjerg, Dan

    2006-01-01

    This paper reviews two different approaches that have been proposed to tackle the problems of model bias with the Kalman filter: the use of a colored noise model and the implementation of a separate bias filter. Both filters are implemented with and without feedback of the bias into the model state....... The colored noise filter formulation is extended to correct both time correlated and uncorrelated model error components. A more stable version of the separate filter without feedback is presented. The filters are implemented in an ensemble framework using Latin hypercube sampling. The techniques...... are illustrated on a simple one-dimensional groundwater problem. The results show that the presented filters outperform the standard Kalman filter and that the implementations with bias feedback work in more general conditions than the implementations without feedback. 2005 Elsevier Ltd. All rights reserved....

  10. EMI filter design

    CERN Document Server

    Ozenbaugh, Richard Lee

    2011-01-01

    With today's electrical and electronics systems requiring increased levels of performance and reliability, the design of robust EMI filters plays a critical role in EMC compliance. Using a mix of practical methods and theoretical analysis, EMI Filter Design, Third Edition presents both a hands-on and academic approach to the design of EMI filters and the selection of components values. The design approaches covered include matrix methods using table data and the use of Fourier analysis, Laplace transforms, and transfer function realization of LC structures. This edition has been fully revised

  11. Self-consistent EXAFS PDF Projection Method by Matched Correction of Fourier Filter Signal Distortion

    International Nuclear Information System (INIS)

    Lee, Jay Min; Yang, Dong-Seok

    2007-01-01

    Inverse problem solving computation was performed for solving PDF (pair distribution function) from simulated data EXAFS based on data FEFF. For a realistic comparison with experimental data, we chose a model of the first sub-shell Mn-0 pair showing the Jahn Teller distortion in crystalline LaMnO3. To restore the Fourier filtering signal distortion, involved in the first sub-shell information isolated from higher shell contents, relevant distortion matching function was computed initially from the proximity model, and iteratively from the prior-guess during consecutive regularization computation. Adaptive computation of EXAFS background correction is an issue of algorithm development, but our preliminary test was performed under the simulated background correction perfectly excluding the higher shell interference. In our numerical result, efficient convergence of iterative solution indicates a self-consistent tendency that a true PDF solution is convinced as a counterpart of genuine chi-data, provided that a background correction function is iteratively solved using an extended algorithm of MEPP (Matched EXAFS PDF Projection) under development

  12. Application of Tandem Two-Dimensional Mass Spectrometry for Top-Down Deep Sequencing of Calmodulin.

    Science.gov (United States)

    Floris, Federico; Chiron, Lionel; Lynch, Alice M; Barrow, Mark P; Delsuc, Marc-André; O'Connor, Peter B

    2018-06-04

    Two-dimensional mass spectrometry (2DMS) involves simultaneous acquisition of the fragmentation patterns of all the analytes in a mixture by correlating their precursor and fragment ions by modulating precursor ions systematically through a fragmentation zone. Tandem two-dimensional mass spectrometry (MS/2DMS) unites the ultra-high accuracy of Fourier transform ion cyclotron resonance (FT-ICR) MS/MS and the simultaneous data-independent fragmentation of 2DMS to achieve extensive inter-residue fragmentation of entire proteins. 2DMS was recently developed for top-down proteomics (TDP), and applied to the analysis of calmodulin (CaM), reporting a cleavage coverage of about ~23% using infrared multiphoton dissociation (IRMPD) as fragmentation technique. The goal of this work is to expand the utility of top-down protein analysis using MS/2DMS in order to extend the cleavage coverage in top-down proteomics further into the interior regions of the protein. In this case, using MS/2DMS, the cleavage coverage of CaM increased from ~23% to ~42%. Graphical Abstract Two-dimensional mass spectrometry, when applied to primary fragment ions from the source, allows deep-sequencing of the protein calmodulin.

  13. Finite difference time domain calculation of three-dimensional phononic band structures using a postprocessing method based on the filter diagonalization

    International Nuclear Information System (INIS)

    Su Xiaoxing; Ma Tianxue; Wang Yuesheng

    2011-01-01

    If the band structure of a three-dimensional (3D) phononic crystal (PNC) is calculated by using the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT)-based postprocessing method, good results can only be ensured by a sufficiently large number of FDTD iterations. On a common computer platform, the total computation time will be very long. To overcome this difficulty, an excellent harmonic inversion algorithm called the filter diagonalization method (FDM) can be used in the postprocessing to reduce the number of FDTD iterations. However, the low efficiency of the FDM, which occurs when a relatively long time series is given, does not necessarily ensure an effective reduction of the total computation time. In this paper, a postprocessing method based on the FDM is proposed. The main procedure of the method is designed considering the aim to make the time spent on the method itself far less than the corresponding time spent on the FDTD iterations. To this end, the FDTD time series is preprocessed to be shortened significantly before the FDM frequency extraction. The preprocessing procedure is performed with the filter and decimation operations, which are widely used in narrow-band signal processing. Numerical results for a typical 3D solid PNC system show that the proposed postprocessing method can be used to effectively reduce the total computation time of the FDTD calculation of 3D phononic band structures.

  14. Finite difference time domain calculation of three-dimensional phononic band structures using a postprocessing method based on the filter diagonalization

    Energy Technology Data Exchange (ETDEWEB)

    Su Xiaoxing [School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044 (China); Ma Tianxue; Wang Yuesheng, E-mail: xxsu@bjtu.edu.cn [Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044 (China)

    2011-10-15

    If the band structure of a three-dimensional (3D) phononic crystal (PNC) is calculated by using the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT)-based postprocessing method, good results can only be ensured by a sufficiently large number of FDTD iterations. On a common computer platform, the total computation time will be very long. To overcome this difficulty, an excellent harmonic inversion algorithm called the filter diagonalization method (FDM) can be used in the postprocessing to reduce the number of FDTD iterations. However, the low efficiency of the FDM, which occurs when a relatively long time series is given, does not necessarily ensure an effective reduction of the total computation time. In this paper, a postprocessing method based on the FDM is proposed. The main procedure of the method is designed considering the aim to make the time spent on the method itself far less than the corresponding time spent on the FDTD iterations. To this end, the FDTD time series is preprocessed to be shortened significantly before the FDM frequency extraction. The preprocessing procedure is performed with the filter and decimation operations, which are widely used in narrow-band signal processing. Numerical results for a typical 3D solid PNC system show that the proposed postprocessing method can be used to effectively reduce the total computation time of the FDTD calculation of 3D phononic band structures.

  15. An improvement of the filter diagonalization-based post-processing method applied to finite difference time domain calculations of three-dimensional phononic band structures

    International Nuclear Information System (INIS)

    Su Xiaoxing; Zhang Chuanzeng; Ma Tianxue; Wang Yuesheng

    2012-01-01

    When three-dimensional (3D) phononic band structures are calculated by using the finite difference time domain (FDTD) method with a relatively small number of iterations, the results can be effectively improved by post-processing the FDTD time series (FDTD-TS) based on the filter diagonalization method (FDM), instead of the classical fast Fourier transform. In this paper, we propose a way to further improve the performance of the FDM-based post-processing method by introducing a relatively large number of observing points to record the FDTD-TS. To this end, the existing scheme of FDTD-TS preprocessing is modified. With the new preprocessing scheme, the processing efficiency of a single FDTD-TS can be improved significantly, and thus the entire post-processing method can have sufficiently high efficiency even when a relatively large number of observing points are used. The feasibility of the proposed method for improvement is verified by the numerical results.

  16. The quantum spectral analysis of the two-dimensional annular billiard system

    International Nuclear Information System (INIS)

    Yan-Hui, Zhang; Ji-Quan, Zhang; Xue-You, Xu; Sheng-Lu, Lin

    2009-01-01

    Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system. (general)

  17. Three-dimensional distributions of elements in biological samples by energy-filtered electron tomography

    Energy Technology Data Exchange (ETDEWEB)

    Leapman, R.D.; Kocsis, E.; Zhang, G.; Talbot, T.L.; Laquerriere, P

    2004-07-15

    By combining electron tomography with energy-filtered electron microscopy, we have shown the feasibility of determining the three-dimensional distributions of phosphorus in biological specimens. Thin sections of the nematode, Caenorhabditis elegans were prepared by high-pressure freezing, freeze-substitution and plastic embedding. Images were recorded at energy losses above and below the phosphorus L{sub 2,3} edge using a post-column imaging filter operating at a beam energy of 120 keV. The unstained specimens exhibited minimal contrast in bright-field images. After it was determined that the specimen was sufficiently thin to allow two-window ratio imaging of phosphorus, pairs of pre-edge and post-edge images were acquired in series over a tilt range of {+-}55 deg. at 5 deg. increments for two orthogonal tilt axes. The projected phosphorus distributions were aligned using the pre-edge images that contained inelastic contrast from colloidal gold particles deposited on the specimen surface. A reconstruction and surface rendering of the phosphorus distribution clearly revealed features 15-20 nm in diameter, which were identified as ribosomes distributed along the stacked membranes of endoplasmic reticulum and in the cytoplasm. The sensitivity of the technique was estimated at <35 phosphorus atoms per voxel based on the known total ribosomal phosphorus content of approximately 7000 atoms. Although a high electron dose of approximately 10{sup 7} e/nm{sup 2} was required to record two-axis tilt series, specimens were sufficiently stable to allow image alignment and tomographic reconstruction.

  18. Band structures of two dimensional solid/air hierarchical phononic crystals

    International Nuclear Information System (INIS)

    Xu, Y.L.; Tian, X.G.; Chen, C.Q.

    2012-01-01

    The hierarchical phononic crystals to be considered show a two-order “hierarchical” feature, which consists of square array arranged macroscopic periodic unit cells with each unit cell itself including four sub-units. Propagation of acoustic wave in such two dimensional solid/air phononic crystals is investigated by the finite element method (FEM) with the Bloch theory. Their band structure, wave filtering property, and the physical mechanism responsible for the broadened band gap are explored. The corresponding ordinary phononic crystal without hierarchical feature is used for comparison. Obtained results show that the solid/air hierarchical phononic crystals possess tunable outstanding band gap features, which are favorable for applications such as sound insulation and vibration attenuation.

  19. Band structures of two dimensional solid/air hierarchical phononic crystals

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Y.L.; Tian, X.G. [State Key Laboratory for Mechanical Structure Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China); Chen, C.Q., E-mail: chencq@tsinghua.edu.cn [Department of Engineering Mechanics, AML and CNMM, Tsinghua University, Beijing 100084 (China)

    2012-06-15

    The hierarchical phononic crystals to be considered show a two-order 'hierarchical' feature, which consists of square array arranged macroscopic periodic unit cells with each unit cell itself including four sub-units. Propagation of acoustic wave in such two dimensional solid/air phononic crystals is investigated by the finite element method (FEM) with the Bloch theory. Their band structure, wave filtering property, and the physical mechanism responsible for the broadened band gap are explored. The corresponding ordinary phononic crystal without hierarchical feature is used for comparison. Obtained results show that the solid/air hierarchical phononic crystals possess tunable outstanding band gap features, which are favorable for applications such as sound insulation and vibration attenuation.

  20. Energy dispersion of charged particles decelerated in a two-dimensional electrostatic field of the type x1/n

    International Nuclear Information System (INIS)

    Zashkvara, V.V.; Bok, A.A.

    1992-01-01

    Two components of the spatial dispersion of particles with respect to kinetic energy can be distinguished of the motion of charged particle beams in electrostatic mirros with a two-dimensional field φ(x,y) ans xz symmetry plane. The first is the longitudinal dispersion, which is along the z axis perpendicular to the field; the second is the transverse dispersion, along the x axis parallel to the field vector in the plane of symmetry. The longitudinal dispersion is a basic characteristic of electrostatic mirrors used as energy analyzers. It has been shown that for first-order angular focusing, the longitudinal dispersion, divided by the focal length, is independent of the structure of the two-dimensional field and is a function only of the angle at which the charged particle beam enters the mirror. The transverse dispersion stems from the energy dependence of the penetration depth of the beam as it is decelerated, and it plays an important role when the energy of a charged particle beam is analyzed by the filtering principle, making use of the property of an electrostatic mirror to transmit or reflect charged particles with kinetic energy in a specified interval. This type of dispersion in electrostatic mirrors with two-dimensional fields has not been analyzed systematically. In the present note the authors consider a particular type of two-dimensional electrostatic field which is characterized by a large transverse dispersion, many times larger than in existing electrostatic reflecting filters employing planar and cylindrical fields

  1. Fourier analysis of finite element preconditioned collocation schemes

    Science.gov (United States)

    Deville, Michel O.; Mund, Ernest H.

    1990-01-01

    The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

  2. An Improved Filtering Method for Quantum Color Image in Frequency Domain

    Science.gov (United States)

    Li, Panchi; Xiao, Hong

    2018-01-01

    In this paper we investigate the use of quantum Fourier transform (QFT) in the field of image processing. We consider QFT-based color image filtering operations and their applications in image smoothing, sharpening, and selective filtering using quantum frequency domain filters. The underlying principle used for constructing the proposed quantum filters is to use the principle of the quantum Oracle to implement the filter function. Compared with the existing methods, our method is not only suitable for color images, but also can flexibly design the notch filters. We provide the quantum circuit that implements the filtering task and present the results of several simulation experiments on color images. The major advantages of the quantum frequency filtering lies in the exploitation of the efficient implementation of the quantum Fourier transform.

  3. Comprehensive two-dimensional liquid chromatography with on-line Fourier-transform-infrared-spectroscopy detection for the characterization of copolymers

    NARCIS (Netherlands)

    Kok, S.J.; Hankemeier, T.; Schoenmakers, P.J.

    2005-01-01

    The on-line coupling of comprehensive two-dimensional liquid chromatography (liquid chromatography × size-exclusion chromatography, LC × SEC) and infrared (IR) spectroscopy has been realized by means of an IR flow cell. The system has been assessed by the functional-group analysis of a series of

  4. Quantum Image Filtering in the Frequency Domain

    Directory of Open Access Journals (Sweden)

    MANTA, V. I.

    2013-08-01

    Full Text Available In this paper we address the emerging field of Quantum Image Processing. We investigate the use of quantum computing systems to represent and manipulate images. In particular, we consider the basic task of image filtering. We prove that a quantum version for this operation can be achieved, even though the quantum convolution of two sequences is physically impossible. In our approach we use the principle of the quantum oracle to implement the filter function. We provide the quantum circuit that implements the filtering task and present the results of several simulation experiments on grayscale images. There are important differences between the classical and the quantum implementations for image filtering. We analyze these differences and show that the major advantage of the quantum approach lies in the exploitation of the efficient implementation of the quantum Fourier transform.

  5. Digital filtering in nuclear medicine

    International Nuclear Information System (INIS)

    Miller, T.R.; Sampathkumaran, S.

    1982-01-01

    Digital filtering is a powerful mathematical technique in computer analysis of nuclear medicine studies. The basic concepts of object-domain and frequency-domain filtering are presented in simple, largely nonmathemaical terms. Computational methods are described using both the Fourier transform and convolution techniques. The frequency response is described and used to represent the behavior of several classes of filters. These concepts are illustrated with examples drawn from a variety of important applications in nuclear medicine

  6. Two-dimensional computer simulation of high intensity proton beams

    CERN Document Server

    Lapostolle, Pierre M

    1972-01-01

    A computer program has been developed which simulates the two- dimensional transverse behaviour of a proton beam in a focusing channel. The model is represented by an assembly of a few thousand 'superparticles' acted upon by their own self-consistent electric field and an external focusing force. The evolution of the system is computed stepwise in time by successively solving Poisson's equation and Newton's law of motion. Fast Fourier transform techniques are used for speed in the solution of Poisson's equation, while extensive area weighting is utilized for the accurate evaluation of electric field components. A computer experiment has been performed on the CERN CDC 6600 computer to study the nonlinear behaviour of an intense beam in phase space, showing under certain circumstances a filamentation due to space charge and an apparent emittance growth. (14 refs).

  7. Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas.

    Science.gov (United States)

    Yan, Xin-Zhong

    2011-07-01

    The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without losing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green's function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.

  8. Optimal noise reduction in 3D reconstructions of single particles using a volume-normalized filter

    Science.gov (United States)

    Sindelar, Charles V.; Grigorieff, Nikolaus

    2012-01-01

    The high noise level found in single-particle electron cryo-microscopy (cryo-EM) image data presents a special challenge for three-dimensional (3D) reconstruction of the imaged molecules. The spectral signal-to-noise ratio (SSNR) and related Fourier shell correlation (FSC) functions are commonly used to assess and mitigate the noise-generated error in the reconstruction. Calculation of the SSNR and FSC usually includes the noise in the solvent region surrounding the particle and therefore does not accurately reflect the signal in the particle density itself. Here we show that the SSNR in a reconstructed 3D particle map is linearly proportional to the fractional volume occupied by the particle. Using this relationship, we devise a novel filter (the “single-particle Wiener filter”) to minimize the error in a reconstructed particle map, if the particle volume is known. Moreover, we show how to approximate this filter even when the volume of the particle is not known, by optimizing the signal within a representative interior region of the particle. We show that the new filter improves on previously proposed error-reduction schemes, including the conventional Wiener filter as well as figure-of-merit weighting, and quantify the relationship between all of these methods by theoretical analysis as well as numeric evaluation of both simulated and experimentally collected data. The single-particle Wiener filter is applicable across a broad range of existing 3D reconstruction techniques, but is particularly well suited to the Fourier inversion method, leading to an efficient and accurate implementation. PMID:22613568

  9. Application of Fourier transforms for microwave radiometric inversions

    Science.gov (United States)

    Holmes, J. J.; Balanis, C. A.; Truman, W. M.

    1975-01-01

    Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

  10. Group-invariant finite Fourier transforms

    International Nuclear Information System (INIS)

    Shenefelt, M.H.

    1988-01-01

    The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible

  11. A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter

    NARCIS (Netherlands)

    Brigo, D.; Hanzon, B.; LeGland, F.

    1998-01-01

    This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is

  12. A non-hydrostatic flat-bottom ocean model entirely based on Fourier expansion

    Science.gov (United States)

    Wirth, A.

    2005-01-01

    We show how to implement free-slip and no-slip boundary conditions in a three dimensional Boussinesq flat-bottom ocean model based on Fourier expansion. Our method is inspired by the immersed or virtual boundary technique in which the effect of boundaries on the flow field is modeled by a virtual force field. Our method, however, explicitly depletes the velocity on the boundary induced by the pressure, while at the same time respecting the incompressibility of the flow field. Spurious spatial oscillations remain at a negligible level in the simulated flow field when using our technique and no filtering of the flow field is necessary. We furthermore show that by using the method presented here the residual velocities at the boundaries are easily reduced to a negligible value. This stands in contradistinction to previous calculations using the immersed or virtual boundary technique. The efficiency is demonstrated by simulating a Rayleigh impulsive flow, for which the time evolution of the simulated flow is compared to an analytic solution, and a three dimensional Boussinesq simulation of ocean convection. The second instance is taken form a well studied oceanographic context: A free slip boundary condition is applied on the upper surface, the modeled sea surface, and a no-slip boundary condition to the lower boundary, the modeled ocean floor. Convergence properties of the method are investigated by solving a two dimensional stationary problem at different spatial resolutions. The work presented here is restricted to a flat ocean floor. Extensions of our method to ocean models with a realistic topography are discussed.

  13. A unified Fourier theory for time-of-flight PET data.

    Science.gov (United States)

    Li, Yusheng; Matej, Samuel; Metzler, Scott D

    2016-01-21

    Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D x-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions--the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are

  14. Seizure-Onset Mapping Based on Time-Variant Multivariate Functional Connectivity Analysis of High-Dimensional Intracranial EEG: A Kalman Filter Approach.

    Science.gov (United States)

    Lie, Octavian V; van Mierlo, Pieter

    2017-01-01

    The visual interpretation of intracranial EEG (iEEG) is the standard method used in complex epilepsy surgery cases to map the regions of seizure onset targeted for resection. Still, visual iEEG analysis is labor-intensive and biased due to interpreter dependency. Multivariate parametric functional connectivity measures using adaptive autoregressive (AR) modeling of the iEEG signals based on the Kalman filter algorithm have been used successfully to localize the electrographic seizure onsets. Due to their high computational cost, these methods have been applied to a limited number of iEEG time-series (Kalman filter implementations, a well-known multivariate adaptive AR model (Arnold et al. 1998) and a simplified, computationally efficient derivation of it, for their potential application to connectivity analysis of high-dimensional (up to 192 channels) iEEG data. When used on simulated seizures together with a multivariate connectivity estimator, the partial directed coherence, the two AR models were compared for their ability to reconstitute the designed seizure signal connections from noisy data. Next, focal seizures from iEEG recordings (73-113 channels) in three patients rendered seizure-free after surgery were mapped with the outdegree, a graph-theory index of outward directed connectivity. Simulation results indicated high levels of mapping accuracy for the two models in the presence of low-to-moderate noise cross-correlation. Accordingly, both AR models correctly mapped the real seizure onset to the resection volume. This study supports the possibility of conducting fully data-driven multivariate connectivity estimations on high-dimensional iEEG datasets using the Kalman filter approach.

  15. Equivalence of two-dimensional gravities

    International Nuclear Information System (INIS)

    Mohammedi, N.

    1990-01-01

    The authors find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL(2,R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2 + 1 dimensional gravity. The authors present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given

  16. Improved Plane-Wave Ultrasound Beamforming by Incorporating Angular Weighting and Coherent Compounding in Fourier Domain.

    Science.gov (United States)

    Chen, Chuan; Hendriks, Gijs A G M; van Sloun, Ruud J G; Hansen, Hendrik H G; de Korte, Chris L

    2018-05-01

    In this paper, a novel processing framework is introduced for Fourier-domain beamforming of plane-wave ultrasound data, which incorporates coherent compounding and angular weighting in the Fourier domain. Angular weighting implies spectral weighting by a 2-D steering-angle-dependent filtering template. The design of this filter is also optimized as part of this paper. Two widely used Fourier-domain plane-wave ultrasound beamforming methods, i.e., Lu's f-k and Stolt's f-k methods, were integrated in the framework. To enable coherent compounding in Fourier domain for the Stolt's f-k method, the original Stolt's f-k method was modified to achieve alignment of the spectra for different steering angles in k-space. The performance of the framework was compared for both methods with and without angular weighting using experimentally obtained data sets (phantom and in vivo), and data sets (phantom) provided by the IEEE IUS 2016 plane-wave beamforming challenge. The addition of angular weighting enhanced the image contrast while preserving image resolution. This resulted in images of equal quality as those obtained by conventionally used delay-and-sum (DAS) beamforming with apodization and coherent compounding. Given the lower computational load of the proposed framework compared to DAS, to our knowledge it can, therefore, be concluded that it outperforms commonly used beamforming methods such as Stolt's f-k, Lu's f-k, and DAS.

  17. The derivative-free Fourier shell identity for photoacoustics.

    Science.gov (United States)

    Baddour, Natalie

    2016-01-01

    In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

  18. Harmonic analysis on local fields and adelic spaces. I

    International Nuclear Information System (INIS)

    Osipov, D V; Parshin, A N

    2008-01-01

    We develop harmonic analysis on the objects of a category C 2 of infinite-dimensional filtered vector spaces over a finite field. This category includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. As the main result, we construct the theory of the Fourier transform on these objects and obtain two-dimensional Poisson formulae

  19. Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform.

    Science.gov (United States)

    Ding, Jian-Jiun; Pei, Soo-Chang; Liu, Chun-Lin

    2012-08-01

    The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.

  20. Two-dimensional metamaterial optics

    International Nuclear Information System (INIS)

    Smolyaninov, I I

    2010-01-01

    While three-dimensional photonic metamaterials are difficult to fabricate, many new concepts and ideas in the metamaterial optics can be realized in two spatial dimensions using planar optics of surface plasmon polaritons. In this paper we review recent progress in this direction. Two-dimensional photonic crystals, hyperbolic metamaterials, and plasmonic focusing devices are demonstrated and used in novel microscopy and waveguiding schemes

  1. Two Integrator Loop Filters: Generation Using NAM Expansion and Review

    Directory of Open Access Journals (Sweden)

    Ahmed M. Soliman

    2010-01-01

    Full Text Available Systematic synthesis method to generate a family of two integrator loop filters based on nodal admittance matrix (NAM expansion is given. Eight equivalent circuits are obtained; six of them are new. Each of the generated circuits uses two grounded capacitors and employs two current conveyors (CCII or two inverting current conveyors (ICCII or a combination of both. The NAM expansion is also used to generate eight equivalent grounded passive elements two integrator loop filters using differential voltage current conveyor (DVCC; six of them are new. Changing the input port of excitation, two new families of eight unity gain lowpass filter circuits each using two CCII or ICCII or combination of both or two DVCC are obtained.

  2. Experimental display of Fourier analysis through the optical physics and its didatical utilization

    International Nuclear Information System (INIS)

    Oliveira, S.M.M. de.

    1983-01-01

    The properties of Fourier analysis through physical optics are displayed experimentally. Within physical optics topics that illustrate didactically Fourier analysis, a subject usually considered purely mathematical are selected. The most important properties of Fourier transform and their utilization in cleaning up images through spatial filtering are presented, in this way the properties of convolution to analyse image formation and characterize some diffraction patterns are also used. (Author) [pt

  3. Error estimates for the Fourier-finite-element approximation of the Lame system in nonsmooth axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    This paper is concerned with the effective implementation of the Fourier-finite-element method, which combines the approximating Fourier and the finite-element methods, for treating the Derichlet problem for the Lam.6 equations in axisymmetric domains Ω-circumflex is contained in R 3 with conical vertices and reentrant edges. The partial Fourier decomposition reduces the three-dimensional boundary value problem to an infinite sequence of decoupled two-dimensional boundary value problems on the plane meridian domain Ω α is contained in R + 2 of Ω-circumflex with solutions u, n (n = 0,1,2,...) being the Fourier coefficients of the solution u of the 3D problem. The asymptotic behavior of the Fourier coefficients near the angular points of Ω α , is described by appropriate singular vector-functions and treated numerically by linear finite elements on locally graded meshes. For the right-hand side function f-circumflex is an element of (L 2 (Ω-circumflex)) 3 it is proved that with appropriate mesh grading the rate of convergence of the combined approximations in (W 2 1 (Ω-circumflex)) 3 is of the order O(h + N -1 ), where h and N are the parameters of the finite-element and Fourier approximations, respectively, with h → 0 and N → ∞. (author)

  4. Analysis of an MCU HEPA filter

    Energy Technology Data Exchange (ETDEWEB)

    Peters, T. B. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Fondeur, F. F. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

    2017-01-01

    A series of direct analyses on three portions (inlet, center, and outlet) of the High Efficiency Particulate Air (HEPA) filter material from the Modular Caustic-Side Solvent Extraction Unit (MCU) have been performed; this includes x-ray methods such as X-Ray Diffraction (XRD), Contained Scanning Electron Microscopy (CSEM) and X-Ray Fluorescence (XRF), as well as Fourier Transform InfraRed spectroscopy (FTIR). Additionally, two leaching studies (one with water, one with dichloromethane) have been performed on three portions (inlet, center, and outlet) of the HEPA filter material, with the leachates being analyzed by Inductively-coupled plasma emission spectroscopy (ICPES), Semi-Volatile Organic Analysis (SVOA) and gammascan. From the results of the analyses, SRNL feels that cesium-depleted solvent is being introduced into the HEPA filter. The most likely avenue for this is mechanical aerosolization of solvent, where the aerosol is then carried along an airstream into the HEPA filter. Once introduced into the HEPA filter media, the solvent wicks throughout the material, and migrates towards the outlet end. Once on the outlet end, continual drying could cause particulate flakes to exit the filter and travel farther down the airstream path.

  5. Application of velocity filtering to optical-flow passive ranging

    Science.gov (United States)

    Barniv, Yair

    1992-01-01

    The performance of the velocity filtering method as applied to optical-flow passive ranging under real-world conditions is evaluated. The theory of the 3-D Fourier transform as applied to constant-speed moving points is reviewed, and the space-domain shift-and-add algorithm is derived from the general 3-D matched filtering formulation. The constant-speed algorithm is then modified to fit the actual speed encountered in the optical flow application, and the passband of that filter is found in terms of depth (sensor/object distance) so as to cover any given range of depths. Two algorithmic solutions for the problems associated with pixel interpolation and object expansion are developed, and experimental results are presented.

  6. Hamiltonian field description of two-dimensional vortex fluids and guiding center plasmas

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1981-03-01

    The equations that describe the motion of two-dimensional vortex fluids and guiding center plasmas are shown to possess underlying field Hamiltonian structure. A Poisson bracket which is given in terms of the vorticity, the physical although noncanonical dynamical variable, casts these equations into Heisenberg form. The Hamiltonian density is the kinetic energy density of the fluid. The well-known conserved quantities are seen to be in involution with respect to this Poisson bracket. Expanding the vorticity in terms of a Fourier-Dirac series transforms the field description given here into the usual canonical equations for discrete vortex motion. A Clebsch potential representation of the vorticity transforms the noncanonical field description into a canonical description

  7. Filtering in the time and frequency domains

    CERN Document Server

    Blinchikoff, Herman

    2001-01-01

    Long regarded as a classic of filter theory and design, this book stands as the most comprehensive treatment of filtering techniques, devices and concepts as well as pertinent mathematical relationships. Analysis and theory are supplemented by detailed design curves, fully explained examples and problem and answer sections. Discussed are the derivation of filtering functions, Fourier, Laplace, Hilbert and z transforms, lowpass responses, the transformation of lowpass into other filter types, the all-pass function, the effect of losses on theoretical responses, matched filtering, methods of tim

  8. Single-exposure two-dimensional superresolution in digital holography using a vertical cavity surface-emitting laser source array.

    Science.gov (United States)

    Granero, Luis; Zalevsky, Zeev; Micó, Vicente

    2011-04-01

    We present a new implementation capable of producing two-dimensional (2D) superresolution (SR) imaging in a single exposure by aperture synthesis in digital lensless Fourier holography when using angular multiplexing provided by a vertical cavity surface-emitting laser source array. The system performs the recording in a single CCD snapshot of a multiplexed hologram coming from the incoherent addition of multiple subholograms, where each contains information about a different 2D spatial frequency band of the object's spectrum. Thus, a set of nonoverlapping bandpass images of the input object can be recovered by Fourier transformation (FT) of the multiplexed hologram. The SR is obtained by coherent addition of the information contained in each bandpass image while generating an enlarged synthetic aperture. Experimental results demonstrate improvement in resolution and image quality.

  9. Three-dimensional Fourier transformation constructive interference in steady state magnetic resonance imaging of the inner ear in patients with unilateral and bilateral Meniere's disease

    NARCIS (Netherlands)

    Mateijsen, DJM; Van Hengel, PWJ; Krikke, AP; Van Huffelen, WM; Wit, HP; Albers, FWJ

    Objective: In this study, three-dimensional Fourier transformation constructive interference in steady state (3DFT-CISS) magnetic resonance imaging was used to quantify the distance between the vertical part of the posterior semicircular canal and the posterior fossa as a measure of the

  10. A unified Fourier theory for time-of-flight PET data

    International Nuclear Information System (INIS)

    Li, Yusheng; Matej, Samuel; Metzler, Scott D

    2016-01-01

    Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier–John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John’s equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D x-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions—the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations

  11. An electronic image processing device featuring continuously selectable two-dimensional bipolar filter functions and real-time operation

    International Nuclear Information System (INIS)

    Charleston, B.D.; Beckman, F.H.; Franco, M.J.; Charleston, D.B.

    1981-01-01

    A versatile electronic-analogue image processing system has been developed for use in improving the quality of various types of images with emphasis on those encountered in experimental and diagnostic medicine. The operational principle utilizes spatial filtering which selectively controls the contrast of an image according to the spatial frequency content of relevant and non-relevant features of the image. Noise can be reduced or eliminated by selectively lowering the contrast of information in the high spatial frequency range. Edge sharpness can be enhanced by accentuating the upper midrange spatial frequencies. Both methods of spatial frequency control may be adjusted continuously in the same image to obtain maximum visibility of the features of interest. A precision video camera is used to view medical diagnostic images, either prints, transparencies or CRT displays. The output of the camera provides the analogue input signal for both the electronic processing system and the video display of the unprocessed image. The video signal input to the electronic processing system is processed by a two-dimensional spatial convolution operation. The system employs charged-coupled devices (CCDs), both tapped analogue delay lines (TADs) and serial analogue delay lines (SADs), to store information in the form of analogue potentials which are constantly being updated as new sampled analogue data arrive at the input. This information is convolved with a programmed bipolar radially symmetrical hexagonal function which may be controlled and varied at each radius by the operator in real-time by adjusting a set of front panel controls or by a programmed microprocessor control. Two TV monitors are used, one for processed image display and the other for constant reference to the original image. The working prototype has a full-screen display matrix size of 200 picture elements per horizontal line by 240 lines. The matrix can be expanded vertically and horizontally for the

  12. Wide wavelength range tunable one-dimensional silicon nitride nano-grating guided mode resonance filter based on azimuthal rotation

    Directory of Open Access Journals (Sweden)

    Ryoji Yukino

    2017-01-01

    Full Text Available We describe wavelength tuning in a one dimensional (1D silicon nitride nano-grating guided mode resonance (GMR structure under conical mounting configuration of the device. When the GMR structure is rotated about the axis perpendicular to the surface of the device (azimuthal rotation for light incident at oblique angles, the conditions for resonance are different than for conventional GMR structures under classical mounting. These resonance conditions enable tuning of the GMR peak position over a wide range of wavelengths. We experimental demonstrate tuning over a range of 375 nm between 500 nm˜875 nm. We present a theoretical model to explain the resonance conditions observed in our experiments and predict the peak positions with show excellent agreement with experiments. Our method for tuning wavelengths is simpler and more efficient than conventional procedures that employ variations in the design parameters of structures or conical mounting of two-dimensional (2D GMR structures and enables a single 1D GMR device to function as a high efficiency wavelength filter over a wide range of wavelengths. We expect tunable filters based on this technique to be applicable in a wide range of fields including astronomy and biomedical imaging.

  13. Numerical computation of the discrete Fourier transform and its applications in the statistic processing of experimental data

    International Nuclear Information System (INIS)

    Marinescu, D.C.; Radulescu, T.G.

    1977-06-01

    The Integral Fourier Transform has a large range of applications in such areas as communication theory, circuit theory, physics, etc. In order to perform discrete Fourier Transform the Finite Fourier Transform is defined; it operates upon N samples of a uniformely sampled continuous function. All the properties known in the continuous case can be found in the discrete case also. The first part of the paper presents the relationship between the Finite Fourier Transform and the Integral one. The computing of a Finite Fourier Transform is a problem in itself since in order to transform a set of N data we have to perform N 2 ''operations'' if the transformation relations are used directly. An algorithm known as the Fast Fourier Transform (FFT) reduces this figure from N 2 to a more reasonable Nlog 2 N, when N is a power of two. The original Cooley and Tuckey algorithm for FFT can be further improved when higher basis are used. The price to be paid in this case is the increase in complexity of such algorithms. The recurrence relations and a comparation among such algorithms are presented. The key point in understanding the application of FFT resides in the convolution theorem which states that the convolution (an N 2 type procedure) of the primitive functions is equivalent to the ordinar multiplication of their transforms. Since filtering is actually a convolution process we present several procedures to perform digital filtering by means of FFT. The best is the one using the segmentation of records and the transformation of pairs of records. In the digital processing of signals, besides digital filtering a special attention is paid to the estimation of various statistical characteristics of a signal as: autocorrelation and correlation functions, periodiograms, density power sepctrum, etc. We give several algorithms for the consistent and unbiased estimation of such functions, by means of FFT. (author)

  14. Improved detection of chronic myocardial infarction with Fourier amplitude and phase imaging in two projections

    International Nuclear Information System (INIS)

    Akins, E.W.; Scott, E.A.; Williams, C.M.

    1987-01-01

    Twenty-seven patients with 33 chronic myocaridal infarctions underwent MR imaging and radionuclide ventriculography at rest. The radionuclide ventriculographs, in left anterior oblique (LAO) and left posterior oblique (LPO) projections, were analyzed by two independent observers by visual inspection and combined Fourier-transformed amplitude and phase imaging. Only 15 (45%) of the 33 infarctions were detected by visual inspection, but 21 (64%) were detected on the LAO Fourier-transformed images along. Thirty (91%) were detected by using both LAO and LPO Fourier-transformed images. On MR imaging, 28 (85%) of the myocardial infarctions appeared as areas of focal wall thinning. Combined Fourier-transformed amplitude and phase imaging in both LAO and LPO views discloses more myocardial infarctions than visual inspection or LAO Fourier-transformed images alone because inferior infarctions, which are frequently missed in the LAO view, are easily seen in the LPO view

  15. Application of Fractional Fourier Transform to Moving Target Indication via Along-Track Interferometry

    Directory of Open Access Journals (Sweden)

    Chiu Shen

    2005-01-01

    Full Text Available A relatively unknown yet powerful technique, the so-called fractional Fourier transform (FrFT, is applied to SAR along-track interferometry (SAR-ATI in order to estimate moving target parameters. By mapping a target's signal onto a fractional Fourier axis, the FrFT permits a constant-velocity target to be focused in the fractional Fourier domain thereby affording orders of magnitude improvement in SCR. Moving target velocity and position parameters are derived and expressed in terms of an optimum fractional angle and a measured fractional Fourier position , allowing a target to be accurately repositioned and its velocity components computed without actually forming an SAR image. The new estimation algorithm is compared with the matched filter bank approach, showing some of the advantages of the FrFT method. The proposed technique is applied to the data acquired by the two-aperture CV580 airborne radar system configured in its along-track mode. Results show that the method is effective in estimating target velocity and position parameters.

  16. Description of the electron-hydrogen collision by the Coulomb Fourier transform method

    International Nuclear Information System (INIS)

    Levin, S.B.

    2005-01-01

    A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals

  17. Reduction and coding of synthetic aperture radar data with Fourier transforms

    Science.gov (United States)

    Tilley, David G.

    1995-01-01

    Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

  18. Backprojection filtering for variable orbit fan-beam tomography

    International Nuclear Information System (INIS)

    Gullberg, G.T.; Zeng, G.L.

    1995-01-01

    Backprojection filtering algorithms are presented for three variable Orbit fan-beam geometries. Expressions for the fan beam projection and backprojection operators are given for a flat detector fan-beam geometry with fixed focal length, with variable focal length, and with fixed focal length and off-center focusing. Backprojection operators are derived for each geometry using transformation of coordinates to transform from a parallel geometry backprojector to a fan-beam backprojector for the appropriate geometry. The backprojection operator includes a factor which is a function of the coordinates of the projection ray and the coordinates of the pixel in the backprojected image. The backprojection filtering algorithm first backprojects the variable orbit fan-beam projection data using the appropriately derived backprojector to obtain a 1/r blurring of the original image then takes the two-dimensional (2D) Fast Fourier Transform (FFT) of the backprojected image, then multiples the transformed image by the 2D ramp filter function, and finally takes the inverse 2D FFT to obtain the reconstructed image. Computer simulations verify that backprojectors with appropriate weighting give artifact free reconstructions of simulated line integral projections. Also, it is shown that it is not necessary to assume a projection model of line integrals, but the projector and backprojector can be defined to model the physics of the imaging detection process. A backprojector for variable orbit fan-beam tomography with fixed focal length is derived which includes an additional factor which is a function of the flux density along the flat detector. It is shown that the impulse response for the composite of the projection and backprojection operations is equal to 1/r

  19. X-ray stress measurement of ferritic steel using fourier analysis of Debye-Scherrer ring

    International Nuclear Information System (INIS)

    Fujimoto, Yohei; Sasaki, Toshihiko; Miyazaki, Toshiyuki

    2015-01-01

    In this study, X-ray stress measurements of ferritic steel based on Fourier analysis are conducted. Taira et al. developed the cosα method for X-ray stress measurements using a two-dimensional X-ray detector. Miyazaki et al. reported that the cosα method can be described more concisely by developing the Fourier series (the Fourier analysis method). The Fourier analysis method is expected to yield the stress measurement with an imperfect Debye-Scherrer ring and there is a possibility that the materials evaluation is different compared with the conventional method, that is, the sin 2 ψ method. In the Fourier analysis method, the strain measured by X-rays is developed as a Fourier series, and all the plane-stress components can be calculated from the Fourier series. In this study, the normal stress calculation was confirmed. In addition, the Fourier-analysis and cosα methods were used for X-ray stress measurements during a four-point bending test on a S45C test piece, and the effectiveness of the Fourier analysis method was confirmed. It was found that the experimental results from the Fourier analysis and cosα methods were nearly identical. In addition, the measurement accuracies of both the methods were equivalent. (author)

  20. Pulse Propagation Effects in Optical 2D Fourier-Transform Spectroscopy: Theory.

    Science.gov (United States)

    Spencer, Austin P; Li, Hebin; Cundiff, Steven T; Jonas, David M

    2015-04-30

    A solution to Maxwell's equations in the three-dimensional frequency domain is used to calculate rephasing two-dimensional Fourier transform (2DFT) spectra of the D2 line of atomic rubidium vapor in argon buffer gas. Experimental distortions from the spatial propagation of pulses through the sample are simulated in 2DFT spectra calculated for the homogeneous Bloch line shape model. Spectral features that appear at optical densities of up to 3 are investigated. As optical density increases, absorptive and dispersive distortions start with peak shape broadening, progress to peak splitting, and ultimately result in a previously unexplored coherent transient twisting of the split peaks. In contrast to the low optical density limit, where the 2D peak shape for the Bloch model depends only on the total dephasing time, these distortions of the 2D peak shape at finite optical density vary with the waiting time and the excited state lifetime through coherent transient effects. Experiment-specific conditions are explored, demonstrating the effects of varying beam overlap within the sample and of pseudo-time domain filtering. For beam overlap starting at the sample entrance, decreasing the length of beam overlap reduces the line width along the ωτ axis but also reduces signal intensity. A pseudo-time domain filter, where signal prior to the center of the last excitation pulse is excluded from the FID-referenced 2D signal, reduces propagation distortions along the ωt axis. It is demonstrated that 2DFT rephasing spectra cannot take advantage of an excitation-detection transformation that can eliminate propagation distortions in 2DFT relaxation spectra. Finally, the high optical density experimental 2DFT spectrum of rubidium vapor in argon buffer gas [J. Phys. Chem. A 2013, 117, 6279-6287] is quantitatively compared, in line width, in depth of peak splitting, and in coherent transient peak twisting, to a simulation with optical density higher than that reported.

  1. FREQUENCY COMPONENT EXTRACTION OF HEARTBEAT CUES WITH SHORT TIME FOURIER TRANSFORM (STFT

    Directory of Open Access Journals (Sweden)

    Sumarna Sumarna

    2017-01-01

      Electro-acoustic human heartbeat detector have been made with the main parts : (a stetoscope (piece chest, (b mic condenser, (c transistor amplifier, and (d cues analysis program with MATLAB. The frequency components that contained in heartbeat. cues have also been extracted with Short Time Fourier Transform (STFT from 9 volunteers. The results of the analysis showed that heart rate appeared in every cue frequency spectrum with their harmony. The steps of the research were including detector instrument design, test and instrument repair, cues heartbeat recording with Sound Forge 10 program and stored in wav file ; cues breaking at the start and the end, and extraction/cues analysis using MATLAB. The MATLAB program included filter (bandpass filter with bandwidth between 0.01 – 110 Hz, cues breaking with hamming window and every part was calculated using Fourier Transform (STFT mechanism and the result were shown in frequency spectrum graph.   Keywords: frequency components extraction, heartbeat cues, Short Time Fourier Transform

  2. Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

    Science.gov (United States)

    Dovlo, Edem; Baddour, Natalie

    2015-01-01

    The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

  3. Half-metallic ferromagnetism prediction in MoS2-based two-dimensional superlattice from first-principles

    Science.gov (United States)

    Wen, Yan-Ni; Gao, Peng-Fei; Xia, Ming-Gang; Zhang, Sheng-Li

    2018-03-01

    Half-metallic ferromagnetism (HMFM) has great potential application in spin filter. However, it is extremely rare, especially in two-dimensional (2D) materials. At present, 2D materials have drawn international interest in spintronic devices. Here, we use ab initio density functional theory (DFT) calculations to study the structural stability and electrical and magnetic properties of the MoS2-based 2D superlattice formed by inserting graphene hexagonal ring in 6 × 6 × 1 MoS2 supercell. Two kinds of structures with hexagonal carbon ring were predicted with structural stability and were shown HMFM. The two structures combine the spin transport capacity of graphene with the magnetism of the defective 2D MoS2. And they have strong covalent bonding between the C and S or Mo atoms near the interface. This work is very useful to help us to design reasonable MoS2-based spin filter.

  4. On the two-dimensional Saigo-Maeda fractional calculus asociated with two-dimensional Aleph TRANSFORM

    Directory of Open Access Journals (Sweden)

    Dinesh Kumar

    2013-11-01

    Full Text Available This paper deals with the study of two-dimensional Saigo-Maeda operators of Weyl type associated with Aleph function defined in this paper. Two theorems on these defined operators are established. Some interesting results associated with the H-functions and generalized Mittag-Leffler functions are deduced from the derived results. One dimensional analog of the derived results is also obtained.

  5. Concrete ensemble Kalman filters with rigorous catastrophic filter divergence.

    Science.gov (United States)

    Kelly, David; Majda, Andrew J; Tong, Xin T

    2015-08-25

    The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature.

  6. z-transform DFT filters and FFT's

    DEFF Research Database (Denmark)

    Bruun, G.

    1978-01-01

    The paper shows how discrete Fourier transformation can be implemented as a filter bank in a way which reduces the number of filter coefficients. A particular implementation of such a filter bank is directly related to the normal complex FFT algorithm. The principle developed further leads to types...... of DFT filter banks which utilize a minimum of complex coefficients. These implementations lead to new forms of FFT's, among which is acos/sinFFT for a real signal which only employs real coefficients. The new FFT algorithms use only half as many real multiplications as does the classical FFT....

  7. Thermal conductivity in one-dimensional nonlinear systems

    Science.gov (United States)

    Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

    2000-03-01

    Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

  8. Three phase active power filter with selective harmonics elimination

    Directory of Open Access Journals (Sweden)

    Sozański Krzysztof

    2016-03-01

    Full Text Available This paper describes a three phase shunt active power filter with selective harmonics elimination. The control algorithm is based on a digital filter bank. The moving Discrete Fourier Transformation is used as an analysis filter bank. The correctness of the algorithm has been verified by simulation and experimental research. The paper includes exemplary results of current waveforms and their spectra from a three phase active power filter.

  9. Rotation-type input-output relationships for Wigner distribution moments in fractional Fourier transform systems

    NARCIS (Netherlands)

    Bastiaans, M.J.; Alieva, T.

    2002-01-01

    It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. This general input-output relationship is then broken down into a

  10. Image quality assessment using two-dimensional complex mel-cepstrum

    Science.gov (United States)

    Cakir, Serdar; Cetin, A. Enis

    2016-11-01

    Assessment of visual quality plays a crucial role in modeling, implementation, and optimization of image- and video-processing applications. The image quality assessment (IQA) techniques basically extract features from the images to generate objective scores. Feature-based IQA methods generally consist of two complementary phases: (1) feature extraction and (2) feature pooling. For feature extraction in the IQA framework, various algorithms have been used and recently, the two-dimensional (2-D) mel-cepstrum (2-DMC) feature extraction scheme has provided promising results in a feature-based IQA framework. However, the 2-DMC feature extraction scheme completely loses image-phase information that may contain high-frequency characteristics and important structural components of the image. In this work, "2-D complex mel-cepstrum" is proposed for feature extraction in an IQA framework. The method tries to integrate Fourier transform phase information into the 2-DMC, which was shown to be an efficient feature extraction scheme for assessment of image quality. Support vector regression is used for feature pooling that provides mapping between the proposed features and the subjective scores. Experimental results show that the proposed technique obtains promising results for the IQA problem by making use of the image-phase information.

  11. Kalman filtering and smoothing for linear wave equations with model error

    International Nuclear Information System (INIS)

    Lee, Wonjung; McDougall, D; Stuart, A M

    2011-01-01

    Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data are acquired sequentially. The Kalman filter plays a central role in many applications because it is exact for linear systems subject to Gaussian noise, and because it forms the basis for many approximate filters which are used in high-dimensional systems. The aim of this paper is to study the effect of model error on the Kalman filter, in the context of linear wave propagation problems. A consistency result is proved when no model error is present, showing recovery of the true signal in the large data limit. This result, however, is not robust: it is also proved that arbitrarily small model error can lead to inconsistent recovery of the signal in the large data limit. If the model error is in the form of a constant shift to the velocity, the filtering and smoothing distributions only recover a partial Fourier expansion, a phenomenon related to aliasing. On the other hand, for a class of wave velocity model errors which are time dependent, it is possible to recover the filtering distribution exactly, but not the smoothing distribution. Numerical results are presented which corroborate the theory, and also propose a computational approach which overcomes the inconsistency in the presence of model error, by relaxing the model

  12. Revisiting the quantum harmonic oscillator via unilateral Fourier transforms

    International Nuclear Information System (INIS)

    Nogueira, Pedro H F; Castro, Antonio S de

    2016-01-01

    The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)

  13. Two-dimensional nuclear magnetic resonance spectroscopy

    International Nuclear Information System (INIS)

    Bax, A.; Lerner, L.

    1986-01-01

    Great spectral simplification can be obtained by spreading the conventional one-dimensional nuclear magnetic resonance (NMR) spectrum in two independent frequency dimensions. This so-called two-dimensional NMR spectroscopy removes spectral overlap, facilitates spectral assignment, and provides a wealth of additional information. For example, conformational information related to interproton distances is available from resonance intensities in certain types of two-dimensional experiments. Another method generates 1 H NMR spectra of a preselected fragment of the molecule, suppressing resonances from other regions and greatly simplifying spectral appearance. Two-dimensional NMR spectroscopy can also be applied to the study of 13 C and 15 N, not only providing valuable connectivity information but also improving sensitivity of 13 C and 15 N detection by up to two orders of magnitude. 45 references, 10 figures

  14. A low threshold nanocavity in a two-dimensional 12-fold photonic quasicrystal

    Science.gov (United States)

    Ren, Jie; Sun, XiaoHong; Wang, Shuai

    2018-05-01

    In this article, a low threshold nanocavity is built and investigated in a two-dimensional 12-fold holographic photonic quasicrystal (PQC). The cavity is formed by using the method of multi-beam common-path interference. By finely adjusting the structure parameters of the cavity, the Q factor and the mode volume are optimized, which are two keys to low-threshold on the basis of Purcell effect. Finally, an optimal cavity is obtained with Q value of 6023 and mode volume of 1.24 ×10-12cm3 . On the other hand, by Fourier Transformation of the electric field components in the cavity, the in-plane wave vectors are calculated and fitted to evaluate the cavity performance. The performance analysis of the cavity further proves the effectiveness of the optimization process. This has a guiding significance for the research of low threshold nano-laser.

  15. Comb-like optical transmission spectra generated from one-dimensional two-segment-connected two-material waveguide networks optimized by genetic algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yu [MOE Key Laboratory of Laser Life Science and Institute of Laser Life Science, College of Biophotonics, South China Normal University, Guangzhou 510631 (China); Yang, Xiangbo, E-mail: xbyang@scnu.edu.cn [MOE Key Laboratory of Laser Life Science and Institute of Laser Life Science, College of Biophotonics, South China Normal University, Guangzhou 510631 (China); School of Physical Education and Sports Science, South China Normal University, Guangzhou 510006 (China); Lu, Jian; Zhang, Guogang [MOE Key Laboratory of Laser Life Science and Institute of Laser Life Science, College of Biophotonics, South China Normal University, Guangzhou 510631 (China); Liu, Chengyi Timon [School of Physical Education and Sports Science, South China Normal University, Guangzhou 510006 (China)

    2014-03-01

    In this Letter, a one-dimensional (1D) two-segment-connected two-material waveguide network (TSCTMWN) is designed to produce comb-like frequency passbands, where each waveguide segment is composed of normal and anomalous dispersion materials and the length ratio of sub-waveguide segments is optimized by genetic algorithm (GA). It is found that 66 comb-like frequency passbands are created in the second frequency unit, maximal relative width difference of which is less than 2×10{sup −5}. It may be useful for the designing of dense wavelength division multiplexings (DWDMs) and multi-channel filters, etc., and provide new applications for GA.

  16. Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

    Science.gov (United States)

    Holmes, J. J.; Balanis, C. A.

    1974-01-01

    Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.

  17. On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential

    International Nuclear Information System (INIS)

    Quan, Xu; Qiang, Tian

    2009-01-01

    This paper discusses the two-dimensional discrete monatomic Fermi–Pasta–Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather. (condensed matter: structure, thermal and mechanical properties)

  18. Two-dimensional models

    International Nuclear Information System (INIS)

    Schroer, Bert; Freie Universitaet, Berlin

    2005-02-01

    It is not possible to compactly review the overwhelming literature on two-dimensional models in a meaningful way without a specific viewpoint; I have therefore tacitly added to the above title the words 'as theoretical laboratories for general quantum field theory'. I dedicate this contribution to the memory of J. A. Swieca with whom I have shared the passion of exploring 2-dimensional models for almost one decade. A shortened version of this article is intended as a contribution to the project 'Encyclopedia of mathematical physics' and comments, suggestions and critical remarks are welcome. (author)

  19. Chemical profiling and adulteration screening of Aquilariae Lignum Resinatum by Fourier transform infrared (FT-IR) spectroscopy and two-dimensional correlation infrared (2D-IR) spectroscopy

    Science.gov (United States)

    Qu, Lei; Chen, Jian-bo; Zhang, Gui-Jun; Sun, Su-qin; Zheng, Jing

    2017-03-01

    As a kind of expensive perfume and valuable herb, Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy is employed to establish a simple and quick method for the adulteration screening of ALR. First, the principal chemical constituents of ALR are characterized by FT-IR spectroscopy at room temperature and two-dimensional correlation infrared (2D-IR) spectroscopy with thermal perturbation. Besides the common cellulose and lignin compounds, a certain amount of resin is the characteristic constituent of ALR. Synchronous and asynchronous 2D-IR spectra indicate that the resin (an unstable secondary metabolite) is more sensitive than cellulose and lignin (stable structural constituents) to the thermal perturbation. Using a certified ALR sample as the reference, the infrared spectral correlation threshold is determined by 30 authentic samples and 6 adulterated samples. The spectral correlation coefficient of an authentic ALR sample to the standard reference should be not less than 0.9886 (p = 0.01). Three commercial adulterated ALR samples are identified by the correlation threshold. Further interpretation of the infrared spectra of the adulterated samples indicates the common adulterating methods - counterfeiting with other kind of wood, adding ingredient such as sand to increase the weight, and adding the cheap resin such as rosin to increase the content of resin compounds. Results of this research prove that FT-IR spectroscopy can be used as a simple and accurate quality control method of ALR.

  20. Application of the windowed-Fourier-transform-based fringe analysis technique for investigating temperature and concentration fields in fluids.

    Science.gov (United States)

    Mohanan, Sharika; Srivastava, Atul

    2014-04-10

    The present work is concerned with the development and application of a novel fringe analysis technique based on the principles of the windowed-Fourier-transform (WFT) for the determination of temperature and concentration fields from interferometric images for a range of heat and mass transfer applications. Based on the extent of the noise level associated with the experimental data, the technique has been coupled with two different phase unwrapping methods: the Itoh algorithm and the quality guided phase unwrapping technique for phase extraction. In order to generate the experimental data, a range of experiments have been carried out which include cooling of a vertical flat plate in free convection conditions, combustion of mono-propellant flames, and growth of organic as well as inorganic crystals from their aqueous solutions. The flat plate and combustion experiments are modeled as heat transfer applications wherein the interest is to determine the whole-field temperature distribution. Aqueous-solution-based crystal growth experiments are performed to simulate the mass transfer phenomena and the interest is to determine the two-dimensional solute concentration field around the growing crystal. A Mach-Zehnder interferometer has been employed to record the path-integrated quantity of interest (temperature and/or concentration) in the form of interferometric images in the experiments. The potential of the WFT method has also been demonstrated on numerically simulated phase data for varying noise levels, and the accuracy in phase extraction have been quantified in terms of the root mean square errors. Three levels of noise, i.e., 0%, 10%, and 20% have been considered. Results of the present study show that the WFT technique allows an accurate extraction of phase values that can subsequently be converted into two-dimensional temperature and/or concentration distribution fields. Moreover, since WFT is a local processing technique, speckle patterns and the inherent

  1. Gaussian particle filter based pose and motion estimation

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Determination of relative three-dimensional (3D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry.A solution to pose and motion estimation problem that uses two-dimensional (2D) intensity images from a single camera is desirable for real-time applications. The difficulty in performing this measurement is that the process of projecting 3D object features to 2D images is a nonlinear transformation. In this paper, the 3D transformation is modeled as a nonlinear stochastic system with the state estimation providing six degrees-of-freedom motion and position values, using line features in image plane as measuring inputs and dual quaternion to represent both rotation and translation in a unified notation. A filtering method called the Gaussian particle filter (GPF) based on the particle filtering concept is presented for 3D pose and motion estimation of a moving target from monocular image sequences. The method has been implemented with simulated data, and simulation results are provided along with comparisons to the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) to show the relative advantages of the GPF. Simulation results showed that GPF is a superior alternative to EKF and UKF.

  2. Two-dimensional multifractal cross-correlation analysis

    International Nuclear Information System (INIS)

    Xi, Caiping; Zhang, Shuning; Xiong, Gang; Zhao, Huichang; Yang, Yonghong

    2017-01-01

    Highlights: • We study the mathematical models of 2D-MFXPF, 2D-MFXDFA and 2D-MFXDMA. • Present the definition of the two-dimensional N 2 -partitioned multiplicative cascading process. • Do the comparative analysis of 2D-MC by 2D-MFXPF, 2D-MFXDFA and 2D-MFXDMA. • Provide a reference on the choice and parameter settings of these methods in practice. - Abstract: There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection.

  3. Mean-square performance of a convex combination of two adaptive filters

    DEFF Research Database (Denmark)

    Garcia, Jeronimo; Figueiras-Vidal, A.R.; Sayed, A.H.

    2006-01-01

    Combination approaches provide an interesting way to improve adaptive filter performance. In this paper, we study the mean-square performance of a convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination i...

  4. Efficient Implementation of Complex Modulated Filter Banks Using Cosine and Sine Modulated Filter Banks

    Directory of Open Access Journals (Sweden)

    Viholainen Ari

    2006-01-01

    Full Text Available The recently introduced exponentially modulated filter bank (EMFB is a -channel uniform, orthogonal, critically sampled, and frequency-selective complex modulated filter bank that satisfies the perfect reconstruction (PR property if the prototype filter of an -channel PR cosine modulated filter bank (CMFB is used. The purpose of this paper is to present various implementation structures for the EMFBs in a unified framework. The key idea is to use cosine and sine modulated filter banks as building blocks and, therefore, polyphase, lattice, and extended lapped transform (ELT type of implementation solutions are studied. The ELT-based EMFBs are observed to be very competitive with the existing modified discrete Fourier transform filter banks (MDFT-FBs when comparing the number of multiplications/additions and the structural simplicity. In addition, EMFB provides an alternative channel stacking arrangement that could be more natural in certain subband processing applications and data transmission systems.

  5. Two-dimensional beam profiles and one-dimensional projections

    Science.gov (United States)

    Findlay, D. J. S.; Jones, B.; Adams, D. J.

    2018-05-01

    One-dimensional projections of improved two-dimensional representations of transverse profiles of particle beams are proposed for fitting to data from harp-type monitors measuring beam profiles on particle accelerators. Composite distributions, with tails smoothly matched on to a central (inverted) parabola, are shown to give noticeably better fits than single gaussian and single parabolic distributions to data from harp-type beam profile monitors all along the proton beam transport lines to the two target stations on the ISIS Spallation Neutron Source. Some implications for inferring beam current densities on the beam axis are noted.

  6. A latent model for collaborative filtering

    DEFF Research Database (Denmark)

    Langseth, Helge; Nielsen, Thomas Dyhre

    2012-01-01

    Recommender systems based on collaborative filtering have received a great deal of interest over the last two decades. In particular, recently proposed methods based on dimensionality reduction techniques and using a symmetrical representation of users and items have shown promising results. Foll...

  7. Symmetrized neutron transport equation and the fast Fourier transform method

    International Nuclear Information System (INIS)

    Sinh, N.Q.; Kisynski, J.; Mika, J.

    1978-01-01

    The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations

  8. 10th International Conference on Progress in Fourier Transform Spectroscopy

    CERN Document Server

    Keresztury, Gábor; Kellner, Robert

    1997-01-01

    19 plenary lectures and 203 poster papers presented at the 10th International Conference of Fourier Transform Spectroscopy in Budapest 1995 give an overview on the state-of-the art of this technology and its wide range of applications. The reader will get information on any aspects of FTS including the latest instrumental developments, e.g. in diode array detection, time resolution FTS, microscopy and spectral mapping, double modulation and two-dimensional FTS.

  9. Comparison of Deconvolution Filters for Photoacoustic Tomography.

    Directory of Open Access Journals (Sweden)

    Dominique Van de Sompel

    Full Text Available In this work, we compare the merits of three temporal data deconvolution methods for use in the filtered backprojection algorithm for photoacoustic tomography (PAT. We evaluate the standard Fourier division technique, the Wiener deconvolution filter, and a Tikhonov L-2 norm regularized matrix inversion method. Our experiments were carried out on subjects of various appearances, namely a pencil lead, two man-made phantoms, an in vivo subcutaneous mouse tumor model, and a perfused and excised mouse brain. All subjects were scanned using an imaging system with a rotatable hemispherical bowl, into which 128 ultrasound transducer elements were embedded in a spiral pattern. We characterized the frequency response of each deconvolution method, compared the final image quality achieved by each deconvolution technique, and evaluated each method's robustness to noise. The frequency response was quantified by measuring the accuracy with which each filter recovered the ideal flat frequency spectrum of an experimentally measured impulse response. Image quality under the various scenarios was quantified by computing noise versus resolution curves for a point source phantom, as well as the full width at half maximum (FWHM and contrast-to-noise ratio (CNR of selected image features such as dots and linear structures in additional imaging subjects. It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum, achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise. While the Wiener filter achieved a similar image resolution, it tended to underrepresent the lower frequency content of the deconvolved signals, and hence of the reconstructed images after backprojection. In addition, its robustness to noise was poorer than that of the Tikhonov

  10. Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

    Science.gov (United States)

    Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

    2016-01-01

    Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

  11. Performance of drippers in two filtering systems using sewage treatment effluent

    Directory of Open Access Journals (Sweden)

    Alexandre B. Dalri

    Full Text Available ABSTRACT The objective of this study was to evaluate the performance of three models of drippers using treated sewage effluent, pure and diluted, and two types of filters, screen and disc. The treated sewage effluent used in the experiment was collected from the city’s treatment plant. The experiment included 12 lateral lines with three types of emitters to apply pure (100% and diluted (50% effluent filtered by screen and disc filters. The combination of those factors set the treatments: T1 (50% effluent diluted in fresh water filtered by a screen filter; T2 (50% effluent diluted in fresh water filtered by a disc filter; T3 (pure effluent filtered by a screen filter; T4 (pure effluent filtered by a disc filter. The results showed that the flat type emitter is less sensitive to clogging, the disc filter is the most suitable to prevent clogging and the use of pure or diluted sewage effluent increases the drippers’ flow rate coefficient of variation.

  12. Lie algebra contractions on two-dimensional hyperboloid

    International Nuclear Information System (INIS)

    Pogosyan, G. S.; Yakhno, A.

    2010-01-01

    The Inoenue-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the four corresponding two-dimensional homogeneous spaces: two-dimensional hyperboloids and two-dimensional Euclidean and pseudo-Euclidean spaces. We show how the nine systems of coordinates on the two-dimensional hyperboloids contracted to the four systems of coordinates on E 2 and eight on E 1,1 . The text was submitted by the authors in English.

  13. Quasi-two-dimensional holography

    International Nuclear Information System (INIS)

    Kutzner, J.; Erhard, A.; Wuestenberg, H.; Zimpfer, J.

    1980-01-01

    The acoustical holography with numerical reconstruction by area scanning is memory- and time-intensive. With the experiences by the linear holography we tried to derive a scanning for the evaluating of the two-dimensional flaw-sizes. In most practical cases it is sufficient to determine the exact depth extension of a flaw, whereas the accuracy of the length extension is less critical. For this reason the applicability of the so-called quasi-two-dimensional holography is appropriate. The used sound field given by special probes is divergent in the inclined plane and light focussed in the perpendicular plane using cylindrical lenses. (orig.) [de

  14. Topology optimization of two-dimensional waveguides

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2003-01-01

    In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....

  15. Traditional Semiconductors in the Two-Dimensional Limit.

    Science.gov (United States)

    Lucking, Michael C; Xie, Weiyu; Choe, Duk-Hyun; West, Damien; Lu, Toh-Ming; Zhang, S B

    2018-02-23

    Interest in two-dimensional materials has exploded in recent years. Not only are they studied due to their novel electronic properties, such as the emergent Dirac fermion in graphene, but also as a new paradigm in which stacking layers of distinct two-dimensional materials may enable different functionality or devices. Here, through first-principles theory, we reveal a large new class of two-dimensional materials which are derived from traditional III-V, II-VI, and I-VII semiconductors. It is found that in the ultrathin limit the great majority of traditional binary semiconductors studied (a series of 28 semiconductors) are not only kinetically stable in a two-dimensional double layer honeycomb structure, but more energetically stable than the truncated wurtzite or zinc-blende structures associated with three dimensional bulk. These findings both greatly increase the landscape of two-dimensional materials and also demonstrate that in the double layer honeycomb form, even ordinary semiconductors, such as GaAs, can exhibit exotic topological properties.

  16. Simultaneous two-wavelength tri-window common-path digital holography

    Science.gov (United States)

    Liu, Lei; Shan, Mingguang; Zhong, Zhi

    2018-06-01

    Two-wavelength common-path off-axis digital holography is proposed with a tri-window in a single shot. It is established using a standard 4f optical image system with a 2D Ronchi grating placed outside the Fourier plane. The input plane consists of three windows: one for the object and the other two for reference. Aided by a spatial filter together with two orthogonal linear polarizers in the Fourier plane, the two-wavelength information is encoded into a multiplexed hologram with two orthogonal spatial frequencies that enable full separation of spectral information in the digital Fourier space without resolution loss. Theoretical analysis and experimental results illustrate that our approach can simultaneously perform quantitative phase imaging at two wavelengths.

  17. Sufficient Controllability Condition for Affine Systems with Two-Dimensional Control and Two-Dimensional Zero Dynamics

    Directory of Open Access Journals (Sweden)

    D. A. Fetisov

    2015-01-01

    Full Text Available The controllability conditions are well known if we speak about linear stationary systems: a linear stationary system is controllable if and only if the dimension of the state vector is equal to the rank of the controllability matrix. The concept of the controllability matrix is extended to affine systems, but relations between affine systems controllability and properties of this matrix are more complicated. Various controllability conditions are set for affine systems, but they deal as usual either with systems of some special form or with controllability in some small neighborhood of the concerned point. An affine system is known to be controllable if the system is equivalent to a system of a canonical form, which is defined and regular in the whole space of states. In this case, the system is said to be feedback linearizable in the space of states. However there are examples, which illustrate that a system can be controllable even if it is not feedback linearizable in any open subset in the space of states. In this article we deal with such systems.Affine systems with two-dimensional control are considered. The system in question is assumed to be equivalent to a system of a quasicanonical form with two-dimensional zero dynamics which is defined and regular in the whole space of states. Therefore the controllability of the original system is equivalent to the controllability of the received system of a quasicanonical form. In this article the sufficient condition for an available solution of the terminal problem is proven for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. The condition is valid in the case of an arbitrary time interval and arbitrary initial and finite states of the system. Therefore the controllability condition is set for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. An example is given which illustrates how the proved

  18. An asymptotic analytical solution to the problem of two moving boundaries with fractional diffusion in one-dimensional drug release devices

    International Nuclear Information System (INIS)

    Yin Chen; Xu Mingyu

    2009-01-01

    We set up a one-dimensional mathematical model with a Caputo fractional operator of a drug released from a polymeric matrix that can be dissolved into a solvent. A two moving boundaries problem in fractional anomalous diffusion (in time) with order α element of (0, 1] under the assumption that the dissolving boundary can be dissolved slowly is presented in this paper. The two-parameter regular perturbation technique and Fourier and Laplace transform methods are used. A dimensionless asymptotic analytical solution is given in terms of the Wright function

  19. Spectrometer Baseline Control Via Spatial Filtering

    Science.gov (United States)

    Burleigh, M. R.; Richey, C. R.; Rinehart, S. A.; Quijada, M. A.; Wollack, E. J.

    2016-01-01

    An absorptive half-moon aperture mask is experimentally explored as a broad-bandwidth means of eliminating spurious spectral features arising from reprocessed radiation in an infrared Fourier transform spectrometer. In the presence of the spatial filter, an order of magnitude improvement in the fidelity of the spectrometer baseline is observed. The method is readily accommodated within the context of commonly employed instrument configurations and leads to a factor of two reduction in optical throughput. A detailed discussion of the underlying mechanism and limitations of the method are provided.

  20. Do the results of respirable dust samples obtained from direct-on-filter X-ray diffraction, direct-on-filter infrared and indirect infrared (KBr pellet) methods correlate?

    CSIR Research Space (South Africa)

    Pretorius, C

    2010-11-01

    Full Text Available The objective of this study was to determine whether a correlation exists between the quartz results obtained from direct-on-filter X-ray Diffraction analysis, direct-on-filter Fourier-Transform Infrared analysis and indirect analysis (Potassium...

  1. Direct-on-Filter α-Quartz Estimation in Respirable Coal Mine Dust Using Transmission Fourier Transform Infrared Spectrometry and Partial Least Squares Regression.

    Science.gov (United States)

    Miller, Arthur L; Weakley, Andrew Todd; Griffiths, Peter R; Cauda, Emanuele G; Bayman, Sean

    2017-05-01

    In order to help reduce silicosis in miners, the National Institute for Occupational Health and Safety (NIOSH) is developing field-portable methods for measuring airborne respirable crystalline silica (RCS), specifically the polymorph α-quartz, in mine dusts. In this study we demonstrate the feasibility of end-of-shift measurement of α-quartz using a direct-on-filter (DoF) method to analyze coal mine dust samples deposited onto polyvinyl chloride filters. The DoF method is potentially amenable for on-site analyses, but deviates from the current regulatory determination of RCS for coal mines by eliminating two sample preparation steps: ashing the sampling filter and redepositing the ash prior to quantification by Fourier transform infrared (FT-IR) spectrometry. In this study, the FT-IR spectra of 66 coal dust samples from active mines were used, and the RCS was quantified by using: (1) an ordinary least squares (OLS) calibration approach that utilizes standard silica material as done in the Mine Safety and Health Administration's P7 method; and (2) a partial least squares (PLS) regression approach. Both were capable of accounting for kaolinite, which can confound the IR analysis of silica. The OLS method utilized analytical standards for silica calibration and kaolin correction, resulting in a good linear correlation with P7 results and minimal bias but with the accuracy limited by the presence of kaolinite. The PLS approach also produced predictions well-correlated to the P7 method, as well as better accuracy in RCS prediction, and no bias due to variable kaolinite mass. Besides decreased sensitivity to mineral or substrate confounders, PLS has the advantage that the analyst is not required to correct for the presence of kaolinite or background interferences related to the substrate, making the method potentially viable for automated RCS prediction in the field. This study demonstrated the efficacy of FT-IR transmission spectrometry for silica determination in

  2. Detection of 320 Gb/s Nyquist OTDM by polarization-insensitive time-domain optical Fourier transformation

    DEFF Research Database (Denmark)

    Hu, Hao; Kong, Deming; Palushani, Evarist

    2013-01-01

    320 Gb/s Nyquist-OTDM is generated by rectangular filtering with a bandwidth of 320 GHz and received by polarization-insensitive time-domain optical Fourier transformation (TD-OFT) followed by passive filtering. After the time-to-frequency mapping in the TD-OFT, the Nyquist-OTDM is converted into...

  3. A Note On Signs Of Fourier Coefficients Of Two Cusp Forms

    Indian Academy of Sciences (India)

    10

    Abstract. Kohnen and Sengupta showed that if two Hecke eigen cusp forms of weight k1 and k2 respectively with 1 < k1 < k2 over. Γ0(N ), have totally real algebraic Fourier coefficients {a(n)} and. {b(n)} respectively for n ≥ 1 with a(1) = 1 = b(1), then there exists an element σ of the absolute Galois group Gal(Q/Q) such.

  4. Sparse Channel Estimation Including the Impact of the Transceiver Filters with Application to OFDM

    DEFF Research Database (Denmark)

    Barbu, Oana-Elena; Pedersen, Niels Lovmand; Manchón, Carles Navarro

    2014-01-01

    Traditionally, the dictionary matrices used in sparse wireless channel estimation have been based on the discrete Fourier transform, following the assumption that the channel frequency response (CFR) can be approximated as a linear combination of a small number of multipath components, each one......) and receive (demodulation) filters. Hence, the assumption of the CFR being sparse in the canonical Fourier dictionary may no longer hold. In this work, we derive a signal model and subsequently a novel dictionary matrix for sparse estimation that account for the impact of transceiver filters. Numerical...... results obtained in an OFDM transmission scenario demonstrate the superior accuracy of a sparse estimator that uses our proposed dictionary rather than the classical Fourier dictionary, and its robustness against a mismatch in the assumed transmit filter characteristics....

  5. Spatial filtering of light by chirped photonic crystals

    International Nuclear Information System (INIS)

    Staliunas, Kestutis; Sanchez-Morcillo, Victor J.

    2009-01-01

    We propose an efficient method for spatial filtering of light beams by propagating them through two-dimensional (also three dimensional) chirped photonic crystals, i.e., through the photonic structures with fixed transverse lattice period and with the longitudinal lattice period varying along the direction of the beam propagation. We prove the proposed idea by numerically solving the paraxial propagation equation in refraction-index-modulated media and we evaluate the efficiency of the process by harmonic-expansion analysis. The technique can be also applied for filtering (for cleaning) of the packages of atomic waves (Bose condensates), also to improve the directionality of acoustic and mechanical waves.

  6. Limited-angle three-dimensional reconstructions using Fourier transform iterations and Radon transform iterations

    International Nuclear Information System (INIS)

    Tam, K.C.; Perez-Mendez, V.

    1981-01-01

    The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been analyzed in detail. it was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect which tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time

  7. Converting Panax ginseng DNA and chemical fingerprints into two-dimensional barcode.

    Science.gov (United States)

    Cai, Yong; Li, Peng; Li, Xi-Wen; Zhao, Jing; Chen, Hai; Yang, Qing; Hu, Hao

    2017-07-01

    In this study, we investigated how to convert the Panax ginseng DNA sequence code and chemical fingerprints into a two-dimensional code. In order to improve the compression efficiency, GATC2Bytes and digital merger compression algorithms are proposed. HPLC chemical fingerprint data of 10 groups of P. ginseng from Northeast China and the internal transcribed spacer 2 (ITS2) sequence code as the DNA sequence code were ready for conversion. In order to convert such data into a two-dimensional code, the following six steps were performed: First, the chemical fingerprint characteristic data sets were obtained through the inflection filtering algorithm. Second, precompression processing of such data sets is undertaken. Third, precompression processing was undertaken with the P. ginseng DNA (ITS2) sequence codes. Fourth, the precompressed chemical fingerprint data and the DNA (ITS2) sequence code were combined in accordance with the set data format. Such combined data can be compressed by Zlib, an open source data compression algorithm. Finally, the compressed data generated a two-dimensional code called a quick response code (QR code). Through the abovementioned converting process, it can be found that the number of bytes needed for storing P. ginseng chemical fingerprints and its DNA (ITS2) sequence code can be greatly reduced. After GTCA2Bytes algorithm processing, the ITS2 compression rate reaches 75% and the chemical fingerprint compression rate exceeds 99.65% via filtration and digital merger compression algorithm processing. Therefore, the overall compression ratio even exceeds 99.36%. The capacity of the formed QR code is around 0.5k, which can easily and successfully be read and identified by any smartphone. P. ginseng chemical fingerprints and its DNA (ITS2) sequence code can form a QR code after data processing, and therefore the QR code can be a perfect carrier of the authenticity and quality of P. ginseng information. This study provides a theoretical

  8. The Pegg–Barnett phase operator and the discrete Fourier transform

    International Nuclear Information System (INIS)

    Perez-Leija, Armando; Szameit, Alexander; Andrade-Morales, Luis A; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

    2016-01-01

    In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg–Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London–Susskind–Glogower phase operator, whose natural logarithm gives rise to the Pegg–Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties. (invited comment)

  9. Holographic and time-resolving ability of pulse-pair two-dimensional velocity interferometry

    International Nuclear Information System (INIS)

    Erskine, David J.; Smith, R. F.; Celliers, P. M.; Collins, G. W.; Bolme, C. A.; Ali, S. J.

    2014-01-01

    Previous velocity interferometers used at research laboratories for shock physics experiments measured target motion at a point or many points on a line on the target. Recently, a two-dimensional (2d) version (2d-velocity interferometer system for any reflector) has been demonstrated using a pair of ultrashort (3 ps) pulses for illumination, separated by 268 ps. We have discovered new abilities for this instrument, by treating the complex output image as a hologram. For data taken in an out of focus configuration, we can Fourier process to bring narrow features such as cracks into sharp focus, which are otherwise completely blurred. This solves a practical problem when using high numerical aperture optics having narrow depth of field to observe moving surface features such as cracks. Furthermore, theory predicts that the target appearance (position and reflectivity) at two separate moments in time are recorded by the main and conjugate images of the same hologram, and are partially separable during analysis for narrow features. Hence, for the cracks we bring into refocus, we can make a two-frame movie with a subnanosecond frame period. Longer and shorter frame periods are possible with different interferometer delays. Since the megapixel optical detectors we use have superior spatial resolution over electronic beam based framing cameras, this technology could be of great use in studying microscopic three-dimensional-behavior of targets at ultrafast times scales. Demonstrations on shocked silicon are shown

  10. Holographic and time-resolving ability of pulse-pair two-dimensional velocity interferometry

    Energy Technology Data Exchange (ETDEWEB)

    Erskine, David J., E-mail: erskine1@llnl.gov; Smith, R. F.; Celliers, P. M.; Collins, G. W. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Bolme, C. A. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Ali, S. J. [Department of Chemistry, University of California, Berkeley, California 94720 (United States)

    2014-06-15

    Previous velocity interferometers used at research laboratories for shock physics experiments measured target motion at a point or many points on a line on the target. Recently, a two-dimensional (2d) version (2d-velocity interferometer system for any reflector) has been demonstrated using a pair of ultrashort (3 ps) pulses for illumination, separated by 268 ps. We have discovered new abilities for this instrument, by treating the complex output image as a hologram. For data taken in an out of focus configuration, we can Fourier process to bring narrow features such as cracks into sharp focus, which are otherwise completely blurred. This solves a practical problem when using high numerical aperture optics having narrow depth of field to observe moving surface features such as cracks. Furthermore, theory predicts that the target appearance (position and reflectivity) at two separate moments in time are recorded by the main and conjugate images of the same hologram, and are partially separable during analysis for narrow features. Hence, for the cracks we bring into refocus, we can make a two-frame movie with a subnanosecond frame period. Longer and shorter frame periods are possible with different interferometer delays. Since the megapixel optical detectors we use have superior spatial resolution over electronic beam based framing cameras, this technology could be of great use in studying microscopic three-dimensional-behavior of targets at ultrafast times scales. Demonstrations on shocked silicon are shown.

  11. Two-dimensional flexible nanoelectronics

    Science.gov (United States)

    Akinwande, Deji; Petrone, Nicholas; Hone, James

    2014-12-01

    2014/2015 represents the tenth anniversary of modern graphene research. Over this decade, graphene has proven to be attractive for thin-film transistors owing to its remarkable electronic, optical, mechanical and thermal properties. Even its major drawback--zero bandgap--has resulted in something positive: a resurgence of interest in two-dimensional semiconductors, such as dichalcogenides and buckled nanomaterials with sizeable bandgaps. With the discovery of hexagonal boron nitride as an ideal dielectric, the materials are now in place to advance integrated flexible nanoelectronics, which uniquely take advantage of the unmatched portfolio of properties of two-dimensional crystals, beyond the capability of conventional thin films for ubiquitous flexible systems.

  12. Fast data reconstructed method of Fourier transform imaging spectrometer based on multi-core CPU

    Science.gov (United States)

    Yu, Chunchao; Du, Debiao; Xia, Zongze; Song, Li; Zheng, Weijian; Yan, Min; Lei, Zhenggang

    2017-10-01

    Imaging spectrometer can gain two-dimensional space image and one-dimensional spectrum at the same time, which shows high utility in color and spectral measurements, the true color image synthesis, military reconnaissance and so on. In order to realize the fast reconstructed processing of the Fourier transform imaging spectrometer data, the paper designed the optimization reconstructed algorithm with OpenMP parallel calculating technology, which was further used for the optimization process for the HyperSpectral Imager of `HJ-1' Chinese satellite. The results show that the method based on multi-core parallel computing technology can control the multi-core CPU hardware resources competently and significantly enhance the calculation of the spectrum reconstruction processing efficiency. If the technology is applied to more cores workstation in parallel computing, it will be possible to complete Fourier transform imaging spectrometer real-time data processing with a single computer.

  13. Self-commissioning notch filter for active damping in three phase LCL-filter based grid converters

    DEFF Research Database (Denmark)

    Alzola, Rafael Pena; Liserre, Marco; Blaabjerg, Frede

    2013-01-01

    inductance variations it is proposed to estimate the resonance frequency by means of Fourier analysis. The Goertzel algorithm, instead of the FFT, is used to reduce the calculation and memory requirements. Thus, the proposed self-commissioning notch filter results robust and consumes little computational...

  14. TMS320C25 Digital Signal Processor For 2-Dimensional Fast Fourier Transform Computation

    International Nuclear Information System (INIS)

    Ardisasmita, M. Syamsa

    1996-01-01

    The Fourier transform is one of the most important mathematical tool in signal processing and analysis, which converts information from the time/spatial domain into the frequency domain. Even with implementation of the Fast Fourier Transform algorithms in imaging data, the discrete Fourier transform execution consume a lot of time. Digital signal processors are designed specifically to perform computation intensive digital signal processing algorithms. By taking advantage of the advanced architecture. parallel processing, and dedicated digital signal processing (DSP) instruction sets. This device can execute million of DSP operations per second. The device architecture, characteristics and feature suitable for fast Fourier transform application and speed-up are discussed

  15. Restoration of three-dimensional MR images degraded by rotational movements

    International Nuclear Information System (INIS)

    Wood, M.L.

    1990-01-01

    This paper describes a method to restore three-dimensional (3D) magnetic resonance (MR) images that have been degraded by rotational movements, such as head nodding by a restless patient. The technique for acquiring the 3D MR images includes additional MR signals, which provide one-dimensional (1D) and two-dimensional (2D) projections of anatomy. The 1D projections detect gross movements, and the 2D projections resolve displacements in one plane. The 2D projections are transformed from Cartesian coordinates to polar coordinates to identify rotation. A spatial transformation to reverse the rotation is applied to the imaging data after they have been Fourier transformed to resolve structures in the plane of rotation, but before the Fourier transform for the third direction

  16. Chemical profiling and adulteration screening of Aquilariae Lignum Resinatum by Fourier transform infrared (FT-IR) spectroscopy and two-dimensional correlation infrared (2D-IR) spectroscopy.

    Science.gov (United States)

    Qu, Lei; Chen, Jian-Bo; Zhang, Gui-Jun; Sun, Su-Qin; Zheng, Jing

    2017-03-05

    As a kind of expensive perfume and valuable herb, Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy is employed to establish a simple and quick method for the adulteration screening of ALR. First, the principal chemical constituents of ALR are characterized by FT-IR spectroscopy at room temperature and two-dimensional correlation infrared (2D-IR) spectroscopy with thermal perturbation. Besides the common cellulose and lignin compounds, a certain amount of resin is the characteristic constituent of ALR. Synchronous and asynchronous 2D-IR spectra indicate that the resin (an unstable secondary metabolite) is more sensitive than cellulose and lignin (stable structural constituents) to the thermal perturbation. Using a certified ALR sample as the reference, the infrared spectral correlation threshold is determined by 30 authentic samples and 6 adulterated samples. The spectral correlation coefficient of an authentic ALR sample to the standard reference should be not less than 0.9886 (p=0.01). Three commercial adulterated ALR samples are identified by the correlation threshold. Further interpretation of the infrared spectra of the adulterated samples indicates the common adulterating methods - counterfeiting with other kind of wood, adding ingredient such as sand to increase the weight, and adding the cheap resin such as rosin to increase the content of resin compounds. Results of this research prove that FT-IR spectroscopy can be used as a simple and accurate quality control method of ALR. Copyright © 2016 Elsevier B.V. All rights reserved.

  17. Multi-band transmission color filters for multi-color white LEDs based visible light communication

    Science.gov (United States)

    Wang, Qixia; Zhu, Zhendong; Gu, Huarong; Chen, Mengzhu; Tan, Qiaofeng

    2017-11-01

    Light-emitting diodes (LEDs) based visible light communication (VLC) can provide license-free bands, high data rates, and high security levels, which is a promising technique that will be extensively applied in future. Multi-band transmission color filters with enough peak transmittance and suitable bandwidth play a pivotal role for boosting signal-noise-ratio in VLC systems. In this paper, multi-band transmission color filters with bandwidth of dozens nanometers are designed by a simple analytical method. Experiment results of one-dimensional (1D) and two-dimensional (2D) tri-band color filters demonstrate the effectiveness of the multi-band transmission color filters and the corresponding analytical method.

  18. Implicit particle filtering for equations with partial noise and application to geomagnetic data assimilation

    Science.gov (United States)

    Morzfeld, M.; Atkins, E.; Chorin, A. J.

    2011-12-01

    covariance matrix Σ is assumed to be non-singular. In the present work we consider the case where the covariance Σ is singular. This happens in particular when the noise is spatially smooth and can be represented by a small number of Fourier coefficients, as is often the case in geophysical applications. We derive an implicit filter for this problem and show that it is very efficient, because the filter operates in a space whose dimension is the rank of Σ, rather than the full model dimension. We compare the implicit filter to SIR, to the Ensemble Kalman Filter and to variational methods, and also study how information from data is propagated from observed to unobserved variables. We illustrate the theory on two coupled nonlinear PDE's in one space dimension that have been used as a test-bed for geomagnetic data assimilation. We observe that the implicit filter gives good results with few (2-10) particles, while SIR requires thousands of particles for similar accuracy. We also find lower limits to the accuracy of the filter's reconstruction as a function of data availability.

  19. Three-dimensional anisotropic adaptive filtering of projection data for noise reduction in cone beam CT

    Energy Technology Data Exchange (ETDEWEB)

    Maier, Andreas; Wigstroem, Lars; Hofmann, Hannes G.; Hornegger, Joachim; Zhu Lei; Strobel, Norbert; Fahrig, Rebecca [Department of Radiology, Stanford University, Stanford, California 94305 (United States); Department of Radiology, Stanford University, Stanford, California 94305 (United States) and Center for Medical Image Science and Visualization, Linkoeping University, Linkoeping (Sweden); Pattern Recognition Laboratory, Department of Computer Science, Friedrich-Alexander University of Erlangen-Nuremberg, 91054, Erlangen (Germany); Nuclear and Radiological Engineering and Medical Physics Programs, George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Siemens AG Healthcare, Forchheim 91301 (Germany); Department of Radiology, Stanford University, Stanford, California 94305 (United States)

    2011-11-15

    Purpose: The combination of quickly rotating C-arm gantry with digital flat panel has enabled the acquisition of three-dimensional data (3D) in the interventional suite. However, image quality is still somewhat limited since the hardware has not been optimized for CT imaging. Adaptive anisotropic filtering has the ability to improve image quality by reducing the noise level and therewith the radiation dose without introducing noticeable blurring. By applying the filtering prior to 3D reconstruction, noise-induced streak artifacts are reduced as compared to processing in the image domain. Methods: 3D anisotropic adaptive filtering was used to process an ensemble of 2D x-ray views acquired along a circular trajectory around an object. After arranging the input data into a 3D space (2D projections + angle), the orientation of structures was estimated using a set of differently oriented filters. The resulting tensor representation of local orientation was utilized to control the anisotropic filtering. Low-pass filtering is applied only along structures to maintain high spatial frequency components perpendicular to these. The evaluation of the proposed algorithm includes numerical simulations, phantom experiments, and in-vivo data which were acquired using an AXIOM Artis dTA C-arm system (Siemens AG, Healthcare Sector, Forchheim, Germany). Spatial resolution and noise levels were compared with and without adaptive filtering. A human observer study was carried out to evaluate low-contrast detectability. Results: The adaptive anisotropic filtering algorithm was found to significantly improve low-contrast detectability by reducing the noise level by half (reduction of the standard deviation in certain areas from 74 to 30 HU). Virtually no degradation of high contrast spatial resolution was observed in the modulation transfer function (MTF) analysis. Although the algorithm is computationally intensive, hardware acceleration using Nvidia's CUDA Interface provided an 8

  20. Three-dimensional anisotropic adaptive filtering of projection data for noise reduction in cone beam CT

    International Nuclear Information System (INIS)

    Maier, Andreas; Wigstroem, Lars; Hofmann, Hannes G.; Hornegger, Joachim; Zhu Lei; Strobel, Norbert; Fahrig, Rebecca

    2011-01-01

    Purpose: The combination of quickly rotating C-arm gantry with digital flat panel has enabled the acquisition of three-dimensional data (3D) in the interventional suite. However, image quality is still somewhat limited since the hardware has not been optimized for CT imaging. Adaptive anisotropic filtering has the ability to improve image quality by reducing the noise level and therewith the radiation dose without introducing noticeable blurring. By applying the filtering prior to 3D reconstruction, noise-induced streak artifacts are reduced as compared to processing in the image domain. Methods: 3D anisotropic adaptive filtering was used to process an ensemble of 2D x-ray views acquired along a circular trajectory around an object. After arranging the input data into a 3D space (2D projections + angle), the orientation of structures was estimated using a set of differently oriented filters. The resulting tensor representation of local orientation was utilized to control the anisotropic filtering. Low-pass filtering is applied only along structures to maintain high spatial frequency components perpendicular to these. The evaluation of the proposed algorithm includes numerical simulations, phantom experiments, and in-vivo data which were acquired using an AXIOM Artis dTA C-arm system (Siemens AG, Healthcare Sector, Forchheim, Germany). Spatial resolution and noise levels were compared with and without adaptive filtering. A human observer study was carried out to evaluate low-contrast detectability. Results: The adaptive anisotropic filtering algorithm was found to significantly improve low-contrast detectability by reducing the noise level by half (reduction of the standard deviation in certain areas from 74 to 30 HU). Virtually no degradation of high contrast spatial resolution was observed in the modulation transfer function (MTF) analysis. Although the algorithm is computationally intensive, hardware acceleration using Nvidia's CUDA Interface provided an 8.9-fold

  1. Approximate solutions for the two-dimensional integral transport equation. Solution of complex two-dimensional transport problems

    International Nuclear Information System (INIS)

    Sanchez, Richard.

    1980-11-01

    This work is divided into two parts: the first part deals with the solution of complex two-dimensional transport problems, the second one (note CEA-N-2166) treats the critically mixed methods of resolution. A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the interface current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding, and water, or homogenized structural material. The cells are divided into zones that are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is effected by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: CALLIOPE uses a cylindrical cell model and one or three terms for the flux expansion, and NAUSICAA uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes, one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark problems and by calculations performed in the APOLLO multigroup code [fr

  2. Instantaneous lineshape analysis of Fourier domain mode-locked lasers.

    Science.gov (United States)

    Todor, Sebastian; Biedermann, Benjamin; Wieser, Wolfgang; Huber, Robert; Jirauschek, Christian

    2011-04-25

    We present a theoretical and experimental analysis of the instantaneous lineshape of Fourier domain mode-locked (FDML) lasers, yielding good agreement. The simulations are performed employing a recently introduced model for FDML operation. Linewidths around 10 GHz are found, which is significantly below the sweep filter bandwidth. The effect of detuning between the sweep filter drive frequency and cavity roundtrip time is studied revealing features that cannot be resolved in the experiment, and shifting of the instantaneous power spectrum against the sweep filter center frequency is analyzed. We show that, in contrast to most other semiconductor based lasers, the instantaneous linewidth is governed neither by external noise sources nor by amplified spontaneous emission, but it is directly determined by the complex FDML dynamics.

  3. Two-dimensional topological field theories coupled to four-dimensional BF theory

    International Nuclear Information System (INIS)

    Montesinos, Merced; Perez, Alejandro

    2008-01-01

    Four-dimensional BF theory admits a natural coupling to extended sources supported on two-dimensional surfaces or string world sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two-dimensional world sheet. We show how two-dimensional Yang-Mills degrees of freedom can be added on the world sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two-dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background-independent quantum field theory where local degrees of freedom at low energies arise from global topological (world sheet) degrees of freedom at the fundamental level

  4. Algorithm for three dimension reconstruction of magnetic resonance tomographs and X-ray images based on Fast Fourier Transform

    International Nuclear Information System (INIS)

    Bueno, Josiane M.; Traina, Agma Juci M.; Cruvinel, Paulo E.

    1995-01-01

    This work presents an algorithm for three-dimensional digital image reconstruction. Such algorithms based on the combination of both a Fast Fourier Transform method with Hamming Window and the use of a tri-linear interpolation function. The algorithm allows not only the generation of three-dimensional spatial spin distribution maps for Magnetic Resonance Tomography data but also X and Y-rays linear attenuation coefficient maps for CT scanners. Results demonstrates the usefulness of the algorithm in three-dimensional image reconstruction by doing first two-dimensional reconstruction and rather after interpolation. The algorithm was developed in C++ language, and there are two available versions: one under the DOS environment, and the other under the UNIX/Sun environment. (author)

  5. Performance evaluation of 3-D enhancement filters for detection of lung cancer from 3-D chest X-ray CT images

    International Nuclear Information System (INIS)

    Shimizu, Akinobu; Hagai, Makoto; Toriwaki, Jun-ichiro; Hasegawa, Jun-ichi.

    1995-01-01

    This paper evaluates the performance of several three dimensional enhancement filters used in procedures for detecting lung cancer shadows from three dimensional (3D) chest X-ray CT images. Two dimensional enhancement filters such as Min-DD filter, Contrast filter and N-Quoit filter have been proposed for enhancing cancer shadows in conventional 2D X-ray images. In this paper, we extend each of these 2D filters to a 3D filter and evaluate its performance experimentally by using CT images with artificial and true lung cancer shadows. As a result, we find that these 3D filters are effective for determining the position of a lung cancer shadow in a 3D chest CT image, as compared with the simple procedure such as smoothing filter, and that the performance of these filters become lower in the hilar area due to the influence of the vessel shadows. (author)

  6. Progress report of a static Fourier transform spectrometer breadboard

    Science.gov (United States)

    Rosak, A.; Tintó, F.

    2017-11-01

    MOLI instrument -for MOtionLess Interferometer- takes advantage of the new concept of static Fourier transform spectrometer. It is a high-resolution spectrometer working over a narrow bandwidth, which is adapted to a wide range of atmospheric sounding missions and compatible with micro-satellite platform. The core of this instrument is an echelette cube. Mirrors on the classical design are replaced by stepped mirrors -integrated into that interference cube- thus suppressing any moving part. The steps' directions being set over a perpendicular axis, the overlap of both stepped mirrors creates a cluster of so-called "echelettes", each one corresponding to a different optical path difference (OPD). Hence the Fourier transform of the incoming radiance is directly imaged on a CCD array in a single acquisition. The frequency domain of the measurements is selected by an interferential filter disposed on the incoming optical path. A rotating wheel equipped with several filters allows the successive measurement of spectra around some bands of interest, i.e. O2, CO2 and CO absorption bands.

  7. PDEPTH—A computer program for the geophysical interpretation of magnetic and gravity profiles through Fourier filtering, source-depth analysis, and forward modeling

    Science.gov (United States)

    Phillips, Jeffrey D.

    2018-01-10

    PDEPTH is an interactive, graphical computer program used to construct interpreted geological source models for observed potential-field geophysical profile data. The current version of PDEPTH has been adapted to the Windows platform from an earlier DOS-based version. The input total-field magnetic anomaly and vertical gravity anomaly profiles can be filtered to produce derivative products such as reduced-to-pole magnetic profiles, pseudogravity profiles, pseudomagnetic profiles, and upward-or-downward-continued profiles. A variety of source-location methods can be applied to the original and filtered profiles to estimate (and display on a cross section) the locations and physical properties of contacts, sheet edges, horizontal line sources, point sources, and interface surfaces. Two-and-a-half-dimensional source bodies having polygonal cross sections can be constructed using a mouse and keyboard. These bodies can then be adjusted until the calculated gravity and magnetic fields of the source bodies are close to the observed profiles. Auxiliary information such as the topographic surface, bathymetric surface, seismic basement, and geologic contact locations can be displayed on the cross section using optional input files. Test data files, used to demonstrate the source location methods in the report, and several utility programs are included.

  8. Beginning Introductory Physics with Two-Dimensional Motion

    Science.gov (United States)

    Huggins, Elisha

    2009-01-01

    During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…

  9. Two-dimensional thermofield bosonization

    International Nuclear Information System (INIS)

    Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.

    2005-01-01

    The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized

  10. MEDOF - MINIMUM EUCLIDEAN DISTANCE OPTIMAL FILTER

    Science.gov (United States)

    Barton, R. S.

    1994-01-01

    values of amplitude and phase for the k whose metric was largest, as well as consistency checks, are reported. A finer search can be done in the neighborhood of the optimal k if desired. The filter finally selected is written to disk in terms of drive values, not in terms of the filter's complex transmittance. Optionally, the impulse response of the filter may be created to permit users to examine the response for the features the algorithm deems important to the recognition process under the selected metric, limitations of the filter SLM, etc. MEDOF uses the filter SLM to its greatest potential, therefore filter competence is not compromised for simplicity of computation. MEDOF is written in C-language for Sun series computers running SunOS. With slight modifications, it has been implemented on DEC VAX series computers using the DEC-C v3.30 compiler, although the documentation does not currently support this platform. MEDOF can also be compiled using Borland International Inc.'s Turbo C++ v1.0, but IBM PC memory restrictions greatly reduce the maximum size of the reference images from which the filters can be calculated. MEDOF requires a two dimensional Fast Fourier Transform (2DFFT). One 2DFFT routine which has been used successfully with MEDOF is a routine found in "Numerical Recipes in C: The Art of Scientific Programming," which is available from Cambridge University Press, New Rochelle, NY 10801. The standard distribution medium for MEDOF is a .25 inch streaming magnetic tape cartridge (Sun QIC-24) in UNIX tar format. MEDOF was developed in 1992-1993.

  11. Two-dimensional x-ray diffraction

    CERN Document Server

    He, Bob B

    2009-01-01

    Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea

  12. Instability of the filtering method for Vlasov's equation

    International Nuclear Information System (INIS)

    Figua, H.; Bouchut, F.; Fijalkow, E.

    1999-01-01

    Klimas has introduced a smoothed Fourier-Fourier method. This method consists in convolving the original distribution function with a Gaussian distribution function, and, next, in solving the new system with a transformed splitting algorithm. Unfortunately, a second-order term appears in the new equation. In this work, it is studied how this term affects the numerical equation. In particular it is proven that instability occurs in the linear version of the Vlasov equation obtained by considering only free non-interacting particles. It is proved that the use of Fourier-Fourier transform is a fundamental requirement to solve this new equation. An important property is pointed out concerning the filtered distribution function in the transformed space. (K.A.)

  13. Edge and line enhancement by adaptive lattice filtering

    International Nuclear Information System (INIS)

    Brolley, J.E.

    1979-01-01

    Digitized images have been two-dimensionally transformed to the Haar sequency domain. High-sequency boosting was performed and the inverse Haar two-dimensional transform applied. The resulting image was then raster-scanned with a continuously adaptive lattice filter. This procedure was applied to a simple image of a photographic step tablet and a complex scene. All of the lines of the step tablet were well defined over the whole dynamic range. Useful definition of lines in the complex scene was obtained

  14. Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging

    International Nuclear Information System (INIS)

    Soloviev, Vadim Y.

    2006-01-01

    A novel adaptive mesh technique in the Fourier domain is introduced for problems in fluorescence lifetime imaging. A dynamical adaptation of the three-dimensional scheme based on the finite volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. Light propagation in the medium is modeled by the telegraph equation, while the lifetime reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the method are demonstrated by image reconstruction of two spherical fluorescent objects embedded in a tissue phantom

  15. Piezoelectricity in Two-Dimensional Materials

    KAUST Repository

    Wu, Tao

    2015-02-25

    Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.

  16. Optimisation of digital noise filtering in the deconvolution of ultrafast kinetic data

    International Nuclear Information System (INIS)

    Banyasz, Akos; Dancs, Gabor; Keszei, Erno

    2005-01-01

    Ultrafast kinetic measurements in the sub-picosecond time range are always distorted by a convolution with the instrumental response function. To restore the undistorted signal, deconvolution of the measured data is needed, which can be done via inverse filtering, using Fourier transforms, if experimental noise can be successfully filtered. However, in the case of experimental data when no underlying physical model is available, no quantitative criteria are known to find an optimal noise filter which would remove excessive noise without distorting the signal itself. In this paper, we analyse the Fourier transforms used during deconvolution and describe a graphical method to find such optimal noise filters. Comparison of graphically found optima to those found by quantitative criteria in the case of known synthetic kinetic signals shows the reliability of the proposed method to get fairly good deconvolved kinetic curves. A few examples of deconvolution of real-life experimental curves with the graphical noise filter optimisation are also shown

  17. Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

    Science.gov (United States)

    Sid, S.; Terrapon, V. E.; Dubief, Y.

    2018-02-01

    The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Reτ=85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wiτ=40 ,100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed

  18. Classification Technique for Ultrasonic Weld Inspection Signals using a Neural Network based on 2-dimensional fourier Transform and Principle Component Analysis

    International Nuclear Information System (INIS)

    Kim, Jae Joon

    2004-01-01

    Neural network-based signal classification systems are increasingly used in the analysis of large volumes of data obtained in NDE applications. Ultrasonic inspection methods on the other hand are commonly used in the nondestructive evaluation of welds to detect flaws. An important characteristic of ultrasonic inspection is the ability to identify the type of discontinuity that gives rise to a peculiar signal. Standard techniques rely on differences in individual A-scans to classify the signals. This paper proposes an ultrasonic signal classification technique based on the information tying in the neighboring signals. The approach is based on a 2-dimensional Fourier transform and the principal component analysis to generate a reduced dimensional feature vector for classification. Results of applying the technique to data obtained from the inspection of actual steel welds are presented

  19. A three-dimensional neutron transport benchmark solution

    International Nuclear Information System (INIS)

    Ganapol, B.D.; Kornreich, D.E.

    1993-01-01

    For one-group neutron transport theory in one dimension, several powerful analytical techniques have been developed to solve the neutron transport equation, including Caseology, Wiener-Hopf factorization, and Fourier and Laplace transform methods. In addition, after a Fourier transform in the transverse plane and formulation of a pseudo problem, two-dimensional (2-D) and three-dimensional (3-D) problems can be solved using the techniques specifically developed for the one-dimensional (1-D) case. Numerical evaluation of the resulting expressions requiring an inversion in the transverse plane have been successful for 2-D problems but becomes exceedingly difficult in the 3-D case. In this paper, we show that by using the symmetry along the beam direction, a 2-D problem can be transformed into a 3-D problem in an infinite medium. The numerical solution to the 3-D problem is then demonstrated. Thus, a true 3-D transport benchmark solution can be obtained from a well-established numerical solution to a 2-D problem

  20. Two-dimensional confinement of heavy fermions

    International Nuclear Information System (INIS)

    Shishido, Hiroaki; Shibauchi, Takasada; Matsuda, Yuji; Terashima, Takahito

    2010-01-01

    Metallic systems with the strongest electron correlations are realized in certain rare-earth and actinide compounds whose physics are dominated by f-electrons. These materials are known as heavy fermions, so called because the effective mass of the conduction electrons is enhanced via correlation effects up to as much as several hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. Here we report on the first realization of a two-dimensional heavy-fermion system, where the dimensionality is adjusted in a controllable fashion by fabricating heterostructures using molecular beam epitaxy. The two-dimensional heavy fermion system displays striking deviations from the standard Fermi liquid low-temperature electronic properties. (author)

  1. Functionalization of liquid-exfoliated two-dimensional 2H-MoS2.

    Science.gov (United States)

    Backes, Claudia; Berner, Nina C; Chen, Xin; Lafargue, Paul; LaPlace, Pierre; Freeley, Mark; Duesberg, Georg S; Coleman, Jonathan N; McDonald, Aidan R

    2015-02-23

    Layered two-dimensional (2D) inorganic transition-metal dichalchogenides (TMDs) have attracted great interest as a result of their potential application in optoelectronics, catalysis, and medicine. However, methods to functionalize and process such 2D TMDs remain scarce. We have established a facile route towards functionalized layered MoS2 . We found that the reaction of liquid-exfoliated 2D MoS2 , with M(OAc)2 salts (M=Ni, Cu, Zn; OAc=acetate) yielded functionalized MoS2 -M(OAc)2 materials. Importantly, this method furnished the 2H-polytype of MoS2 which is a semiconductor. X-ray photoelectron spectroscopy (XPS), diffuse reflectance infrared Fourier transform spectroscopy (DRIFT-IR), and thermogravimetric analysis (TGA) provide strong evidence for the coordination of MoS2 surface sulfur atoms to the M(OAc)2 salt. Interestingly, functionalization of 2H-MoS2 allows for its dispersion/processing in more conventional laboratory solvents. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  2. Two-dimensional topological photonics

    Science.gov (United States)

    Khanikaev, Alexander B.; Shvets, Gennady

    2017-12-01

    Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.

  3. Frequency Domain Image Filtering Using CUDA

    Directory of Open Access Journals (Sweden)

    Muhammad Awais Rajput

    2014-10-01

    Full Text Available In this paper, we investigate the implementation of image filtering in frequency domain using NVIDIA?s CUDA (Compute Unified Device Architecture. In contrast to signal and image filtering in spatial domain which uses convolution operations and hence is more compute-intensive for filters having larger spatial extent, the frequency domain filtering uses FFT (Fast Fourier Transform which is much faster and significantly reduces the computational complexity of the filtering. We implement the frequency domain filtering on CPU and GPU respectively and analyze the speed-up obtained from the CUDA?s parallel processing paradigm. In order to demonstrate the efficiency of frequency domain filtering on CUDA, we implement three frequency domain filters, i.e., Butterworth, low-pass and Gaussian for processing different sizes of images on CPU and GPU respectively and perform the GPU vs. CPU benchmarks. The results presented in this paper show that the frequency domain filtering with CUDA achieves significant speed-up over the CPU processing in frequency domain with the same level of (output image quality on both the processing architectures

  4. Frequency domain image filtering using cuda

    International Nuclear Information System (INIS)

    Rajput, M.A.; Khan, U.A.

    2014-01-01

    In this paper, we investigate the implementation of image filtering in frequency domain using NVIDIA's CUDA (Compute Unified Device Architecture). In contrast to signal and image filtering in spatial domain which uses convolution operations and hence is more compute-intensive for filters having larger spatial extent, the frequency domain filtering uses FFT (Fast Fourier Transform) which is much faster and significantly reduces the computational complexity of the filtering. We implement the frequency domain filtering on CPU and GPU respectively and analyze the speed-up obtained from the CUDA's parallel processing paradigm. In order to demonstrate the efficiency of frequency domain filtering on CUDA, we implement three frequency domain filters, i.e., Butter worth, low-pass and Gaussian for processing different sizes of images on CPU and GPU respectively and perform the GPU vs. CPU benchmarks. The results presented in this paper show that the frequency domain filtering with CUDA achieves significant speed-up over the CPU processing in frequency domain with the same level of (output) image quality on both the processing architectures. (author)

  5. Structures of two-dimensional three-body systems

    International Nuclear Information System (INIS)

    Ruan, W.Y.; Liu, Y.Y.; Bao, C.G.

    1996-01-01

    Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spatial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. (author)

  6. Fast generation of Fresnel holograms based on multirate filtering.

    Science.gov (United States)

    Tsang, Peter; Liu, Jung-Ping; Cheung, Wai-Keung; Poon, Ting-Chung

    2009-12-01

    One of the major problems in computer-generated holography is the high computation cost involved for the calculation of fringe patterns. Recently, the problem has been addressed by imposing a horizontal parallax only constraint whereby the process can be simplified to the computation of one-dimensional sublines, each representing a scan plane of the object scene. Subsequently the sublines can be expanded to a two-dimensional hologram through multiplication with a reference signal. Furthermore, economical hardware is available with which sublines can be generated in a computationally free manner with high throughput of approximately 100 M pixels/second. Apart from decreasing the computation loading, the sublines can be treated as intermediate data that can be compressed by simply downsampling the number of sublines. Despite these favorable features, the method is suitable only for the generation of white light (rainbow) holograms, and the resolution of the reconstructed image is inferior to the classical Fresnel hologram. We propose to generate holograms from one-dimensional sublines so that the above-mentioned problems can be alleviated. However, such an approach also leads to a substantial increase in computation loading. To overcome this problem we encapsulated the conversion of sublines to holograms as a multirate filtering process and implemented the latter by use of a fast Fourier transform. Evaluation reveals that, for holograms of moderate size, our method is capable of operating 40,000 times faster than the calculation of Fresnel holograms based on the precomputed table lookup method. Although there is no relative vertical parallax between object points at different distance planes, a global vertical parallax is preserved for the object scene as a whole and the reconstructed image can be observed easily.

  7. Single-shot parallel full range complex Fourier-domain optical coherence tomography

    International Nuclear Information System (INIS)

    Huang Bingjie; Bu Peng; Nan Nan; Wang Xiangzhao

    2011-01-01

    We present a method of parallel full range complex Fourier-domain optical coherence tomography (FDOCT) that is capable of acquiring an artifacts-free two-dimensional (2-D) cross-sectional image, i.e. a full range B-scan tomogram, by a single shot of 2-D CCD camera. This method is based on a spatial carrier technique, in which the spatial carrier-frequency is instantaneously introduced into the 2-D spectral interferogram registered in parallel FDOCT by using a grating-generated reference beam. The spatial-carrier-contained 2-D spectral interferogram is processed through Fourier transformation to obtain a complex 2-D spectral interferogram. From the 2-D complex spectral interferomgram, a full range B-scan tomogram is reconstructed. The principle of our method is confirmed by imaging an onion sample.

  8. Innovative design method of automobile profile based on Fourier descriptor

    Science.gov (United States)

    Gao, Shuyong; Fu, Chaoxing; Xia, Fan; Shen, Wei

    2017-10-01

    Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.

  9. Wavepacket dynamics in one-dimensional system with long-range correlated disorder

    Science.gov (United States)

    Yamada, Hiroaki S.

    2018-03-01

    We numerically investigate dynamical property in the one-dimensional tight-binding model with long-range correlated disorder having power spectrum 1 /fα (α: spectrum exponent) generated by Fourier filtering method. For relatively small α MSD) of the initially localized wavepacket shows ballistic spread and localizes as time elapses. It is shown that α-dependence of the dynamical localization length determined by the MSD exhibits a simple scaling law in the localization regime for the relatively weak disorder strength W. Furthermore, scaled MSD by the dynamical localization length almost obeys an universal function from the ballistic to the localization regime in the various combinations of the parameters α and W.

  10. Algorithm for three dimension reconstruction of magnetic resonance tomographs and X-ray images based on Fast Fourier Transform; Algoritmo para reconstrucao tridimensional de imagens de tomografos de ressonancia magnetica e de raio-X baseado no uso de Transformada Rapida de Fourier

    Energy Technology Data Exchange (ETDEWEB)

    Bueno, Josiane M.; Traina, Agma Juci M. [Sao Paulo Univ., Sao Carlos, SP (Brazil). Inst. de Ciencias Matematicas; Cruvinel, Paulo E. [EMBRAPA, Sao Carlos, SP (Brazil). CNPDIA

    1995-12-31

    This work presents an algorithm for three-dimensional digital image reconstruction. Such algorithms based on the combination of both a Fast Fourier Transform method with Hamming Window and the use of a tri-linear interpolation function. The algorithm allows not only the generation of three-dimensional spatial spin distribution maps for Magnetic Resonance Tomography data but also X and Y-rays linear attenuation coefficient maps for CT scanners. Results demonstrates the usefulness of the algorithm in three-dimensional image reconstruction by doing first two-dimensional reconstruction and rather after interpolation. The algorithm was developed in C++ language, and there are two available versions: one under the DOS environment, and the other under the UNIX/Sun environment. (author) 10 refs., 5 figs.

  11. High-Selectivity Filter Banks for Spectral Analysis of Music Signals

    Directory of Open Access Journals (Sweden)

    Luiz W. P. Biscainho

    2007-01-01

    Full Text Available This paper approaches, under a unified framework, several algorithms for the spectral analysis of musical signals. Such algorithms include the fast Fourier transform (FFT, the fast filter bank (FFB, the constant-Q transform (CQT, and the bounded-Q transform (BQT, previously known from the associated literature. Two new methods are then introduced, namely, the constant-Q fast filter bank (CQFFB and the bounded-Q fast filter bank (BQFFB, combining the positive characteristics of the previously mentioned algorithms. The provided analyses indicate that the proposed BQFFB achieves an excellent compromise between the reduced computational effort of the FFT, the high selectivity of each output channel of the FFB, and the efficient distribution of frequency channels associated to the CQT and BQT methods. Examples are included to illustrate the performances of these methods in the spectral analysis of music signals.

  12. Preparation of Polyaniline/Filter-paper Composite for Removal of Coomassie Brilliant Blue

    DEFF Research Database (Denmark)

    Liu, Wanwan; Li, Xiaoqiang; Li, Mengjuan

    2015-01-01

    Polyaniline/filter-paper (PANI/FP) composite was prepared by in-situ polymerization of polyaniline onto filter-paper and subsequently evaluated for the removal of Coomassie brilliant blue (CBB) from aqueous solution. Scanning electron microscopy (SEM), thermogravimetric analysis (TGA) and Fourier...

  13. Fourier Transform Mass Spectrometry

    Science.gov (United States)

    Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

    2011-01-01

    This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

  14. Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer

    Energy Technology Data Exchange (ETDEWEB)

    Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.

    1993-10-01

    We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.

  15. X-ray imaging device for one-dimensional and two-dimensional radioscopy

    International Nuclear Information System (INIS)

    1978-01-01

    The X-ray imaging device for the selectable one-dimensional or two-dimensional pictures of objects illuminated by X-rays, comprising an X-ray source, an X-ray screen, and an opto-electrical picture development device placed behind the screen, is characterized by an anamorphotic optical system, which is positioned with a one-dimensional illumination between the X-ray screen and the opto-electrical device and that a two-dimensional illumination will be developed, and that in view of the lens system which forms part of the opto-electrical device, there is placed an X-ray screen in a specified beam direction so that a magnified image may be formed by equalisation of the distance between the X-ray screen and the lens system. (G.C.)

  16. Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

    International Nuclear Information System (INIS)

    Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

    2014-01-01

    A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

  17. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.

    Science.gov (United States)

    Pavlov, Maxim V

    2014-12-08

    In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

  18. Novel target design algorithm for two-dimensional optical storage (TwoDOS)

    NARCIS (Netherlands)

    Huang, Li; Chong, T.C.; Vijaya Kumar, B.V.K.; Kobori, H.

    2004-01-01

    In this paper we introduce the Hankel transform based channel model of Two-Dimensional Optical Storage (TwoDOS) system. Based on this model, the two-dimensional (2D) minimum mean-square error (MMSE) equalizer has been derived and applied to some simple but common cases. The performance of the 2D

  19. The su(2)α Hahn oscillator and a discrete Fourier-Hahn transform

    International Nuclear Information System (INIS)

    Jafarov, E I; Stoilova, N I; Van der Jeugt, J

    2011-01-01

    We define the quadratic algebra su(2) α which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2) α . We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2) α . It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this so-called discrete Fourier-Hahn transform is computed explicitly. The matrix of this discrete Fourier-Hahn transform has many interesting properties, similar to those of the traditional discrete Fourier transform. (paper)

  20. Microbunching instability in a chicane: Two-dimensional mean field treatment

    Directory of Open Access Journals (Sweden)

    Gabriele Bassi

    2009-08-01

    Full Text Available We study the microbunching instability in a bunch compressor by a parallel code with some improved numerical algorithms. The two-dimensional charge/current distribution is represented by a Fourier series, with coefficients determined through Monte Carlo sampling over an ensemble of tracked points. This gives a globally smooth distribution with low noise. The field equations are solved accurately in the lab frame using retarded potentials and a novel choice of integration variables that eliminates singularities. We apply the scheme with parameters for the first bunch compressor system of FERMI@Elettra, with emphasis on the amplification of a perturbation at a particular wavelength and the associated longitudinal bunch spectrum. Gain curves are in rough agreement with those of the linearized Vlasov system at intermediate wavelengths, but show some deviation at the smallest wavelengths treated and show the breakdown of a coasting beam assumption at long wavelengths. The linearized Vlasov system is discussed in some detail. A new 2D integral equation is derived which reduces to a well-known 1D integral equation in the coasting beam case.

  1. Bessel–Gauss resonator with internal amplitude filter

    CSIR Research Space (South Africa)

    Litvin, IA

    2008-05-01

    Full Text Available The authors investigate a conventional resonator configuration, using only spherical curvature optical elements, for the generation of Bessel–Gauss beams. This is achieved through the deployment of a suitable amplitude filter at a Fourier plane...

  2. Two-dimensional ferroelectrics

    Energy Technology Data Exchange (ETDEWEB)

    Blinov, L M; Fridkin, Vladimir M; Palto, Sergei P [A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russian Federaion (Russian Federation); Bune, A V; Dowben, P A; Ducharme, Stephen [Department of Physics and Astronomy, Behlen Laboratory of Physics, Center for Materials Research and Analysis, University of Nebraska-Linkoln, Linkoln, NE (United States)

    2000-03-31

    The investigation of the finite-size effect in ferroelectric crystals and films has been limited by the experimental conditions. The smallest demonstrated ferroelectric crystals had a diameter of {approx}200 A and the thinnest ferroelectric films were {approx}200 A thick, macroscopic sizes on an atomic scale. Langmuir-Blodgett deposition of films one monolayer at a time has produced high quality ferroelectric films as thin as 10 A, made from polyvinylidene fluoride and its copolymers. These ultrathin films permitted the ultimate investigation of finite-size effects on the atomic thickness scale. Langmuir-Blodgett films also revealed the fundamental two-dimensional character of ferroelectricity in these materials by demonstrating that there is no so-called critical thickness; films as thin as two monolayers (1 nm) are ferroelectric, with a transition temperature near that of the bulk material. The films exhibit all the main properties of ferroelectricity with a first-order ferroelectric-paraelectric phase transition: polarization hysteresis (switching); the jump in spontaneous polarization at the phase transition temperature; thermal hysteresis in the polarization; the increase in the transition temperature with applied field; double hysteresis above the phase transition temperature; and the existence of the ferroelectric critical point. The films also exhibit a new phase transition associated with the two-dimensional layers. (reviews of topical problems)

  3. Multiple-channel ultra-violet absorbance detector for two-dimensional chromatographic separations.

    Science.gov (United States)

    Lynch, Kyle B; Yang, Yu; Ren, Jiangtao; Liu, Shaorong

    2018-05-01

    In recent years, much research has gone into developing online comprehensive two-dimensional liquid chromatographic systems allowing for high peak capacities in comparable separation times to that of one-dimensional liquid chromatographic systems. However, the speed requirements in the second dimension (2nd-D) still remain one challenge for complex biological samples due to the current configuration of two column/two detector systems. Utilization of multiple 2nd-D columns can mitigate this challenge. To adapt this approach, we need a multiple channel detector. Here we develop a versatile multichannel ultraviolet (UV) light absorbance detector that is capable of simultaneously monitoring separations in 12 columns. The detector consists of a deuterium lighthouse, a flow cell assembly (a 13-channel flow cell fitted with a 13-photodiode-detection system), and a data acquisition and monitoring terminal. Through the use of a custom high optical quality furcated fiber to improve light transmission, precise machining of a flow cell to reduce background stray light through precision alignment, and sensitive electronic circuitry to reduce electronic noise through an active low pass filter, the background noise level is measured in the tens of µAU. We obtain a linear dynamic range of close to three orders of magnitude. Compared to a commercialized multichannel UV light absorbance detector like the Waters 2488 UV/Vis, our device provides an increase in channel detection while residing within the same noise region and linear range. Copyright © 2018 Elsevier B.V. All rights reserved.

  4. Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data

    Directory of Open Access Journals (Sweden)

    Darian M. Onchiș

    2011-09-01

    Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.

  5. Fourier transforms principles and applications

    CERN Document Server

    Hansen, Eric W

    2014-01-01

    Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods.  Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.

  6. Two-Dimensional Materials for Sensing: Graphene and Beyond

    Directory of Open Access Journals (Sweden)

    Seba Sara Varghese

    2015-09-01

    Full Text Available Two-dimensional materials have attracted great scientific attention due to their unusual and fascinating properties for use in electronics, spintronics, photovoltaics, medicine, composites, etc. Graphene, transition metal dichalcogenides such as MoS2, phosphorene, etc., which belong to the family of two-dimensional materials, have shown great promise for gas sensing applications due to their high surface-to-volume ratio, low noise and sensitivity of electronic properties to the changes in the surroundings. Two-dimensional nanostructured semiconducting metal oxide based gas sensors have also been recognized as successful gas detection devices. This review aims to provide the latest advancements in the field of gas sensors based on various two-dimensional materials with the main focus on sensor performance metrics such as sensitivity, specificity, detection limit, response time, and reversibility. Both experimental and theoretical studies on the gas sensing properties of graphene and other two-dimensional materials beyond graphene are also discussed. The article concludes with the current challenges and future prospects for two-dimensional materials in gas sensor applications.

  7. Experimental and clinical analyses of optimum Fourier filtering in ECG-gated blood pool scintigraphy

    International Nuclear Information System (INIS)

    Shimabukuro, Kunisada

    1988-01-01

    A phantom study was undertaken to determine the optimum order harmonics in Fourier analysis for volume curves obtained by ECG-gated blood pool scintigraphy. The volume curve obtained by Tc-99m scintigraphy was computed by the 1st through 10th order harmonics of Fourier transform. The shape of each volume curve fitted by Fourier transform was compared with the shape of the generated ideal curve. Curves fitted with the 3rd or more order harmonics were approximate to the ideal curve in shape during the systolic phase. The 6th to 10th order harmonics were suitable for the early diastole phase. As determined by peak ejection rate and peak filling rate (PFR), the 6th order harmonics was superior to the 3rd order harmonics in evaluating early diastolic abnormalities. In the clinical settings, there was no difference between the 3rd and 6th order harmonics in evaluating systolic abnormalities; however, the 6th order harmonics was more sensitive than the 3rd order harmonics in evaluating early diastolic abnormalities. The 6th order harmonics significantly reflected PFR in the group of hypertrophic cardiomyopathy (n=10) and time to PFR in the groups of old myocardial infarction (n=10) and angina pectoris (n=10). In conclusion, the 6th to 9th order harmonics of Fourier analysis may be useful in analyzing both systolic and early diastolic phases inf left ventricular volume curves obtained from ECG-gated cardiac blood pool scintigraphy. (Namekawa, K)

  8. Two-dimensional calculus

    CERN Document Server

    Osserman, Robert

    2011-01-01

    The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o

  9. Phase transitions in two-dimensional systems

    International Nuclear Information System (INIS)

    Salinas, S.R.A.

    1983-01-01

    Some experiences are related using synchrotron radiation beams, to characterize solid-liquid (fusion) and commensurate solid-uncommensurate solid transitions in two-dimensional systems. Some ideas involved in the modern theories of two-dimensional fusion are shortly exposed. The systems treated consist of noble gases (Kr,Ar,Xe) adsorbed in the basal plane of graphite and thin films formed by some liquid crystal shells. (L.C.) [pt

  10. 360-degrees profilometry using strip-light projection coupled to Fourier phase-demodulation.

    Science.gov (United States)

    Servin, Manuel; Padilla, Moises; Garnica, Guillermo

    2016-01-11

    360 degrees (360°) digitalization of three dimensional (3D) solids using a projected light-strip is a well-established technique in academic and commercial profilometers. These profilometers project a light-strip over the digitizing solid while the solid is rotated a full revolution or 360-degrees. Then, a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based light-strip centroid estimation, we propose to use Fourier phase-demodulation for 360° solid digitalization. The advantage of Fourier demodulation over strip-centroid estimation is that the accuracy of phase-demodulation linearly-increases with the fringe density, while in strip-light the centroid-estimation errors are independent. Here we proposed first to construct a carrier-frequency fringe-pattern by closely adding the individual light-strip images recorded while the solid is being rotated. Next, this high-density fringe-pattern is phase-demodulated using the standard Fourier technique. To test the feasibility of this Fourier demodulation approach, we have digitized two solids with increasing topographic complexity: a Rubik's cube and a plastic model of a human-skull. According to our results, phase demodulation based on the Fourier technique is less noisy than triangulation based on centroid light-strip estimation. Moreover, Fourier demodulation also provides the amplitude of the analytic signal which is a valuable information for the visualization of surface details.

  11. Study of two-dimensional Debye clusters using Brownian motion

    International Nuclear Information System (INIS)

    Sheridan, T.E.; Theisen, W.L.

    2006-01-01

    A two-dimensional Debye cluster is a system of n identical particles confined in a parabolic well and interacting through a screened Coulomb (i.e., a Debye-Hueckel or Yukawa) potential with a Debye length λ. Experiments were performed for 27 clusters with n=3-63 particles (9 μm diam) in a capacitively coupled 9 W rf discharge at a neutral argon pressure of 13.6 mTorr. In the strong-coupling regime each particle exhibits small amplitude Brownian motion about its equilibrium position. These motions were projected onto the center-of-mass and breathing modes and Fourier analyzed to give resonance curves from which the mode frequencies, amplitudes, and damping rates were determined. The ratio of the breathing frequency to the center-of-mass frequency was compared with theory to self-consistently determine the Debye shielding parameter κ, Debye length λ, particle charge q, and mode temperatures. It is found that 1 < or approx. κ < or approx. 2, and κ decreases weakly with n. The particle charge averaged over all measurements is -14 200±200 e, and q decreases slightly with n. The two center-of-mass modes and the breathing mode are found to have the same temperature, indicating that the clusters are in thermal equilibrium with the neutral gas. The average cluster temperature is 399±5 K

  12. Are consistent equal-weight particle filters possible?

    Science.gov (United States)

    van Leeuwen, P. J.

    2017-12-01

    Particle filters are fully nonlinear data-assimilation methods that could potentially change the way we do data-assimilation in highly nonlinear high-dimensional geophysical systems. However, the standard particle filter in which the observations come in by changing the relative weights of the particles is degenerate. This means that one particle obtains weight one, and all other particles obtain a very small weight, effectively meaning that the ensemble of particles reduces to that one particle. For over 10 years now scientists have searched for solutions to this problem. One obvious solution seems to be localisation, in which each part of the state only sees a limited number of observations. However, for a realistic localisation radius based on physical arguments, the number of observations is typically too large, and the filter is still degenerate. Another route taken is trying to find proposal densities that lead to more similar particle weights. There is a simple proof, however, that shows that there is an optimum, the so-called optimal proposal density, and that optimum will lead to a degenerate filter. On the other hand, it is easy to come up with a counter example of a particle filter that is not degenerate in high-dimensional systems. Furthermore, several particle filters have been developed recently that claim to have equal or equivalent weights. In this presentation I will show how to construct a particle filter that is never degenerate in high-dimensional systems, and how that is still consistent with the proof that one cannot do better than the optimal proposal density. Furthermore, it will be shown how equal- and equivalent-weights particle filters fit within this framework. This insight will then lead to new ways to generate particle filters that are non-degenerate, opening up the field of nonlinear filtering in high-dimensional systems.

  13. Quantum copying and simplification of the quantum Fourier transform

    Science.gov (United States)

    Niu, Chi-Sheng

    Theoretical studies of quantum computation and quantum information theory are presented in this thesis. Three topics are considered: simplification of the quantum Fourier transform in Shor's algorithm, optimal eavesdropping in the BB84 quantum cryptographic protocol, and quantum copying of one qubit. The quantum Fourier transform preceding the final measurement in Shor's algorithm is simplified by replacing a network of quantum gates with one that has fewer and simpler gates controlled by classical signals. This simplification results from an analysis of the network using the consistent history approach to quantum mechanics. The optimal amount of information which an eavesdropper can gain, for a given level of noise in the communication channel, is worked out for the BB84 quantum cryptographic protocol. The optimal eavesdropping strategy is expressed in terms of various quantum networks. A consistent history analysis of these networks using two conjugate quantum bases shows how the information gain in one basis influences the noise level in the conjugate basis. The no-cloning property of quantum systems, which is the physics behind quantum cryptography, is studied by considering copying machines that generate two imperfect copies of one qubit. The best qualities these copies can have are worked out with the help of the Bloch sphere representation for one qubit, and a quantum network is worked out for an optimal copying machine. If the copying machine does not have additional ancillary qubits, the copying process can be viewed using a 2-dimensional subspace in a product space of two qubits. A special representation of such a two-dimensional subspace makes possible a complete characterization of this type of copying. This characterization in turn leads to simplified eavesdropping strategies in the BB84 and the B92 quantum cryptographic protocols.

  14. The theory of critical phenomena in two-dimensional systems

    International Nuclear Information System (INIS)

    Olvera de la C, M.

    1981-01-01

    An exposition of the theory of critical phenomena in two-dimensional physical systems is presented. The first six chapters deal with the mean field theory of critical phenomena, scale invariance of the thermodynamic functions, Kadanoff's spin block construction, Wilson's renormalization group treatment of critical phenomena in configuration space, and the two-dimensional Ising model on a triangular lattice. The second part of this work is made of four chapters devoted to the application of the ideas expounded in the first part to the discussion of critical phenomena in superfluid films, two-dimensional crystals and the two-dimensional XY model of magnetic systems. Chapters seven to ten are devoted to the following subjects: analysis of long range order in one, two, and three-dimensional physical systems. Topological defects in the XY model, in superfluid films and in two-dimensional crystals. The Thouless-Kosterlitz iterated mean field theory of the dipole gas. The renormalization group treatment of the XY model, superfluid films and two-dimensional crystal. (author)

  15. Surface acoustic waves in two dimensional phononic crystal with anisotropic inclusions

    Directory of Open Access Journals (Sweden)

    Ketata H.

    2012-06-01

    Full Text Available An analysis is given to the band structure of the two dimensional solid phononic crystal considered as a semi infinite medium. The lattice includes an array of elastic anisotropic materials with different shapes embedded in a uniform matrix. For illustration two kinds of phononic materials are assumed. A particular attention is devoted to the computational procedure which is mainly based on the plane wave expansion (PWE method. It has been adapted to Matlab environment. Numerical calculations of the dispersion curves have been achieved by introducing particular functions which transform motion equations into an Eigen value problem. Significant improvements are obtained by increasing reasonably the number of Fourier components even when a large elastic mismatch is assumed. Such approach can be generalized to different types of symmetry and permit new physical properties as piezoelectricity to be added. The actual semi infinite phononic structure with a free surface has been shown to support surface acoustic waves (SAW. The obtained dispersion curves reveal band gaps in the SAW branches. It has been found that the influence, of the filling factor and anisotropy on their band gaps, is different from that of bulk waves.

  16. Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

    Science.gov (United States)

    Barnett, Patrick D; Strange, K Alicia; Angel, S Michael

    2017-06-01

    This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

  17. Simulation for noise cancellation using LMS adaptive filter

    Science.gov (United States)

    Lee, Jia-Haw; Ooi, Lu-Ean; Ko, Ying-Hao; Teoh, Choe-Yung

    2017-06-01

    In this paper, the fundamental algorithm of noise cancellation, Least Mean Square (LMS) algorithm is studied and enhanced with adaptive filter. The simulation of the noise cancellation using LMS adaptive filter algorithm is developed. The noise corrupted speech signal and the engine noise signal are used as inputs for LMS adaptive filter algorithm. The filtered signal is compared to the original noise-free speech signal in order to highlight the level of attenuation of the noise signal. The result shows that the noise signal is successfully canceled by the developed adaptive filter. The difference of the noise-free speech signal and filtered signal are calculated and the outcome implies that the filtered signal is approaching the noise-free speech signal upon the adaptive filtering. The frequency range of the successfully canceled noise by the LMS adaptive filter algorithm is determined by performing Fast Fourier Transform (FFT) on the signals. The LMS adaptive filter algorithm shows significant noise cancellation at lower frequency range.

  18. Finite element Fourier and Abbe transform methods for generalization of aperture function and geometry in Fraunhofer diffraction theory

    International Nuclear Information System (INIS)

    Kraus, H.G.

    1991-01-01

    This paper discusses methods for calculating Fraunhofer intensity fields resulting from diffraction through one- and two-dimensional apertures are presented. These methods are based on the geometric concept of finite elements and on Fourier and Abbe transforms. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define aperture(s) of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s) which may be of continuous or discontinuous form. The transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is most evident in two dimensions, where several examples are presented which include secondary obstructions, straight and curved secondary spider supports, multiple-mirror arrays, synthetic aperture arrays, segmented mirrors, apertures covered by screens, apodization, and phase plates. Typically, the finite element Abbe transform method results in significant gains in computational efficiency over the finite element Fourier transform method, but is also subject to some loss in generality

  19. Median Modified Wiener Filter for nonlinear adaptive spatial denoising of protein NMR multidimensional spectra

    KAUST Repository

    Cannistraci, Carlo Vittorio

    2015-01-26

    Denoising multidimensional NMR-spectra is a fundamental step in NMR protein structure determination. The state-of-the-art method uses wavelet-denoising, which may suffer when applied to non-stationary signals affected by Gaussian-white-noise mixed with strong impulsive artifacts, like those in multi-dimensional NMR-spectra. Regrettably, Wavelet\\'s performance depends on a combinatorial search of wavelet shapes and parameters; and multi-dimensional extension of wavelet-denoising is highly non-trivial, which hampers its application to multidimensional NMR-spectra. Here, we endorse a diverse philosophy of denoising NMR-spectra: less is more! We consider spatial filters that have only one parameter to tune: the window-size. We propose, for the first time, the 3D extension of the median-modified-Wiener-filter (MMWF), an adaptive variant of the median-filter, and also its novel variation named MMWF*. We test the proposed filters and the Wiener-filter, an adaptive variant of the mean-filter, on a benchmark set that contains 16 two-dimensional and three-dimensional NMR-spectra extracted from eight proteins. Our results demonstrate that the adaptive spatial filters significantly outperform their non-adaptive versions. The performance of the new MMWF* on 2D/3D-spectra is even better than wavelet-denoising. Noticeably, MMWF* produces stable high performance almost invariant for diverse window-size settings: this signifies a consistent advantage in the implementation of automatic pipelines for protein NMR-spectra analysis.

  20. Median Modified Wiener Filter for nonlinear adaptive spatial denoising of protein NMR multidimensional spectra

    KAUST Repository

    Cannistraci, Carlo Vittorio; Abbas, Ahmed; Gao, Xin

    2015-01-01

    Denoising multidimensional NMR-spectra is a fundamental step in NMR protein structure determination. The state-of-the-art method uses wavelet-denoising, which may suffer when applied to non-stationary signals affected by Gaussian-white-noise mixed with strong impulsive artifacts, like those in multi-dimensional NMR-spectra. Regrettably, Wavelet's performance depends on a combinatorial search of wavelet shapes and parameters; and multi-dimensional extension of wavelet-denoising is highly non-trivial, which hampers its application to multidimensional NMR-spectra. Here, we endorse a diverse philosophy of denoising NMR-spectra: less is more! We consider spatial filters that have only one parameter to tune: the window-size. We propose, for the first time, the 3D extension of the median-modified-Wiener-filter (MMWF), an adaptive variant of the median-filter, and also its novel variation named MMWF*. We test the proposed filters and the Wiener-filter, an adaptive variant of the mean-filter, on a benchmark set that contains 16 two-dimensional and three-dimensional NMR-spectra extracted from eight proteins. Our results demonstrate that the adaptive spatial filters significantly outperform their non-adaptive versions. The performance of the new MMWF* on 2D/3D-spectra is even better than wavelet-denoising. Noticeably, MMWF* produces stable high performance almost invariant for diverse window-size settings: this signifies a consistent advantage in the implementation of automatic pipelines for protein NMR-spectra analysis.

  1. Two-dimensional coherence analysis of magnetic and gravity data from the Cascer Quadrangle, Wyoming. Final report

    International Nuclear Information System (INIS)

    QEB, Inc. has completed a two-dimensional coherence analysis of gravity and magnetic data from the Casper, Wyoming NTMS quadrangle. Magnetic data from an airborne survey were reduced to produce a Residual Magnetic map, and gravity data obtained from several sources were reduced to produce a Complete Bouguer Gravity map. Both sets of data were upward continued to a plane one kilometer above the surface; and then, to make the magnetic and gravity data comparable, the magnetic data were transformed to pseudo-gravity data by the application of Poisson's relationship for rocks that are both dense and magnetic relative to the surrounding rocks. A pseudo-gravity map was then produced and an analysis made of the two-dimensional coherence between the upward continued Bouguer gravity and the pseudo-gravity data. Based on the results of the coherence analysis, digital filters were designed to either pass or reject wavelength bands with high coherence

  2. An alternative path to the boundary: The CFT as the Fourier space of AdS

    Science.gov (United States)

    Tolfree, Ian M.

    2009-12-01

    In this thesis we shed new light on the conjectured duality between an n + 1 dimensional theory of gravity in anti de Sitter space (AdS) and an n dimensional conformal field theory (CFT) by showing that the CFT can be interpreted as the Fourier space of AdS. We then make use of this to gain insight into the nature of black hole entropy. In the first part of this thesis, we give an introduction to the ideas of and review the basics of the AdS/CFT. In the next section we make use of well known integral geometry techniques to derive the Fourier transformation of a function on AdS and see it is a function with compact support on the boundary. Comparing this to the literature, we find that the Green's functions from the literature are actually the Fourier weights of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier coefficients of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD like theories. In the last section, we then build upon this to study the BTZ black hole. Named after its authors, Banados, Teitelboim and Zanelli, the BTZ black hole is a three dimensional (two space plus one time dimension) black hole in anti de Sitter space. Following standard procedures for modifying Fourier Transformations to accommodate quotient spaces we arrive at a mapping in a black hole background consistent with known results that yields the exact micro-states of a scalar field in a black hole background. We find that the micro-states are the Fourier coefficients on the boundary, which transform under the principal series representation of SL(2, R). Using the knowledge of how to represent a bulk scalar field in the CFT, and knowing how a black hole interacts with a scalar field, we deduce the

  3. Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions.

    Science.gov (United States)

    Kim, Hwi; Min, Sung-Wook; Lee, Byoungho; Poon, Ting-Chung

    2008-07-01

    We propose a novel optical sectioning method for optical scanning holography, which is performed in phase space by using Wigner distribution functions together with the fractional Fourier transform. The principle of phase-space optical sectioning for one-dimensional signals, such as slit objects, and two-dimensional signals, such as rectangular objects, is first discussed. Computer simulation results are then presented to substantiate the proposed idea.

  4. Two-level Robust Measurement Fusion Kalman Filter for Clustering Sensor Networks

    Institute of Scientific and Technical Information of China (English)

    ZHANG Peng; QI Wen-Juan; DENG Zi-Li

    2014-01-01

    This paper investigates the distributed fusion Kalman filtering over clustering sensor networks. The sensor network is partitioned as clusters by the nearest neighbor rule and each cluster consists of sensing nodes and cluster-head. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, two-level robust measurement fusion Kalman filter is presented for the clustering sensor network systems with uncertain noise variances. It can significantly reduce the communication load and save energy when the number of sensors is very large. A Lyapunov equation approach for the robustness analysis is presented, by which the robustness of the local and fused Kalman filters is proved. The concept of the robust accuracy is presented, and the robust accuracy relations among the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the two-level weighted measurement fuser is equal to that of the global centralized robust fuser and is higher than those of each local robust filter and each local weighted measurement fuser. A simulation example shows the correctness and effectiveness of the proposed results.

  5. Soft x-ray microscope using Fourier transform holography

    International Nuclear Information System (INIS)

    McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H.

    1989-01-01

    A Fourier transform holographic microscope with an anticipated resolution of better than 100 nm has been built. Extensive testing of the apparatus has begun. Preliminary results include the recording of interference fringes using 3.6 nm x-rays. The microscope employs a charge-coupled device (CCD) detector array of 576 x 384 elements. The system is illuminated by soft x-rays from a high brightness undulator. The reference point source is formed by a Fresnel zone plate with a finest outer zone width of 50 nm. Sufficient temporal coherence for hologram formation is obtained by a spherical grating monochromator. The x-ray hologram intensities at the recording plane are to be collected, digitized and reconstructed by computer. Data acquisition is under CAMAC control, while image display and off-line processing takes place on a VAX graphics workstation. Computational models of Fourier transform hologram synthesis, and reconstruction in the presence of noise, have demonstrated the feasibility of numerical methods in two dimensions, and that three-dimensional information is potentially recoverable. 13 refs., 3 figs

  6. A momentum filter for atomic gas

    International Nuclear Information System (INIS)

    Xiong, Wei; Zhou, Xiaoji; Yue, Xuguang; Zhai, Yueyang; Chen, Xuzong

    2013-01-01

    We propose and demonstrate a momentum filter for atomic gas-based on a designed Talbot–Lau interferometer. It consists of two identical optical standing-wave pulses separated by a delay equal to odd multiples of the half Talbot time. The one-dimensional momentum width along the long direction of a cigar-shaped condensate is rapidly and greatly purified to a minimum, which corresponds to the ground state energy of the confining trap in our experiment. We find good agreement between theoretical analysis and experimental results. The filter is also effective for non-condensed cold atoms and could be applied widely. (paper)

  7. Fourier-based approach to interpolation in single-slice helical computed tomography

    International Nuclear Information System (INIS)

    La Riviere, Patrick J.; Pan Xiaochuan

    2001-01-01

    It has recently been shown that longitudinal aliasing can be a significant and detrimental presence in reconstructed single-slice helical computed tomography (CT) volumes. This aliasing arises because the directly measured data in helical CT are generally undersampled by a factor of at least 2 in the longitudinal direction and because the exploitation of the redundancy of fanbeam data acquired over 360 degree sign to generate additional longitudinal samples does not automatically eliminate the aliasing. In this paper we demonstrate that for pitches near 1 or lower, the redundant fanbeam data, when used properly, can provide sufficient information to satisfy a generalized sampling theorem and thus to eliminate aliasing. We develop and evaluate a Fourier-based algorithm, called 180FT, that accomplishes this. As background we present a second Fourier-based approach, called 360FT, that makes use only of the directly measured data. Both Fourier-based approaches exploit the fast Fourier transform and the Fourier shift theorem to generate from the helical projection data a set of fanbeam sinograms corresponding to equispaced transverse slices. Slice-by-slice reconstruction is then performed by use of two-dimensional fanbeam algorithms. The proposed approaches are compared to their counterparts based on the use of linear interpolation - the 360LI and 180LI approaches. The aliasing suppression property of the 180FT approach is a clear advantage of the approach and represents a step toward the desirable goal of achieving uniform longitudinal resolution properties in reconstructed helical CT volumes

  8. Advantage of Fast Fourier Interpolation for laser modeling

    International Nuclear Information System (INIS)

    Epatko, I.V.; Serov, R.V.

    2006-01-01

    The abilities of a new algorithm: the 2-dimensional Fast Fourier Interpolation (FFI) with magnification factor (zoom) 2 n whose purpose is to improve the spatial resolution when necessary, are analyzed in details. FFI procedure is useful when diaphragm/aperture size is less than half of the current simulation scale. The computation noise due to FFI procedure is less than 10 -6 . The additional time for FFI is approximately equal to one Fast Fourier Transform execution time. For some applications using FFI procedure, the execution time decreases by a 10 4 factor compared with other laser simulation codes. (authors)

  9. Fourier-muunnoksesta

    OpenAIRE

    NIEMELÄ, EERO

    2008-01-01

    Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...

  10. Photonic crystal ring resonator based optical filters for photonic integrated circuits

    International Nuclear Information System (INIS)

    Robinson, S.

    2014-01-01

    In this paper, a two Dimensional (2D) Photonic Crystal Ring Resonator (PCRR) based optical Filters namely Add Drop Filter, Bandpass Filter, and Bandstop Filter are designed for Photonic Integrated Circuits (PICs). The normalized output response of the filters is obtained using 2D Finite Difference Time Domain (FDTD) method and the band diagram of periodic and non-periodic structure is attained by Plane Wave Expansion (PWE) method. The size of the device is minimized from a scale of few tens of millimeters to the order of micrometers. The overall size of the filters is around 11.4 μm × 11.4 μm which is highly suitable of photonic integrated circuits

  11. Two- and three-dimensional CT analysis of ankle fractures

    International Nuclear Information System (INIS)

    Magid, D.; Fishman, E.K.; Ney, D.R.; Kuhlman, J.E.

    1988-01-01

    CT with coronal and sagittal reformatting (two-dimensional CT) and animated volumetric image rendering (three-dimensional CT) was used to assess ankle fractures. Partial volume limits transaxial CT in assessments of horizontally oriented structures. Two-dimensional CT, being orthogonal to the plafond, superior mortise, talar dome, and tibial epiphysis, often provides the most clinically useful images. Two-dimensional CT is most useful in characterizing potentially confusing fractures, such as Tillaux (anterior tubercle), triplane, osteochondral talar dome, or nondisplaced talar neck fractures, and it is the best study to confirm intraarticular fragments. Two-and three-dimensional CT best indicate the percentage of articular surface involvement and best demonstrate postoperative results or complications (hardware migration, residual step-off, delayed union, DJD, AVN, etc). Animated three-dimensional images are the preferred means of integrating the two-dimensional findings for surgical planning, as these images more closely simulate the clinical problem

  12. On two-dimensionalization of three-dimensional turbulence in shell models

    DEFF Research Database (Denmark)

    Chakraborty, Sagar; Jensen, Mogens Høgh; Sarkar, A.

    2010-01-01

    Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell m......-similar PDFs for longitudinal velocity differences are also presented for the rotating 3D turbulence case....

  13. Two-dimensional turbulent convection

    Science.gov (United States)

    Mazzino, Andrea

    2017-11-01

    We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh-Taylor and mean-gradient-forced Rayleigh-Bénard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan, "Inertial ranges in two-dimensional turbulence," Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection" [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374-1389 (1962)].

  14. Fourier transform ion cyclotron resonance mass spectrometry

    Science.gov (United States)

    Marshall, Alan G.

    1998-06-01

    As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.

  15. Tunable Channel Drop Filter in a Two-Dimensional Photonic Crystal Modulated by a Nematic Liquid Crystal

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available Photonic crystals (PCs have many potential applications because of their ability to control light-wave propagation and because PC-based waveguides may be integrated into optical circuits. We propose a novel tunable PC channel drop filter based on nematic liquid crystals and investigate its properties numerically by using the finite-difference time-domain (FDTD method. The refractive indices of liquid crystals can be actively modulated after infiltrating nematic liquid crystals into the microcavity in PC waveguides with square lattices. Then we can control light propagation in a PC waveguide. We analyze the Q -factors and resonance frequencies of a tunable PC channel drop filter by considering various indices modulation of liquid crystals. The novel component can be used as wavelength division multiplexing in photonic integrated circuits.

  16. A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

    Science.gov (United States)

    Debnath, Lokenath

    2012-01-01

    This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

  17. Multi-perspective views of students’ difficulties with one-dimensional vector and two-dimensional vector

    Science.gov (United States)

    Fauzi, Ahmad; Ratna Kawuri, Kunthi; Pratiwi, Retno

    2017-01-01

    Researchers of students’ conceptual change usually collects data from written tests and interviews. Moreover, reports of conceptual change often simply refer to changes in concepts, such as on a test, without any identification of the learning processes that have taken place. Research has shown that students have difficulties with vectors in university introductory physics courses and high school physics courses. In this study, we intended to explore students’ understanding of one-dimensional and two-dimensional vector in multi perspective views. In this research, we explore students’ understanding through test perspective and interviews perspective. Our research study adopted the mixed-methodology design. The participants of this research were sixty students of third semester of physics education department. The data of this research were collected by testand interviews. In this study, we divided the students’ understanding of one-dimensional vector and two-dimensional vector in two categories, namely vector skills of the addition of one-dimensionaland two-dimensional vector and the relation between vector skills and conceptual understanding. From the investigation, only 44% of students provided correct answer for vector skills of the addition of one-dimensional and two-dimensional vector and only 27% students provided correct answer for the relation between vector skills and conceptual understanding.

  18. Optimizing separations in online comprehensive two-dimensional liquid chromatography.

    Science.gov (United States)

    Pirok, Bob W J; Gargano, Andrea F G; Schoenmakers, Peter J

    2018-01-01

    Online comprehensive two-dimensional liquid chromatography has become an attractive option for the analysis of complex nonvolatile samples found in various fields (e.g. environmental studies, food, life, and polymer sciences). Two-dimensional liquid chromatography complements the highly popular hyphenated systems that combine liquid chromatography with mass spectrometry. Two-dimensional liquid chromatography is also applied to the analysis of samples that are not compatible with mass spectrometry (e.g. high-molecular-weight polymers), providing important information on the distribution of the sample components along chemical dimensions (molecular weight, charge, lipophilicity, stereochemistry, etc.). Also, in comparison with conventional one-dimensional liquid chromatography, two-dimensional liquid chromatography provides a greater separation power (peak capacity). Because of the additional selectivity and higher peak capacity, the combination of two-dimensional liquid chromatography with mass spectrometry allows for simpler mixtures of compounds to be introduced in the ion source at any given time, improving quantitative analysis by reducing matrix effects. In this review, we summarize the rationale and principles of two-dimensional liquid chromatography experiments, describe advantages and disadvantages of combining different selectivities and discuss strategies to improve the quality of two-dimensional liquid chromatography separations. © 2017 The Authors. Journal of Separation Science published by WILEY-VCH Verlag GmbH & Co. KGaA.

  19. Traceability and Quality Control in Traditional Chinese Medicine: From Chemical Fingerprint to Two-Dimensional Barcode

    Directory of Open Access Journals (Sweden)

    Yong Cai

    2015-01-01

    Full Text Available Chemical fingerprinting is currently a widely used tool that enables rapid and accurate quality evaluation of Traditional Chinese Medicine (TCM. However, chemical fingerprints are not amenable to information storage, recognition, and retrieval, which limit their use in Chinese medicine traceability. In this study, samples of three kinds of Chinese medicines were randomly selected and chemical fingerprints were then constructed by using high performance liquid chromatography. Based on chemical data, the process of converting the TCM chemical fingerprint into two-dimensional code is presented; preprocess and filtering algorithm are also proposed aiming at standardizing the large amount of original raw data. In order to know which type of two-dimensional code (2D is suitable for storing data of chemical fingerprints, current popular types of 2D codes are analyzed and compared. Results show that QR Code is suitable for recording the TCM chemical fingerprint. The fingerprint information of TCM can be converted into data format that can be stored as 2D code for traceability and quality control.

  20. Effectiveness of various transport synthetic acceleration methods with and without GMRES

    International Nuclear Information System (INIS)

    Chang, J.H.; Adams, M.L.

    2005-01-01

    We explore the effectiveness of three types of transport synthetic acceleration (TSA) methods as stand-alone methods and as pre-conditioners within the GMRES Krylov solver. The three types are β TSA, 'stretched' TSA, and 'stretched and filtered' (SF) TSA. We analyzed the effectiveness of these algorithms using Fourier mode analysis of model two-dimensional problems with periodic boundary conditions, including problems with alternating layers of different materials. The analyses revealed that both β-TSA and stretched TSA can diverge for fairly weak heterogeneities. Performance of SF TSA, even with the optimum filtering parameter, degrades with heterogeneity. However, with GMRES, all TSA methods are convergent. SF TSA with the optimum filtering parameter was the most effective method. Numerical results support our Fourier mode analysis. (authors)

  1. Filtering of SPECT reconstructions made using Bellini's attenuation correction method

    International Nuclear Information System (INIS)

    Glick, S.J.; Penney, B.C.; King, M.A.

    1991-01-01

    This paper evaluates a three-dimensional (3D) Wiener filter which is used to restore SPECT reconstructions which were made using Bellini's method of attenuation correction. Its performance is compared to that of several pre-reconstruction filers: the one-dimensional (1D) Butterworth, the two-dimensional (2D) Butterworth, and a 2D Wiener filer. A simulation study is used to compare the four filtering methods. An approximation to a clinical liver spleen study was used as the source distribution and algorithm which accounts for the depth and distance dependent blurring in SPECT was used to compute noise free projections. To study the effect of filtering method on tumor detection accuracy, a 2 cm diameter, cool spherical tumor (40% contrast) was placed at a known, but random, location with the liver. Projection sets for ten tumor locations were computed and five noise realizations of each set were obtained by introducing Poisson noise. The simulated projections were either: filtered with the 1D or 2D Butterworth or the 2D Wiener and then reconstructed using Bellini's intrinsic attenuation correction, or reconstructed first, then filtered with the 3D Wiener. The criteria used for comparison were: normalized mean square error (NMSE), cold spot contrast, and accuracy of tumor detection with an automated numerical method. Results indicate that restorations obtained with 3D Wiener filtering yielded significantly higher lesion contrast and lower NMSE values compared to the other methods of processing. The Wiener restoration filters and the 2D Butterworth all provided similar measures of detectability, which were noticeably higher than that obtained with 1D Butterworth smoothing

  2. An algorithm for three-dimensional imaging in the positron camera

    International Nuclear Information System (INIS)

    Chen Kun; Ma Mei; Xu Rongfen; Shen Miaohe

    1986-01-01

    A mathematical algorithm of back-projection filtered for image reconstructions using two-dimensional signals detected from parallel multiwire proportional chambers is described. The approaches of pseudo three-dimensional and full three-dimensional image reconstructions are introduced, and the available point response functions are defined as well. The designing parameters and computation procedure of the full three-dimensional method is presented

  3. Comparison of two ring artefact removal filters used for neutron tomography reconstruction

    International Nuclear Information System (INIS)

    Vontobel, P.

    2007-01-01

    Full text of publication follows: The reduction of ring artefacts in transmission tomography reconstruction, by filtering sino-grams, is a common practice for most radiation modalities. Using simulated and measured neutron transmission data, an analysis of two ring artefact suppression schemes is given. The choice of the ring filtering parameters has to take the noise characteristics of the measured raw projection data into account. Introduction The appearance of ring artefacts in transmission tomography data is quite common. They are due to deficiencies in the measured projections and show as vertical lines in the sinogram representation of all projections of a single slice. A vertical line in the sinogram is due to a single pixel or a group of n pixels on the detector, which is less or more sensitive than the average pixel and shows even after flat-field correction. Most annoying ring artefacts are due to partly dead pixels, which cannot be identified easily on the projection images. Their effect only show in the sinogram or later on the reconstructed slice images. Therefore ring artefact mitigation starts with the analysis of sinogram images or analysis of reconstructed slices. Analysis of two ring filtering algorithms: The first ring filtering method sums first sinogram rows (i.e. over all angles) and divides it by the number of rows (ave) and generate a smoothed version of this sum (smoothing width 3,5,7,9 pixels). The difference diff = ave - smooth(ave) is then subtracted from each row. This is a very simple and efficient correction scheme. The second method relies on morphological filtering the sinogram i.e. using a combination of a morphological 'Top hat' and a 'Bot hat' operation on the data. A filtering threshold is determined depending on the number of detected lines in the sinogram. Summary and conclusion: Using simulated an measured neutron transmission data two ring filtering algorithms are evaluated. A careful choice of filtering parameters is

  4. Two-dimensional liquid chromatography

    DEFF Research Database (Denmark)

    Græsbøll, Rune

    -dimensional separation space. Optimization of gradients in online RP×RP is more difficult than in normal HPLC as a result of the increased number of parameters and their influence on each other. Modeling the coverage of the compounds across the two-dimensional chromatogram as a result of a change in gradients could...... be used for optimization purposes, and reduce the time spend on optimization. In this thesis (chapter 6), and manuscript B, a measure of the coverage of the compounds in the twodimensional separation space is defined. It is then shown that this measure can be modeled for changes in the gradient in both...

  5. Method of local pointed function reduction of original shape in Fourier transformation

    International Nuclear Information System (INIS)

    Dosch, H.; Slavyanov, S.Yu.

    2002-01-01

    The method for analytical reduction of the original shape in the one-dimensional Fourier transformation by the fourier image modulus is proposed. The basic concept of the method consists in the presentation of the model shape in the form of the local peak functions sum. The eigenfunctions, generated by the linear differential equations with the polynomial coefficients, are selected as the latter ones. This provides for the possibility of managing the Fourier transformation without numerical integration. This reduces the reverse task to the nonlinear regression with a small number of the evaluated parameters and to the numerical or asymptotic study on the model peak functions - the eigenfunctions of the differential tasks and their fourier images [ru

  6. Supramolecular nano-architectures and two-dimensional/three-dimensional aggregation of a bolaamphiphilic diacid at the air/water interface

    International Nuclear Information System (INIS)

    Jiao Tifeng; Liu Minghua

    2005-01-01

    The spreading behavior and nano-architectures of a bolaamphiphilic diacid, 1, 13-tridecandicarboxylic acid (TDA) on water surface and the subphase containing Eu(III) ion were investigated. It was found that although TDA itself could not spread on water surface, it could form an ultrathin film on the aqueous subphase containing Eu(III) ion. In addition, interesting nano-architectures were observed for the transferred film on mica surface. It was found that the formation and change of the nano-architectures were depended on the surface pressure and concentration of Eu(III) ion in the subphase. A rectangular slide morphology was observed for the film spread on an aqueous subphase containing lower concentration of Eu(III), while a walnut-like nano-architectures were observed for the film spread on a higher concentration of Eu(III) ion. Flower structure was observed at a higher surface pressure. The nano-architecture can be further regulated through mixing TDA with octadecylamine (OA) in which linear fiber nanostructure was obtained. It was revealed that while the nano-architectures were formed mainly through a three dimensional aggregation in the case of TDA/Eu(III) films, a two-dimensional aggregation occurred when TDA was mixed with OA. A series of methods such as atomic force microscope, field emission scanning electron microscopy, Fourier transform infrared spectroscopy and X-ray diffraction were used to characterize the supramolecular structures. A possible mechanism for the formation of these nano-architectures was discussed

  7. Two-dimensional simulation of sintering process

    International Nuclear Information System (INIS)

    Vasconcelos, Vanderley de; Pinto, Lucio Carlos Martins; Vasconcelos, Wander L.

    1996-01-01

    The results of two-dimensional simulations are directly applied to systems in which one of the dimensions is much smaller than the others, and to sections of three dimensional models. Moreover, these simulations are the first step of the analysis of more complex three-dimensional systems. In this work, two basic features of the sintering process are studied: the types of particle size distributions related to the powder production processes and the evolution of geometric parameters of the resultant microstructures during the solid-state sintering. Random packing of equal spheres is considered in the sintering simulation. The packing algorithm does not take into account the interactive forces between the particles. The used sintering algorithm causes the densification of the particle set. (author)

  8. Simple spectral method for solving propagation problems in cylindrical geometry with fast Fourier transforms

    International Nuclear Information System (INIS)

    Feit, M.D.; Fleck, J.A. Jr.

    1989-01-01

    We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage

  9. Transport methods: general. 7. Formulation of a Fourier-Boltzmann Transformation to Solve the Three-Dimensional Transport Equation

    International Nuclear Information System (INIS)

    Stancic, V.

    2001-01-01

    This paper presents some elements of a new approach to solve analytically the linearized three-dimensional (3-D) transport equation of neutral particles. Since this task is of such special importance, we present some results of a paper that is still in progress. The most important is that using this transformation, an integro-differential equation with an analytical solution is obtained. For this purpose, a simplest 3-D equation is being considered which describes the transport process in an infinite medium. Until now, this equation has been analytically considered either using the Laplace transform with respect to time parameter t or applying the Fourier transform over the space coordinate. Both of them reduce the number of differential terms in the equation; however, evaluation of the inverse transformation is complicated. In this paper, we introduce for the first time a Fourier transform induced by the Boltzmann operator. For this, we use a complete set of 3-D eigenfunctions of the Boltzmann transport operator defined in a similar way as those that have been already used in 3-D transport theory as a basic set to transform the transport equation. This set consists of a continuous part and a discrete one with spectral measure. The density distribution equation shows the known form asymptotic behavior. Several applications are to be performed using this equation and compared to the benchmark one. Such an analysis certainly would be out of the available space

  10. Combination of Wiener filtering and singular value decomposition filtering for volume imaging PET

    International Nuclear Information System (INIS)

    Shao, L.; Lewitt, R.M.; Karp, J.S.

    1995-01-01

    Although the three-dimensional (3D) multi-slice rebinning (MSRB) algorithm in PET is fast and practical, and provides an accurate reconstruction, the MSRB image, in general, suffers from the noise amplified by its singular value decomposition (SVD) filtering operation in the axial direction. Their aim in this study is to combine the use of the Wiener filter (WF) with the SVD to decrease the noise and improve the image quality. The SVD filtering ''deconvolves'' the spatially variant axial response function while the WF suppresses the noise and reduces the blurring not modeled by the axial SVD filter but included in the system modulation transfer function. Therefore, the synthesis of these two techniques combines the advantages of both filters. The authors applied this approach to the volume imaging HEAD PENN-PET brain scanner with an axial extent of 256 mm. This combined filter was evaluated in terms of spatial resolution, image contrast, and signal-to-noise ratio with several phantoms, such as a cold sphere phantom and 3D brain phantom. Specifically, the authors studied both the SVD filter with an axial Wiener filter and the SVD filter with a 3D Wiener filter, and compared the filtered images to those from the 3D reprojection (3DRP) reconstruction algorithm. Their results indicate that the Wiener filter increases the signal-to-noise ratio and also improves the contrast. For the MSRB images of the 3D brain phantom, after 3D WF, both the Gray/White and Gray/Ventricle ratios were improved from 1.8 to 2.8 and 2.1 to 4.1, respectively. In addition, the image quality with the MSRB algorithm is close to that of the 3DRP algorithm with 3D WF applied to both image reconstructions

  11. Chaotic dynamics in two-dimensional noninvertible maps

    CERN Document Server

    Mira, Christian; Cathala, Jean-Claude; Gardini, Laura

    1996-01-01

    This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this resea

  12. Testing a Fourier Accelerated Hybrid Monte Carlo Algorithm

    OpenAIRE

    Catterall, S.; Karamov, S.

    2001-01-01

    We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for dynamical fermion simulations of non-gauge models. We test the algorithm in supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice field theory. We find dramatic reductions in the autocorrelation time of the algorithm in comparison to standard HMC.

  13. Application of a method for comparing one-dimensional and two-dimensional models of a ground-water flow system

    International Nuclear Information System (INIS)

    Naymik, T.G.

    1978-01-01

    To evaluate the inability of a one-dimensional ground-water model to interact continuously with surrounding hydraulic head gradients, simulations using one-dimensional and two-dimensional ground-water flow models were compared. This approach used two types of models: flow-conserving one-and-two dimensional models, and one-dimensional and two-dimensional models designed to yield two-dimensional solutions. The hydraulic conductivities of controlling features were varied and model comparison was based on the travel times of marker particles. The solutions within each of the two model types compare reasonably well, but a three-dimensional solution is required to quantify the comparison

  14. Wiener discrete cosine transform-based image filtering

    Science.gov (United States)

    Pogrebnyak, Oleksiy; Lukin, Vladimir V.

    2012-10-01

    A classical problem of additive white (spatially uncorrelated) Gaussian noise suppression in grayscale images is considered. The main attention is paid to discrete cosine transform (DCT)-based denoising, in particular, to image processing in blocks of a limited size. The efficiency of DCT-based image filtering with hard thresholding is studied for different sizes of overlapped blocks. A multiscale approach that aggregates the outputs of DCT filters having different overlapped block sizes is proposed. Later, a two-stage denoising procedure that presumes the use of the multiscale DCT-based filtering with hard thresholding at the first stage and a multiscale Wiener DCT-based filtering at the second stage is proposed and tested. The efficiency of the proposed multiscale DCT-based filtering is compared to the state-of-the-art block-matching and three-dimensional filter. Next, the potentially reachable multiscale filtering efficiency in terms of output mean square error (MSE) is studied. The obtained results are of the same order as those obtained by Chatterjee's approach based on nonlocal patch processing. It is shown that the ideal Wiener DCT-based filter potential is usually higher when noise variance is high.

  15. Terahertz spectroscopy of two-dimensional subwavelength plasmonic structures

    Energy Technology Data Exchange (ETDEWEB)

    Azad, Abul K [Los Alamos National Laboratory; Chen, Houtong [Los Alamos National Laboratory; Taylor, Antoinette [Los Alamos National Laboratory; O' Hara, John F [Los Alamos National Laboratory; Han, Jiaguang [OSU; Lu, Xinchao [OSU; Zhang, Weili [OSU

    2009-01-01

    The fascinating properties of plasmonic structures have had significant impact on the development of next generation ultracompact photonic and optoelectronic components. We study two-dimensional plasmonic structures functioning at terahertz frequencies. Resonant terahertz response due to surface plasmons and dipole localized surface plasmons were investigated by the state-of-the-art terahertz time domain spectroscopy (THz-TDS) using both transmission and reflection configurations. Extraordinary terahertz transmission was demonstrated through the subwavelength metallic hole arrays made from good conducting metals as well as poor metals. Metallic arrays m!lde from Pb, generally a poor metal, and having optically thin thicknesses less than one-third of a skin depth also contributed in enhanced THz transmission. A direct transition of a surface plasmon resonance from a photonic crystal minimum was observed in a photo-doped semiconductor array. Electrical controls of the surface plasmon resonances by hybridization of the Schottkey diode between the metallic grating and the semiconductor substrate are investigated as a function of the applied reverse bias. In addition, we have demonstrated photo-induced creation and annihilation of surface plasmons with appropriate semiconductors at room temperature. According to the Fano model, the transmission properties are characterized by two essential contributions: resonant excitation of surface plasmons and nonresonant direct transmission. Such plasmonic structures may find fascinating applications in terahertz imaging, biomedical sensing, subwavelength terahertz spectroscopy, tunable filters, and integrated terahertz devices.

  16. Two-dimensional analytic weighting functions for limb scattering

    Science.gov (United States)

    Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

    2017-10-01

    Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

  17. Accelerating two-dimensional nuclear magnetic resonance correlation spectroscopy via selective coherence transfer

    Science.gov (United States)

    Ye, Qimiao; Chen, Lin; Qiu, Wenqi; Lin, Liangjie; Sun, Huijun; Cai, Shuhui; Wei, Zhiliang; Chen, Zhong

    2017-01-01

    Nuclear magnetic resonance (NMR) spectroscopy serves as an important tool for both qualitative and quantitative analyses of various systems in chemistry, biology, and medicine. However, applications of one-dimensional 1H NMR are often restrained by the presence of severe overlap among different resonances. The advent of two-dimensional (2D) 1H NMR constitutes a promising alternative by extending the crowded resonances into a plane and thereby alleviating the spectral congestions. However, the enhanced ability in discriminating resonances is achieved at the cost of extended experimental duration due to necessity of various scans with progressive delays to construct the indirect dimension. Therefore, in this study, we propose a selective coherence transfer (SECOT) method to accelerate acquisitions of 2D correlation spectroscopy by converting chemical shifts into spatial positions within the effective sample length and then performing an echo planar spectroscopic imaging module to record the spatial and spectral information, which generates 2D correlation spectrum after 2D Fourier transformation. The feasibility and effectiveness of SECOT have been verified by a set of experiments under both homogeneous and inhomogeneous magnetic fields. Moreover, evaluations of SECOT for quantitative analyses are carried out on samples with a series of different concentrations. Based on these experimental results, the SECOT may open important perspectives for fast, accurate, and stable investigations of various chemical systems both qualitatively and quantitatively.

  18. Analog fourier transform channelizer and OFDM receiver

    OpenAIRE

    2007-01-01

    An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...

  19. Fourier transform infrared spectroscopy microscopic imaging classification based on spatial-spectral features

    Science.gov (United States)

    Liu, Lian; Yang, Xiukun; Zhong, Mingliang; Liu, Yao; Jing, Xiaojun; Yang, Qin

    2018-04-01

    The discrete fractional Brownian incremental random (DFBIR) field is used to describe the irregular, random, and highly complex shapes of natural objects such as coastlines and biological tissues, for which traditional Euclidean geometry cannot be used. In this paper, an anisotropic variable window (AVW) directional operator based on the DFBIR field model is proposed for extracting spatial characteristics of Fourier transform infrared spectroscopy (FTIR) microscopic imaging. Probabilistic principal component analysis first extracts spectral features, and then the spatial features of the proposed AVW directional operator are combined with the former to construct a spatial-spectral structure, which increases feature-related information and helps a support vector machine classifier to obtain more efficient distribution-related information. Compared to Haralick’s grey-level co-occurrence matrix, Gabor filters, and local binary patterns (e.g. uniform LBPs, rotation-invariant LBPs, uniform rotation-invariant LBPs), experiments on three FTIR spectroscopy microscopic imaging datasets show that the proposed AVW directional operator is more advantageous in terms of classification accuracy, particularly for low-dimensional spaces of spatial characteristics.

  20. Depth-enhanced three-dimensional-two-dimensional convertible display based on modified integral imaging.

    Science.gov (United States)

    Park, Jae-Hyeung; Kim, Hak-Rin; Kim, Yunhee; Kim, Joohwan; Hong, Jisoo; Lee, Sin-Doo; Lee, Byoungho

    2004-12-01

    A depth-enhanced three-dimensional-two-dimensional convertible display that uses a polymer-dispersed liquid crystal based on the principle of integral imaging is proposed. In the proposed method, a lens array is located behind a transmission-type display panel to form an array of point-light sources, and a polymer-dispersed liquid crystal is electrically controlled to pass or to scatter light coming from these point-light sources. Therefore, three-dimensional-two-dimensional conversion is accomplished electrically without any mechanical movement. Moreover, the nonimaging structure of the proposed method increases the expressible depth range considerably. We explain the method of operation and present experimental results.

  1. Active RC filter based implementation analysis part of two channel hybrid filter bank

    Directory of Open Access Journals (Sweden)

    Stojanović Vidosav

    2014-01-01

    Full Text Available In the present paper, a new design method for continuous-time powersymmetric active RC filters for Hybrid Filter Bank (HFB is proposed. Some theoretical properties of continious-time power-symmetric filters bank in a more general perspective are studied. This includes the derivation of a new general analytical form, and a study of poles and zeros locations in s-plane. In the proposed design method the analytic solution of filter coefficients is solved in sdomain using only one nonlinear equation Finally, the proposed approximation is compared to standard approximations. It was shown that attenuation and group delay characteristic of the proposed filter lie between Butterworth and elliptic characteristics. [Projekat Ministarstva nauke Republike Srbije, br. 32009TR

  2. Fourier Transform Spectrometer System

    Science.gov (United States)

    Campbell, Joel F. (Inventor)

    2014-01-01

    A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.

  3. Using FDFD Technique in Two-Dimensional TE Analysis for Modeling Clutter in Wall Penetrating Radar

    Directory of Open Access Journals (Sweden)

    David Insana

    2014-01-01

    Full Text Available Finite difference frequency domain (FDFD computational electromagnetic modeling is implemented to perform a two-dimensional TEz analysis for the application of wall penetrating radar (WPR. Resolving small targets of interest, embedded in a strong clutter environment of unknown configuration, is difficult. Field interaction between clutter elements will dominate the received fields back-scattered from the scene. Removing the effects of clutter ultimately relies on the accuracy of the model. Analysis starts with a simple model that continues to build based on the dominant scattering features of the scene. FDFD provides a steady state frequency response to a discrete excitation. Taking the fast Fourier transform of the wideband response of the scene, at several external transmit/receive locations, produces 2D images of the clutter, which are used to mature the model.

  4. A three-dimensional correlation method for registration of medical images in radiology

    Energy Technology Data Exchange (ETDEWEB)

    Georgiou, Michalakis; Sfakianakis, George N [Department of Radiology, University of Miami, Jackson Memorial Hospital, Miami, FL 33136 (United States); Nagel, Joachim H [Institute of Biomedical Engineering, University of Stuttgart, Stuttgart 70174 (Germany)

    1999-12-31

    The availability of methods to register multi-modality images in order to `fuse` them to correlate their information is increasingly becoming an important requirement for various diagnostic and therapeutic procedures. A variety of image registration methods have been developed but they remain limited to specific clinical applications. Assuming rigid body transformation, two images can be registered if their differences are calculated in terms of translation, rotation and scaling. This paper describes the development and testing of a new correlation based approach for three-dimensional image registration. First, the scaling factors introduced by the imaging devices are calculated and compensated for. Then, the two images become translation invariant by computing their three-dimensional Fourier magnitude spectra. Subsequently, spherical coordinate transformation is performed and then the three-dimensional rotation is computed using a novice approach referred to as {sup p}olar Shells{sup .} The method of polar shells maps the three angles of rotation into one rotation and two translations of a two-dimensional function and then proceeds to calculate them using appropriate transformations based on the Fourier invariance properties. A basic assumption in the method is that the three-dimensional rotation is constrained to one large and two relatively small angles. This assumption is generally satisfied in normal clinical settings. The new three-dimensional image registration method was tested with simulations using computer generated phantom data as well as actual clinical data. Performance analysis and accuracy evaluation of the method using computer simulations yielded errors in the sub-pixel range. (authors) 6 refs., 3 figs.

  5. A three-dimensional correlation method for registration of medical images in radiology

    International Nuclear Information System (INIS)

    Georgiou, Michalakis; Sfakianakis, George N.; Nagel, Joachim H.

    1998-01-01

    The availability of methods to register multi-modality images in order to 'fuse' them to correlate their information is increasingly becoming an important requirement for various diagnostic and therapeutic procedures. A variety of image registration methods have been developed but they remain limited to specific clinical applications. Assuming rigid body transformation, two images can be registered if their differences are calculated in terms of translation, rotation and scaling. This paper describes the development and testing of a new correlation based approach for three-dimensional image registration. First, the scaling factors introduced by the imaging devices are calculated and compensated for. Then, the two images become translation invariant by computing their three-dimensional Fourier magnitude spectra. Subsequently, spherical coordinate transformation is performed and then the three-dimensional rotation is computed using a novice approach referred to as p olar Shells . The method of polar shells maps the three angles of rotation into one rotation and two translations of a two-dimensional function and then proceeds to calculate them using appropriate transformations based on the Fourier invariance properties. A basic assumption in the method is that the three-dimensional rotation is constrained to one large and two relatively small angles. This assumption is generally satisfied in normal clinical settings. The new three-dimensional image registration method was tested with simulations using computer generated phantom data as well as actual clinical data. Performance analysis and accuracy evaluation of the method using computer simulations yielded errors in the sub-pixel range. (authors)

  6. Fourier transform resampling: Theory and application

    International Nuclear Information System (INIS)

    Hawkins, W.G.

    1996-01-01

    One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)

  7. Functional inks and printing of two-dimensional materials.

    Science.gov (United States)

    Hu, Guohua; Kang, Joohoon; Ng, Leonard W T; Zhu, Xiaoxi; Howe, Richard C T; Jones, Christopher G; Hersam, Mark C; Hasan, Tawfique

    2018-05-08

    Graphene and related two-dimensional materials provide an ideal platform for next generation disruptive technologies and applications. Exploiting these solution-processed two-dimensional materials in printing can accelerate this development by allowing additive patterning on both rigid and conformable substrates for flexible device design and large-scale, high-speed, cost-effective manufacturing. In this review, we summarise the current progress on ink formulation of two-dimensional materials and the printable applications enabled by them. We also present our perspectives on their research and technological future prospects.

  8. Photometric Separation of Stellar Properties Using SDSS Filters

    Science.gov (United States)

    Lenz, Dawn D.; Newberg, Jo; Rosner, Robert; Richards, Gordon T.; Stoughton, Chris

    1998-12-01

    Using synthetic photometry of Kurucz model spectra, we explore the colors of stars as a function of temperature, metallicity, and surface gravity with Sloan Digital Sky Survey (SDSS) filters, u'g'r'i'z'. The synthetic colors show qualitative agreement with the few published observations in these filters. We find that the locus of synthetic stars is basically two-dimensional for 4500 advantageous to use more than two colors when determining stellar properties by color. Strategic observations in SDSS filters are required to resolve the source of a ~5% discrepancy between synthetic colors of Gunn-Stryker stars, Kurucz models, and external determinations of the metallicities and surface gravities. The synthetic star colors can be used to investigate the properties of any normal star and to construct analytic expressions for the photometric prediction of stellar properties in special cases.

  9. K-FIX: a computer program for transient, two-dimensional, two-fluid flow. THREED: an extension of the K-FIX code for three-dimensional calculations

    International Nuclear Information System (INIS)

    Rivard, W.C.; Torrey, M.D.

    1978-10-01

    The transient, two-dimensional, two-fluid code K-FIX has been extended to perform three-dimensional calculations. This capability is achieved by adding five modification sets of FORTRAN statements to the basic two-dimensional code. The modifications are listed and described, and a complete listing of the three-dimensional code is provided. Results of an example problem are provided for verification

  10. Performance Evaluation of Two Different Industrial Foam Filters with LiMCA II Data

    Science.gov (United States)

    Syvertsen, Martin; Bao, Sarina

    2015-04-01

    Plant-scale filtration experiments with molten aluminum have been carried out with two different types of 10 × 10 × 2 in, 30 ppi ceramic foam filters. The filters were produced in the same production line where the only difference was the composition of the ceramic slurry used for the filter production. The inclusion contents in the aluminum melt before and after the filters were measured with two constantly running liquid metal cleanliness analyzer (LiMCA) II units. Three methods for analyzing the recorded data are presented. A significant difference in the filtration performance as function of time was found when settling of inclusions in the melt was taken into account. Statistical treatment of the time dependent LiMCA II data was performed.

  11. Stabilizing the thermal lattice Boltzmann method by spatial filtering.

    Science.gov (United States)

    Gillissen, J J J

    2016-10-01

    We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

  12. Analysis of low-pass filters for approximate deconvolution closure modelling in one-dimensional decaying Burgers turbulence

    Science.gov (United States)

    San, O.

    2016-01-01

    The idea of spatial filtering is central in approximate deconvolution large-eddy simulation (AD-LES) of turbulent flows. The need for low-pass filters naturally arises in the approximate deconvolution approach which is based solely on mathematical approximations by employing repeated filtering operators. Two families of low-pass spatial filters are studied in this paper: the Butterworth filters and the Padé filters. With a selection of various filtering parameters, variants of the AD-LES are systematically applied to the decaying Burgers turbulence problem, which is a standard prototype for more complex turbulent flows. Comparing with the direct numerical simulations, it is shown that all forms of the AD-LES approaches predict significantly better results than the under-resolved simulations at the same grid resolution. However, the results highly depend on the selection of the filtering procedure and the filter design. It is concluded that a complete attenuation for the smallest scales is crucial to prevent energy accumulation at the grid cut-off.

  13. Combustion stratification study of partially premixed combustion using Fourier transform analysis of OH* chemiluminescence images

    KAUST Repository

    Izadi Najafabadi, Mohammad

    2017-11-06

    A relatively high level of stratification (qualitatively: lack of homogeneity) is one of the main advantages of partially premixed combustion over the homogeneous charge compression ignition concept. Stratification can smooth the heat release rate and improve the controllability of combustion. In order to compare stratification levels of different partially premixed combustion strategies or other combustion concepts, an objective and meaningful definition of “stratification level” is required. Such a definition is currently lacking; qualitative/quantitative definitions in the literature cannot properly distinguish various levels of stratification. The main purpose of this study is to objectively define combustion stratification (not to be confused with fuel stratification) based on high-speed OH* chemiluminescence imaging, which is assumed to provide spatial information regarding heat release. Stratification essentially being equivalent to spatial structure, we base our definition on two-dimensional Fourier transforms of photographs of OH* chemiluminescence. A light-duty optical diesel engine has been used to perform the OH* bandpass imaging on. Four experimental points are evaluated, with injection timings in the homogeneous regime as well as in the stratified partially premixed combustion regime. Two-dimensional Fourier transforms translate these chemiluminescence images into a range of spatial frequencies. The frequency information is used to define combustion stratification, using a novel normalization procedure. The results indicate that this new definition, based on Fourier analysis of OH* bandpass images, overcomes the drawbacks of previous definitions used in the literature and is a promising method to compare the level of combustion stratification between different experiments.

  14. Two-dimensional critical phenomena

    International Nuclear Information System (INIS)

    Saleur, H.

    1987-09-01

    Two dimensional critical systems are studied using transformation to free fields and conformal invariance methods. The relations between the two approaches are also studied. The analytical results obtained generally depend on universality hypotheses or on renormalization group trajectories which are not established rigorously, so numerical verifications, mainly using the transfer matrix approach, are presented. The exact determination of critical exponents; the partition functions of critical models on toruses; and results as the critical point is approached are discussed [fr

  15. The Fourier decomposition method for nonlinear and non-stationary time series analysis.

    Science.gov (United States)

    Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik

    2017-03-01

    for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

  16. Efficient Fourier-based algorithms for time-periodic unsteady problems

    Science.gov (United States)

    Gopinath, Arathi Kamath

    2007-12-01

    This dissertation work proposes two algorithms for the simulation of time-periodic unsteady problems via the solution of Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. These algorithms use a Fourier representation in time and hence solve for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). In contrast to conventional Fourier-based techniques which solve the governing equations in frequency space, the new algorithms perform all the calculations in the time domain, and hence require minimal modifications to an existing solver. The complete space-time solution is obtained by iterating in a fifth pseudo-time dimension. Various time-periodic problems such as helicopter rotors, wind turbines, turbomachinery and flapping-wings can be simulated using the Time Spectral method. The algorithm is first validated using pitching airfoil/wing test cases. The method is further extended to turbomachinery problems, and computational results verified by comparison with a time-accurate calculation. The technique can be very memory intensive for large problems, since the solution is computed (and hence stored) simultaneously at all time levels. Often, the blade counts of a turbomachine are rescaled such that a periodic fraction of the annulus can be solved. This approximation enables the solution to be obtained at a fraction of the cost of a full-scale time-accurate solution. For a viscous computation over a three-dimensional single-stage rescaled compressor, an order of magnitude savings is achieved. The second algorithm, the reduced-order Harmonic Balance method is applicable only to turbomachinery flows, and offers even larger computational savings than the Time Spectral method. It simulates the true geometry of the turbomachine using only one blade passage per blade row as the computational domain. In each blade row of the turbomachine, only the dominant frequencies are resolved, namely

  17. Decontamination of two filter boxes after a fire

    International Nuclear Information System (INIS)

    Cerre, P.; Mestre, E.; Lafitte, T.

    1961-01-01

    As a primary filter of the venting system caught fire in a hot cell of the Laboratory of Examination of Irradiated Fuels, this filter (as well as the secondary filter) has been removed, wrapped in polyvinyl sheets, and transported into the decontamination station. The authors report the details of the handling and decontamination operations: modifications to the station arrangement, measures of radiation protection, decontamination and measurements, observations made when disassembling the filter and filter-boxes [fr

  18. Two-dimensional systems from introduction to state of the art

    CERN Document Server

    Benzaouia, Abdellah; Tadeo, Fernando

    2016-01-01

    A solution permitting the stabilization of 2-dimensional (2-D) continuous-time saturated system under state feedback control is presented in this book. The problems of delay and saturation are treated at the same time. The authors obtain novel results on continuous 2-D systems using the unidirectional Lyapunov function. The control synthesis and the saturation and delay conditions are presented as linear matrix inequalities. Illustrative examples are worked through to show the effectiveness of the approach and many comparisons are made with existing results. The second half of the book moves on to consider robust stabilization and filtering of 2-D systems with particular consideration being given to 2-D fuzzy systems. Solutions for the filter-design problems are demonstrated by computer simulation. The text builds up to the development of state feedback control for 2-D Takagi–Sugeno systems with stochastic perturbation. Conservatism is reduced by using slack matrices and the coupling between the Lyapunov ma...

  19. Amplifying and compressing optical filter based on one-dimensional ternary photonic crystal structure containing gain medium

    Science.gov (United States)

    Jamshidi-Ghaleh, Kazem; Ebrahimpour, Zeinab; Moslemi, Fatemeh

    2015-07-01

    The transmission spectrum properties of the one-dimensional ternary photonic crystal (1DTPC) structure, composed of dielectric (D), metal (M) and gain (G) materials, with three different arrangements of (DGM)N, (GDM)N and (DMG)N, where N is the number of periodicity, were investigated. Two full photonic band gaps and N-1 resonant peaks, localized between them, were observed on transmittance spectra on near-UV spectrum region. When the gained layer was placed in front of the metal, the peaks appeared with higher resolution. There is a peak, localized on the higher band-edge of the first gap, which shows very interesting property than the other peaks. Thus, it amplifies and compresses faster with increase in the N and strength of the gain coefficient. The effects of the gain coefficient and periodicity number are graphically illustrated. This communication presents a PC structure that can be a good candidate to design an amplifying and compressing single or multi-channel optical filter in the UV region.

  20. Multilevel ensemble Kalman filtering

    KAUST Repository

    Hoel, Haakon

    2016-01-08

    The ensemble Kalman filter (EnKF) is a sequential filtering method that uses an ensemble of particle paths to estimate the means and covariances required by the Kalman filter by the use of sample moments, i.e., the Monte Carlo method. EnKF is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of particles is high. The multilevel Monte Carlo method (MLMC) is an extension of classical Monte Carlo methods which by sampling stochastic realizations on a hierarchy of resolutions may reduce the computational cost of moment approximations by orders of magnitude. In this work we have combined the ideas of MLMC and EnKF to construct the multilevel ensemble Kalman filter (MLEnKF) for the setting of finite dimensional state and observation spaces. The main ideas of this method is to compute particle paths on a hierarchy of resolutions and to apply multilevel estimators on the ensemble hierarchy of particles to compute Kalman filter means and covariances. Theoretical results and a numerical study of the performance gains of MLEnKF over EnKF will be presented. Some ideas on the extension of MLEnKF to settings with infinite dimensional state spaces will also be presented.

  1. Multilevel ensemble Kalman filtering

    KAUST Repository

    Hoel, Haakon; Chernov, Alexey; Law, Kody; Nobile, Fabio; Tempone, Raul

    2016-01-01

    The ensemble Kalman filter (EnKF) is a sequential filtering method that uses an ensemble of particle paths to estimate the means and covariances required by the Kalman filter by the use of sample moments, i.e., the Monte Carlo method. EnKF is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of particles is high. The multilevel Monte Carlo method (MLMC) is an extension of classical Monte Carlo methods which by sampling stochastic realizations on a hierarchy of resolutions may reduce the computational cost of moment approximations by orders of magnitude. In this work we have combined the ideas of MLMC and EnKF to construct the multilevel ensemble Kalman filter (MLEnKF) for the setting of finite dimensional state and observation spaces. The main ideas of this method is to compute particle paths on a hierarchy of resolutions and to apply multilevel estimators on the ensemble hierarchy of particles to compute Kalman filter means and covariances. Theoretical results and a numerical study of the performance gains of MLEnKF over EnKF will be presented. Some ideas on the extension of MLEnKF to settings with infinite dimensional state spaces will also be presented.

  2. Two-dimensional capillary origami

    Energy Technology Data Exchange (ETDEWEB)

    Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu

    2016-01-08

    We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.

  3. Two-dimensional capillary origami

    International Nuclear Information System (INIS)

    Brubaker, N.D.; Lega, J.

    2016-01-01

    We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.

  4. Two-layer type filter for removal of radioactive iodine

    Energy Technology Data Exchange (ETDEWEB)

    Taoki, M

    1976-04-16

    The object is to provide a filter for removing radioactive iodine, which is used for disposal of gaseous waste in an atomic power plant, to particularly hold a pressure loss lower. The filter according to the present invention comprises two layers, which are filled at a front stage with active carbon, which is small in pressure loss and has a good collective efficiency relative to iodine, and at a rear stage with silver zeolite, which has a good collective efficiency relative to both iodine and methyl iodine, whereby respective adsorbent are effectively utilized to minimize pressure loss even if a large quantity of air.

  5. Two-layer type filter for removal of radioactive iodine

    International Nuclear Information System (INIS)

    Taoki, Masafumi.

    1976-01-01

    Object: To provide a filter for removing radioactive iodine, which is used for disposal of gaseous waste in an atomic power plant, to particularly hold a pressure loss lower. Structure: The filter according to the present invention comprises two layers, which are filled at a front stage with active carbon, which is small in pressure loss and has a good collective efficiency relative to iodine, and at a rear stage with silver zeolite, which has a good collective efficiency relative to both iodine and methyl iodine, whereby respective adsorbent are effectively utilized to minimize pressure loss even if a large quantity of air. (Kamimura, M.)

  6. Two-dimensional black holes and non-commutative spaces

    International Nuclear Information System (INIS)

    Sadeghi, J.

    2008-01-01

    We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon

  7. Removing tidal-period variations from time-series data using low-pass digital filters

    Science.gov (United States)

    Walters, Roy A.; Heston, Cynthia

    1982-01-01

    Several low-pass, digital filters are examined for their ability to remove tidal Period Variations from a time-series of water surface elevation for San Francisco Bay. The most efficient filter is the one which is applied to the Fourier coefficients of the transformed data, and the filtered data recovered through an inverse transform. The ability of the filters to remove the tidal components increased in the following order: 1) cosine-Lanczos filter, 2) cosine-Lanczos squared filter; 3) Godin filter; and 4) a transform fitter. The Godin fitter is not sufficiently sharp to prevent severe attenuation of 2–3 day variations in surface elevation resulting from weather events.

  8. Series load induction heating inverter state estimator using Kalman filter

    Directory of Open Access Journals (Sweden)

    Szelitzky T.

    2011-12-01

    Full Text Available LQR and H2 controllers require access to the states of the controlled system. The method based on description function with Fourier series results in a model with immeasurable states. For this reason, we proposed a Kalman filter based state estimator, which not only filters the input signals, but also computes the unobservable states of the system. The algorithm of the filter was implemented in LabVIEW v8.6 and tested on recorded data obtained from a 10-40 kHz series load frequency controlled induction heating inverter.

  9. Two-dimensional vibrational-electronic spectroscopy

    Science.gov (United States)

    Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira

    2015-10-01

    Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([FeIII(CN)6]3- dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5FeIICNRuIII(NH3)5]- dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.

  10. Two-dimensional vibrational-electronic spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira, E-mail: mkhalil@uw.edu [Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195 (United States)

    2015-10-21

    Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (ν{sub CN}) and either a ligand-to-metal charge transfer transition ([Fe{sup III}(CN){sub 6}]{sup 3−} dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN){sub 5}Fe{sup II}CNRu{sup III}(NH{sub 3}){sub 5}]{sup −} dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific ν{sub CN} modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a

  11. Two-dimensional Navier-Stokes turbulence in bounded domains

    NARCIS (Netherlands)

    Clercx, H.J.H.; van Heijst, G.J.F.

    In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the

  12. Two-dimensional Navier-Stokes turbulence in bounded domains

    NARCIS (Netherlands)

    Clercx, H.J.H.; Heijst, van G.J.F.

    2009-01-01

    In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the

  13. Piezoelectricity in Two-Dimensional Materials

    KAUST Repository

    Wu, Tao; Zhang, Hua

    2015-01-01

    Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards

  14. Fast Kalman-like filtering for large-dimensional linear and Gaussian state-space models

    KAUST Repository

    Ait-El-Fquih, Boujemaa; Hoteit, Ibrahim

    2015-01-01

    This paper considers the filtering problem for linear and Gaussian state-space models with large dimensions, a setup in which the optimal Kalman Filter (KF) might not be applicable owing to the excessive cost of manipulating huge covariance matrices. Among the most popular alternatives that enable cheaper and reasonable computation is the Ensemble KF (EnKF), a Monte Carlo-based approximation. In this paper, we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic-based algorithms based on the Variational Bayesian (VB) approach. More specifically, we derive two iterative KF-like algorithms that differ in the way they operate between two successive filtering estimates; one involves a smoothing estimate and the other involves a prediction estimate. Despite its iterative nature, the prediction-based algorithm provides a computational cost that is, on the one hand, independent of the number of iterations in the limit of very large state dimensions, and on the other hand, always much smaller than the cost of the EnKF. The cost of the smoothing-based algorithm depends on the number of iterations that may, in some situations, make this algorithm slower than the EnKF. The performances of the proposed filters are studied and compared to those of the KF and EnKF through a numerical example.

  15. Fast Kalman-like filtering for large-dimensional linear and Gaussian state-space models

    KAUST Repository

    Ait-El-Fquih, Boujemaa

    2015-08-13

    This paper considers the filtering problem for linear and Gaussian state-space models with large dimensions, a setup in which the optimal Kalman Filter (KF) might not be applicable owing to the excessive cost of manipulating huge covariance matrices. Among the most popular alternatives that enable cheaper and reasonable computation is the Ensemble KF (EnKF), a Monte Carlo-based approximation. In this paper, we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic-based algorithms based on the Variational Bayesian (VB) approach. More specifically, we derive two iterative KF-like algorithms that differ in the way they operate between two successive filtering estimates; one involves a smoothing estimate and the other involves a prediction estimate. Despite its iterative nature, the prediction-based algorithm provides a computational cost that is, on the one hand, independent of the number of iterations in the limit of very large state dimensions, and on the other hand, always much smaller than the cost of the EnKF. The cost of the smoothing-based algorithm depends on the number of iterations that may, in some situations, make this algorithm slower than the EnKF. The performances of the proposed filters are studied and compared to those of the KF and EnKF through a numerical example.

  16. Fourier series

    CERN Document Server

    Tolstov, Georgi P

    1962-01-01

    Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie

  17. Development of Two-Dimensional NMR

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 11. Development of Two-Dimensional NMR: Strucure Determination of Biomolecules in Solution. Anil Kumar. General Article Volume 20 Issue 11 November 2015 pp 995-1002 ...

  18. Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.

    Science.gov (United States)

    Volkov, V V; Han, M G; Zhu, Y

    2013-11-01

    We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. Published by Elsevier B.V.

  19. ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES

    OpenAIRE

    Nikola Stefanović

    2007-01-01

    In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic ...

  20. Infrared magneto-spectroscopy of two-dimensional and three-dimensional massless fermions: A comparison

    Energy Technology Data Exchange (ETDEWEB)

    Orlita, M., E-mail: milan.orlita@lncmi.cnrs.fr [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2 (Czech Republic); Faugeras, C.; Barra, A.-L.; Martinez, G.; Potemski, M. [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Basko, D. M. [LPMMC UMR 5493, Université Grenoble 1/CNRS, B.P. 166, 38042 Grenoble (France); Zholudev, M. S. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Teppe, F.; Knap, W. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Gavrilenko, V. I. [Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Mikhailov, N. N.; Dvoretskii, S. A. [A.V. Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090 (Russian Federation); Neugebauer, P. [Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart (Germany); Berger, C. [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Institut Néel/CNRS-UJF BP 166, F-38042 Grenoble Cedex 9 (France); Heer, W. A. de [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)

    2015-03-21

    Here, we report on a magneto-optical study of two distinct systems hosting massless fermions—two-dimensional graphene and three-dimensional HgCdTe tuned to the zero band gap condition at the point of the semiconductor-to-semimetal topological transition. Both materials exhibit, in the quantum regime, a fairly rich magneto-optical response, which is composed from a series of intra- and interband inter-Landau level resonances with for massless fermions typical √(B) dependence. The impact of the system's dimensionality and of the strength of the spin-orbit interaction on the optical response is also discussed.

  1. One-dimensional versus two-dimensional electronic states in vicinal surfaces

    International Nuclear Information System (INIS)

    Ortega, J E; Ruiz-Oses, M; Cordon, J; Mugarza, A; Kuntze, J; Schiller, F

    2005-01-01

    Vicinal surfaces with periodic arrays of steps are among the simplest lateral nanostructures. In particular, noble metal surfaces vicinal to the (1 1 1) plane are excellent test systems to explore the basic electronic properties in one-dimensional superlattices by means of angular photoemission. These surfaces are characterized by strong emissions from free-electron-like surface states that scatter at step edges. Thereby, the two-dimensional surface state displays superlattice band folding and, depending on the step lattice constant d, it splits into one-dimensional quantum well levels. Here we use high-resolution, angle-resolved photoemission to analyse surface states in a variety of samples, in trying to illustrate the changes in surface state bands as a function of d

  2. Analysis of multidimensional difference-of-Gaussians filters in terms of directly observable parameters.

    Science.gov (United States)

    Cope, Davis; Blakeslee, Barbara; McCourt, Mark E

    2013-05-01

    The difference-of-Gaussians (DOG) filter is a widely used model for the receptive field of neurons in the retina and lateral geniculate nucleus (LGN) and is a potential model in general for responses modulated by an excitatory center with an inhibitory surrounding region. A DOG filter is defined by three standard parameters: the center and surround sigmas (which define the variance of the radially symmetric Gaussians) and the balance (which defines the linear combination of the two Gaussians). These parameters are not directly observable and are typically determined by nonlinear parameter estimation methods applied to the frequency response function. DOG filters show both low-pass (optimal response at zero frequency) and bandpass (optimal response at a nonzero frequency) behavior. This paper reformulates the DOG filter in terms of a directly observable parameter, the zero-crossing radius, and two new (but not directly observable) parameters. In the two-dimensional parameter space, the exact region corresponding to bandpass behavior is determined. A detailed description of the frequency response characteristics of the DOG filter is obtained. It is also found that the directly observable optimal frequency and optimal gain (the ratio of the response at optimal frequency to the response at zero frequency) provide an alternate coordinate system for the bandpass region. Altogether, the DOG filter and its three standard implicit parameters can be determined by three directly observable values. The two-dimensional bandpass region is a potential tool for the analysis of populations of DOG filters (for example, populations of neurons in the retina or LGN), because the clustering of points in this parameter space may indicate an underlying organizational principle. This paper concentrates on circular Gaussians, but the results generalize to multidimensional radially symmetric Gaussians and are given as an appendix.

  3. Densis. Densimetric representation of two-dimensional matrices

    International Nuclear Information System (INIS)

    Los Arcos Merino, J.M.

    1978-01-01

    Densis is a Fortran V program which allows off-line control of a Calcomp digital plotter, to represent a two-dimensional matrix of numerical elements in the form of a variable shading intensity map in two colours. Each matrix element is associated to a square of a grid which is traced over by lines whose number is a function of the element value according to a selected scale. Program features, subroutine structure and running instructions, are described. Some typical results, for gamma-gamma coincidence experimental data and a sampled two-dimensional function, are indicated. (author)

  4. Two-dimensional receptive-field organization in striate cortical neurons of the cat.

    Science.gov (United States)

    Sun, M; Bonds, A B

    1994-01-01

    The two-dimensional organization of receptive fields (RFs) of 44 cells in the cat visual cortex and four cells from the cat LGN was measured by stimulation with either dots or bars of light. The light bars were presented in different positions and orientations centered on the RFs. The RFs found were arbitrarily divided into four general types: Punctate, resembling DOG filters (11%); those resembling Gabor filters (9%); elongate (36%); and multipeaked-type (44%). Elongate RFs, usually found in simple cells, could show more than one excitatory band or bifurcation of excitatory regions. Although regions inhibitory to a given stimulus transition (e.g. ON) often coincided with regions excitatory to the opposite transition (e.g. OFF), this was by no means the rule. Measurements were highly repeatable and stable over periods of at least 1 h. A comparison between measurements made with dots and with bars showed reasonable matches in about 40% of the cases. In general, bar-based measurements revealed larger RFs with more structure, especially with respect to inhibitory regions. Inactivation of lower cortical layers (V-VI) by local GABA injection was found to reduce sharpness of detail and to increase both receptive-field size and noise in upper layer cells, suggesting vertically organized RF mechanisms. Across the population, some cells bore close resemblance to theoretically proposed filters, while others had a complexity that was clearly not generalizable, to the extent that they seemed more suited to detection of specific structures. We would speculate that the broadly varying forms of cat cortical receptive fields result from developmental processes akin to those that form ocular-dominance columns, but on a smaller scale.

  5. Analysis of Maneuvering Targets with Complex Motions by Two-Dimensional Product Modified Lv's Distribution for Quadratic Frequency Modulation Signals.

    Science.gov (United States)

    Jing, Fulong; Jiao, Shuhong; Hou, Changbo; Si, Weijian; Wang, Yu

    2017-06-21

    For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed-referred to as the Two-Dimensional product modified Lv's distribution (2D-PMLVD)-for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.

  6. Dynamics of a bilayer membrane coupled to a two-dimensional cytoskeleton: Scale transfers of membrane deformations

    Science.gov (United States)

    Okamoto, Ryuichi; Komura, Shigeyuki; Fournier, Jean-Baptiste

    2017-07-01

    We theoretically investigate the dynamics of a floating lipid bilayer membrane coupled with a two-dimensional cytoskeleton network, taking into account explicitly the intermonolayer friction, the discrete lattice structure of the cytoskeleton, and its prestress. The lattice structure breaks lateral continuous translational symmetry and couples Fourier modes with different wave vectors. It is shown that within a short time interval a long-wavelength deformation excites a collection of modes with wavelengths shorter than the lattice spacing. These modes relax slowly with a common renormalized rate originating from the long-wavelength mode. As a result, and because of the prestress, the slowest relaxation is governed by the intermonolayer friction. Conversely, and most interestingly, forces applied at the scale of the cytoskeleton for a sufficiently long time can cooperatively excite large-scale modes.

  7. Resonance fluorescence based two- and three-dimensional atom localization

    Science.gov (United States)

    Wahab, Abdul; Rahmatullah; Qamar, Sajid

    2016-06-01

    Two- and three-dimensional atom localization in a two-level atom-field system via resonance fluorescence is suggested. For the two-dimensional localization, the atom interacts with two orthogonal standing-wave fields, whereas for the three-dimensional atom localization, the atom interacts with three orthogonal standing-wave fields. The effect of the detuning and phase shifts associated with the corresponding standing-wave fields is investigated. A precision enhancement in position measurement of the single atom can be noticed via the control of the detuning and phase shifts.

  8. Toward two-dimensional search engines

    International Nuclear Information System (INIS)

    Ermann, L; Shepelyansky, D L; Chepelianskii, A D

    2012-01-01

    We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank–CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed. (paper)

  9. Subjective figure reversal in two- and three-dimensional perceptual space.

    Science.gov (United States)

    Radilová, J; Radil-Weiss, T

    1984-08-01

    A permanently illuminated pattern of Mach's truncated pyramid can be perceived according to the experimental instruction given, either as a three-dimensional reversible figure with spontaneously changing convex and concave interpretation (in one experiment), or as a two-dimensional reversible figure-ground pattern (in another experiment). The reversal rate was about twice as slow, without the subjects being aware of it, if it was perceived as a three-dimensional figure compared to the situation when it was perceived as two-dimensional. It may be hypothetized that in the three-dimensional case, the process of perception requires more sequential steps than in the two-dimensional one.

  10. Self-Fourier functions and coherent laser combination

    International Nuclear Information System (INIS)

    Corcoran, C J; Pasch, K A

    2004-01-01

    The Gaussian and Comb functions are generally quoted as being the two basic functions that are their own Fourier transforms. In 1991, Caola presented a recipe for generating functions that are their own Fourier transforms by symmetrizing any transformable function and then adding its own Fourier transform to it. In this letter, we present a new method for generating a set of functions that are exactly their own Fourier transforms, and which have direct application to laser cavity design for a wide variety of applications. The generated set includes the Gaussian and Comb functions as special cases and forms a continuous bridge of functions between them. The new generating method uses the Gaussian and Comb functions as bases and does not rely on the Fourier operator itself. This self-Fourier function promises to be particularly useful in high-power laser design through coherent laser beam combination. Although these results are presented in a single dimension as with a linear array, the results are equally valid in two dimensions. (letter to the editor)

  11. Two multi-dimensional uncertainty relations

    International Nuclear Information System (INIS)

    Skala, L; Kapsa, V

    2008-01-01

    Two multi-dimensional uncertainty relations, one related to the probability density and the other one related to the probability density current, are derived and discussed. Both relations are stronger than the usual uncertainty relations for the coordinates and momentum

  12. High-Resolution Two-Dimensional Optical Spectroscopy of Electron Spins

    Directory of Open Access Journals (Sweden)

    M. Salewski

    2017-08-01

    Full Text Available Multidimensional coherent optical spectroscopy is one of the most powerful tools for investigating complex quantum mechanical systems. While it was conceived decades ago in magnetic resonance spectroscopy using microwaves and radio waves, it has recently been extended into the visible and UV spectral range. However, resolving MHz energy splittings with ultrashort laser pulses still remains a challenge. Here, we analyze two-dimensional Fourier spectra for resonant optical excitation of resident electrons to localized trions or donor-bound excitons in semiconductor nanostructures subject to a transverse magnetic field. Particular attention is devoted to Raman coherence spectra, which allow one to accurately evaluate tiny splittings of the electron ground state and to determine the relaxation times in the electron spin ensemble. A stimulated steplike Raman process induced by a sequence of two laser pulses creates a coherent superposition of the ground-state doublet which can be retrieved only optically because of selective excitation of the same subensemble with a third pulse. This provides the unique opportunity to distinguish between different complexes that are closely spaced in energy in an ensemble. The related experimental demonstration is based on photon-echo measurements in an n-type CdTe/(Cd,MgTe quantum-well structure detected by a heterodyne technique. The difference in the sub-μeV range between the Zeeman splittings of donor-bound electrons and electrons localized at potential fluctuations can be resolved even though the homogeneous linewidth of the optical transitions is larger by 2 orders of magnitude.

  13. Mechanical exfoliation of two-dimensional materials

    Science.gov (United States)

    Gao, Enlai; Lin, Shao-Zhen; Qin, Zhao; Buehler, Markus J.; Feng, Xi-Qiao; Xu, Zhiping

    2018-06-01

    Two-dimensional materials such as graphene and transition metal dichalcogenides have been identified and drawn much attention over the last few years for their unique structural and electronic properties. However, their rise begins only after these materials are successfully isolated from their layered assemblies or adhesive substrates into individual monolayers. Mechanical exfoliation and transfer are the most successful techniques to obtain high-quality single- or few-layer nanocrystals from their native multi-layer structures or their substrate for growth, which involves interfacial peeling and intralayer tearing processes that are controlled by material properties, geometry and the kinetics of exfoliation. This procedure is rationalized in this work through theoretical analysis and atomistic simulations. We propose a criterion to assess the feasibility for the exfoliation of two-dimensional sheets from an adhesive substrate without fracturing itself, and explore the effects of material and interface properties, as well as the geometrical, kinetic factors on the peeling behaviors and the torn morphology. This multi-scale approach elucidates the microscopic mechanism of the mechanical processes, offering predictive models and tools for the design of experimental procedures to obtain single- or few-layer two-dimensional materials and structures.

  14. A three-dimensional Dirichlet-to-Neumann operator for water waves over topography

    Science.gov (United States)

    Andrade, D.; Nachbin, A.

    2018-06-01

    Surface water waves are considered propagating over highly variable non-smooth topographies. For this three dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modeling and evolution to the two dimensional free surface. The corresponding Fourier-type operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care and a Galerkin method is provided accordingly. One dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large amplitude, rapidly varying topography. An alternative, conformal mapping based, method is used for benchmarking. A two dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three dimensional DtN operator.

  15. Event-triggered Kalman-consensus filter for two-target tracking sensor networks.

    Science.gov (United States)

    Su, Housheng; Li, Zhenghao; Ye, Yanyan

    2017-11-01

    This paper is concerned with the problem of event-triggered Kalman-consensus filter for two-target tracking sensor networks. According to the event-triggered protocol and the mean-square analysis, a suboptimal Kalman gain matrix is derived and a suboptimal event-triggered distributed filter is obtained. Based on the Kalman-consensus filter protocol, all sensors which only depend on its neighbors' information can track their corresponding targets. Furthermore, utilizing Lyapunov method and matrix theory, some sufficient conditions are presented for ensuring the stability of the system. Finally, a simulation example is presented to verify the effectiveness of the proposed event-triggered protocol. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  16. Defect of focus in two-line resolution with Hanning amplitude filters

    Science.gov (United States)

    Karunasagar, D.; Bhikshamaiah, G.; Keshavulu Goud, M.; Lacha Goud, S.

    In the presence of defocusing the modified Sparrow limits of resolution for two-line objects have been investigated for a diffraction-limited coherent optical system apodized by generalized Hanning amplitude filters. These limits have been studied as a function of different parameters such as intensity ratio, the order of the filter for various amounts of apodization parameter. Results reveal that in some situations the defocusing is effective in enhancing the resolution of an optical system.

  17. Normal-Gamma-Bernoulli Peak Detection for Analysis of Comprehensive Two-Dimensional Gas Chromatography Mass Spectrometry Data.

    Science.gov (United States)

    Kim, Seongho; Jang, Hyejeong; Koo, Imhoi; Lee, Joohyoung; Zhang, Xiang

    2017-01-01

    Compared to other analytical platforms, comprehensive two-dimensional gas chromatography coupled with mass spectrometry (GC×GC-MS) has much increased separation power for analysis of complex samples and thus is increasingly used in metabolomics for biomarker discovery. However, accurate peak detection remains a bottleneck for wide applications of GC×GC-MS. Therefore, the normal-exponential-Bernoulli (NEB) model is generalized by gamma distribution and a new peak detection algorithm using the normal-gamma-Bernoulli (NGB) model is developed. Unlike the NEB model, the NGB model has no closed-form analytical solution, hampering its practical use in peak detection. To circumvent this difficulty, three numerical approaches, which are fast Fourier transform (FFT), the first-order and the second-order delta methods (D1 and D2), are introduced. The applications to simulated data and two real GC×GC-MS data sets show that the NGB-D1 method performs the best in terms of both computational expense and peak detection performance.

  18. A pseudospectral matrix method for time-dependent tensor fields on a spherical shell

    International Nuclear Information System (INIS)

    Brügmann, Bernd

    2013-01-01

    We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the double Fourier method, we employ a filter to address time-step limitations and certain stability issues. We find that a tensor filter based on spin-weighted spherical harmonics is successful, while two simplified, non-spin-weighted filters do not lead to stable evolutions. The derivatives and the filter are implemented by matrix multiplication for efficiency. A key technical point is the construction of a matrix multiplication method for the spin-weighted spherical harmonic filter. As example for the efficient parallelization of the double Fourier, spin-weighted filter method we discuss an implementation on a GPU, which achieves a speed-up of up to a factor of 20 compared to a single core CPU implementation

  19. Asymptotics for Two-dimensional Atoms

    DEFF Research Database (Denmark)

    Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip

    2012-01-01

    We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....

  20. Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨ θ⟩ directly from ⟨ θ2D⟩ by Fourier analysis.

    Science.gov (United States)

    Søndergaard, Anders Aspegren; Shepperson, Benjamin; Stapelfeldt, Henrik

    2017-07-07

    We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos 2 θ⟩, directly from its two-dimensional counterpart, ⟨cos 2 θ 2D ⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos 2 θ 2D ⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos 2 θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos 2 θ 2D ⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos 2 θ⟩ is obtained and, finally, ⟨cos 2 θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos 2 θ⟩ trace from a measured ⟨cos 2 θ 2D ⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos 2 θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I 2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos 2 θ 2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos 2 θ 2D ⟩ and ⟨cos 2 θ⟩ in general.