Two-dimensional fourier transform spectrometer
Energy Technology Data Exchange (ETDEWEB)
DeFlores, Lauren; Tokmakoff, Andrei
2016-10-25
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.
Two-dimensional fourier transform spectrometer
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.
Optimal Padding for the Two-Dimensional Fast Fourier Transform
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
Two-dimensional Fourier transform ESR correlation spectroscopy
Gorcester, Jeff; Freed, Jack H.
1988-04-01
We describe our pulsed two-dimensional Fourier transform ESR experiment and demonstrate its applicabilty for the double resonance of motionally narrowed nitroxides. Multiple pulse irradiation of the entire nitroxide spectrum enables the correlation of two precessional periods, allowing observation of cross correlations between hyperfine lines introduced by magnetization transfer in the case of a three-pulse experiment (2D ELDOR), or coherence transfer in the case of a two-pulse experiment (COSY). Cross correlations are revealed by the presence of cross peaks which connect the autocorrelation lines appearing along the diagonal ω1=ω2. The amplitudes of these cross peaks are determined by the rates of magnetization transfer in the 2D ELDOR experiment. The density operator theory for the experiment is outlined and applied to the determination of Heisenberg exchange (HE) rates in 2,2,6,6-tetramethyl-4-piperidone-N-oxyl-d15 (PD-tempone) dissolved in toluene-d8. The quantitative accuracy of this experiment is established by comparison with the HE rate measured from the dependence of the spin echo T2 on nitroxide concentration.
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.
Sun, Zhiwei; Zhi, Ya'nan; Liu, Liren; Sun, Jianfeng; Zhou, Yu; Hou, Peipei
2013-09-01
The synthetic aperture imaging ladar (SAIL) systems typically generate large amounts of data difficult to compress with digital method. This paper presents an optical SAIL processor based on compensation of quadratic phase of echo in azimuth direction and two dimensional Fourier transform. The optical processor mainly consists of one phase-only liquid crystal spatial modulator(LCSLM) to load the phase data of target echo and one cylindrical lens to compensate the quadratic phase and one spherical lens to fulfill the task of two dimensional Fourier transform. We show the imaging processing result of practical target echo obtained by a synthetic aperture imaging ladar demonstrator. The optical processor is compact and lightweight and could provide inherent parallel and the speed-of-light computing capability, it has a promising application future especially in onboard and satellite borne SAIL systems.
Ioup, G. E.; Ioup, J. W.
1985-01-01
Appendix 4 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer discusses coordinate axes, location of origin, and redundancy for the one- and two-dimensional Fourier transform for complex and real data.
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.
Anzai, Hiroshi; Joshi, Neeraj Kumar; Fuyuki, Masanori; Wada, Akihide
2015-01-01
A Fourier transform two-dimensional fluorescence excitation spectrometer (FT-2DFES) was developed based on the multiplex technique using a tandem Fabry-Pérot interferometer (tandem FPI). In addition to the advantage of the multiplex technique, the main advantage of the tandem FPI is applicable to the modulation of transition with a large absorption bandwidth (larger than 100 nm) and is thus applicable to the modulation of the excitation of molecules in the condensed phase. As a demonstration of the effectiveness of FT-2DFES, we succeeded in separately observing the fluorescence excitation peaks from a mixed methanol solution of laser dyes (coumarin 480, rhodamine 6G, DCM (4-dicyanomethylene-2-methyl-6-(p-(dimethylamino)styryl)-4H-pyran), and LDS750). Furthermore, the energy transfer from rhodamine 6G to LDS750 was observed.
Davis, Benjamin L; 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.
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.
National Research Council Canada - National Science Library
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
2015-01-01
...) 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...
Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance
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.
Two-Dimensional Fourier Transform Electronic Spectroscopy of Peridinin and Peridinin Analogs
Khosravi, Soroush; Bishop, Michael; Obaid, Razib; Whitelock, Hope; Carroll, Ann Marie; Lafountain, Amy; Frank, Harry; Beck, Warren; Gibson, George; Berrah, Nora
2016-05-01
The peridinin chlorophyll- a protein (PCP) is a light harvesting complex in dinoflagellates that exhibits a carotenoid-to-chlorophyll (Chl) a excitation energy transfer (EET) efficiency of 85-95%. Unlike most light harvesting complexes, where the number of carotenoids is less than Chl, each subunit of PCP contains eight tightly-packed peridinins surrounding two Chl a molecules. The unusual solvent polarity dependence of the lowest excited S1 state of peridinin suggests the presence of an intramolecular charge-transfer (ICT) state. The nature of the ICT state, its coupling to the S1 of peridinin, and whether it enables the high EET efficiency is still unclear. Two-dimensional electronic Fourier transform spectroscopy (2DES) is a powerful method capable of examining these issues. The present work examines the ICT state of peridinin and peridinin analogs that have diminished ICT character. 2DES data adding new insight into the spectral signatures and nature of the ICT state in peridinin will be presented. Funded by the DoE-BES, Grant No. DE-SC0012376.
Generazio, E. R.
1988-01-01
Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain-size distribution function from which the mean grain shape, size, and orientation can be obtained.
Generazio, E. R.
1986-01-01
Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain size distribution function from which the mean grain shape, size, and orientation can be obtained.
Multifrequency Two-Dimensional Fourier Transform ESR: An X/Ku Band Spectrometer
Borbat, Petr P.; Crepeau, Richard H.; Freed, Jack H.
1997-08-01
A two-dimensional Fourier Transform ESR (2D FT ESR) spectrometer operating at 9.25 and 17.35 GHz is described. The Ku-band bridge uses an efficient heterodyne technique wherein 9.25 GHz is the intermediate frequency. At Ku-band the sensitivity is increased by almost an order of magnitude. One may routinely collect a full 2D ELDOR spectrum in less than 20 min for a sample containing 0.5-5 nmol of nitroxide spin-probe in the slow-motional regime. Broad spectral coverage at Ku-band is obtained by use of a bridged loop-gap resonator (BLGR) and of a dielectric ring resonator (DR). It is shown that an even more uniform spectral excitation is obtained by using shorter microwave pulses of about 3 ns duration. The dead-time at Ku-band is just 30-40 ns, yielding an improved SNR in 2D ELDOR spectra of nitroxide spin-probes withT2as short as 20-30 ns. A comparison of 2D ELDOR spectra obtained at 9.25 and 17.35 GHz for spin-labeled phospholipid probes (16PC) in 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG) membrane vesicles showed that both spectra could be satisfactorily simulated using the same set of model parameters even though they are markedly different in appearance. The improved sensitivity and shorter dead-time at Ku-band made it possible to obtain orientation-dependent 2D ELDOR spectra of the Cholestane (CSL) spin-probe in macroscopically aligned lipid bilayers of egg yolk PC using samples containing only 1 mg of lipid and just 5 nmol of spin-probe.
Two-dimensional Fourier transform ESR in the slow-motional and rigid limits: 2D-ELDOR
Patyal, Baldev R.; Crepeau, Richard H.; Gamliel, Dan; Freed, Jack H.
1990-12-01
The two-dimensional Fourier transform ESP techniques of stimulated SECSY and 2D-ELDOR are shown to be powerful methods for the study of slow motions for nitroxides. Stimulated SECSY provides magnetization transfer rates, whereas 2D-ELDOR displays how the rotational motions spread the spins out from their initial spectral positions to new spectral positions, as a function of mixing time. The role of nuclear modulation in studies of structure and dynamics is also considered.
Theory of two-dimensional Fourier transform electron spin resonance for ordered and viscous fluids
Lee, Sanghyuk; Budil, David E.; Freed, Jack H.
1994-10-01
A comprehensive theory for interpreting two-dimensional Fourier transform (2D-FT) electron spin resonance (ESR) experiments that is based on the stochastic Liouville equation is presented. It encompasses the full range of motional rates from fast through very slow motions, and it also provides for microscopic as well as macroscopic molecular ordering. In these respects it is as sophisticated in its treatment of molecular dynamics as the theory currently employed for analyzing cw ESR spectra. The general properties of the pulse propagator superoperator, which describes the microwave pulses in Liouville space, are analyzed in terms of the coherence transfer pathways appropriate for COSY (correlation spectroscopy), SECSY (spin-echo correlation spectroscopy), and 2D-ELDOR (electron-electron double resonance) sequences wherein either the free-induction decay (FID) or echo decay is sampled. Important distinctions are made among the sources of inhomogeneous broadening, which include (a) incomplete spectral averaging in the slow-motional regime, (b) unresolved superhyperfine structure and related sources, and (c) microscopic molecular ordering but macroscopic disorder (MOMD). The differing effects these sources of inhomogeneous broadening have on the two mirror image coherence pathways observed in the dual quadrature 2D experiments, as well as on the auto vs crosspeaks of 2D-ELDOR, is described. The theory is applied to simulate experiments of nitroxide spin labels in complex fluids such as membrane vesicles, where the MOMD model applies and these distinctions are particularly relevant, in order to extract dynamic and ordering parameters. The recovery of homogeneous linewidths from FID-based COSY experiments on complex fluids with significant inhomogeneous broadening is also described. The theory is applied to the ultraslow motional regime, and a simple method is developed to determine rotational rates from the broadening of the autopeaks of the 2D-ELDOR spectra as a
van Agthoven, Maria A; Delsuc, Marc-André; Bodenhausen, Geoffrey; Rolando, Christian
2013-01-01
Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry (MS) achieves high resolution and mass accuracy, allowing the identification of the raw chemical formulae of ions in complex samples. Using ion isolation and fragmentation (MS/MS), we can obtain more structural information, but MS/MS is time- and sample-consuming because each ion must be isolated before fragmentation. In 1987, Pfändler et al. proposed an experiment for 2D FT-ICR MS in order to fragment ions without isolating them and to visualize the fragmentations of complex samples in a single 2D mass spectrum, like 2D NMR spectroscopy. Because of limitations of electronics and computers, few studies have been conducted with this technique. The improvement of modern computers and the use of digital electronics for FT-ICR hardware now make it possible to acquire 2D mass spectra over a broad mass range. The original experiments used in-cell collision-induced dissociation, which caused a loss of resolution. Gas-free fragmentation modes such as infrared multiphoton dissociation and electron capture dissociation allow one to measure high-resolution 2D mass spectra. Consequently, there is renewed interest to develop 2D FT-ICR MS into an efficient analytical method. Improvements introduced in 2D NMR spectroscopy can also be transposed to 2D FT-ICR MS. We describe the history of 2D FT-ICR MS, introduce recent improvements, and present analytical applications to map the fragmentation of peptides. Finally, we provide a glossary which defines a few keywords for the 2D FT-ICR MS field.
Huang, Anmin; Zhou, Qun; Liu, Junliang; Fei, Benhua; Sun, Suqin
2008-07-01
Dalbergia odorifera T. Chen, Pterocarpus santalinus L.F. and Pterocarpus soyauxii are three kinds of the most valuable wood species, which are hard to distinguish. In this paper, differentiation of D. odorifera, P. santalinus and P. soyauxii was carried out by using Fourier transform infrared spectroscopy (FT-IR), second derivative IR spectra and two-dimensional correlation infrared (2D-IR) spectroscopy. The three woods have their characteristic peaks in conventional IR spectra. For example, D. odorifera has obvious absorption peaks at 1640 and 1612 cm -1; P. santalinus has only one peak at 1614 cm -1; and P. soyauxii has one peak at 1619 cm -1 and one shoulder peak at 1597 cm -1. To enhance spectrum resolution and amplify the differences between the IR spectra of different woods, the second derivative technology was adopted to examine the three wood samples. More differences could be observed in the region of 800-1700 cm -1. Then, the thermal perturbation is applied to distinguish different wood samples in an easier way, because of the spectral resolution being enhanced by the 2D correlation spectroscopy. In the region of 1300-1800 cm -1, D. odorifera has five auto-peaks at 1518, 1575, 1594, 1620 and 1667 cm -1; P. santalinus has four auto-peaks at 1469, 1518, 1627 and 1639 cm -1 and P. soyauxii has only two auto-peaks at 1627 and 1639 cm -1. It is proved that the 2D correlation IR spectroscopy can be a new method to distinguish D. odorifera, P. santalinus and P. soyauxii.
Su, Yonggang; Tang, Chen; Li, Biyuan; Chen, Xia; Xu, Wenjun; Cai, Yuanxue
2017-01-20
We propose an optical color image encryption system based on the single-lens Fourier transform, the Fresnel transform, and the chaotic random phase masks (CRPMs). The proposed encryption system contains only one optical lens, which makes it more efficient and concise to implement. The introduction of the Fresnel transform makes the first phase mask of the proposed system also act as the main secret key when the input image is a non-negative amplitude-only map. The two CRPMs generated by dual two-dimensional chaotic maps can provide more security to the proposed system. In the proposed system, the key management is more convenient and the transmission volume is reduced greatly. In addition, the secret keys can be updated conveniently in each encryption process to invalidate the chosen plaintext attack and the known plaintext attack. Numerical simulation results have demonstrated the feasibility and security of the proposed encryption system.
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
Energy Technology Data Exchange (ETDEWEB)
Vilardy, Juan M; Giacometto, F; Torres, C O; Mattos, L, E-mail: vilardy.juan@unicesar.edu.co [Laboratorio de Optica e Informatica, Universidad Popular del Cesar, Sede balneario Hurtado, Valledupar, Cesar (Colombia)
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.
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.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper demonstrates the application of step-scan phase modulation Fourier transform infrared photoacoustic spectroscopy(FTIR-PAS) in non-destructively depth profiling of styrene-butadiene-styrene block copolymer/polyethylene terephthalate(SBS/PET) layered materials.The surface thicknesses of three layered samples were determined to be 1.2,4.3 and 9.4μm by using phase difference analysis,overcoming the spatial detection limits of FTIR.Combined with generalized two-dimensional(G2D) FTIR correlation analysis,the spatial origins of peaks in the SBS/PET spectrum are identified with those having overlapping peaks between different layers are resolved.
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.
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.
Guo, Yizhen; Lv, Beiran; Wang, Jingjuan; Liu, Yang; Sun, Suqin; Xiao, Yao; Lu, Lina; Xiang, Li; Yang, Yanfang; Qu, Lei; Meng, Qinghong
2016-01-01
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.
Zumbühl, Stefan; Scherrer, Nadim C; Eggenberger, Urs
2014-01-01
The interpretation of standard Fourier transform infrared spectra (FT-IR) on oil-based paint samples often suffers from interfering bands of the different compounds, namely, binder, oxidative aging products, carboxylates formed during aging, and several pigments and fillers. The distinction of the aging products such as ketone and carboxylic acid functional groups pose the next problem, as these interfere with the triglyceride esters of the oil. A sample preparation and derivatization technique using gaseous sulfur tetrafluoride (SF4), was thus developed with the aim to discriminate overlapping signals and achieve a signal enhancement on superposed compounds. Of particular interest in this context is the signal elimination of the broad carboxylate bands of the typical reaction products developing during the aging processes in oil-based paints, as well as signal interference originating from several typical pigments in this spectral range. Furthermore, it is possible to distinguish the different carbonyl-containing functional groups upon selective alteration. The derivatization treatment can be applied to both microsamples and polished cross sections. It increases the selectivity of the infrared spectroscopy technique in a fundamental manner and permits the identification and two-dimensional (2D) localization of binder components in aged paint samples at the micrometer scale. The combination of SF4 derivatization with high-resolution 2D FT-IR focal plane array (FPA) imaging delivers considerable advances to the study of micro-morphological processes involving organic compounds.
Liu, Xin-hu; Xu, Chang-hua; Sun, Su-qin; Huang, Jian; Zhang, Ke; Li, Guo-yu; Zhu, Yun; Zhou, Qun; Zhang, Zhi-cheng; Wang, Jin-hui
2012-11-01
In this study, six varieties of Danshen from different populations and genuine ("Daodi" in Chinese transliteration) regions were discriminated and identified by a three-step infrared spectroscopy method (Fourier transform-infrared spectroscopy (FT-IR) coupled with second derivative infrared spectroscopy (SD-IR) and two dimensional correlation infrared spectroscopy (2D-IR)). Though only small differences were found among the FT-IR spectra of the six Danshen samples, the positions and intensities of peaks at 3393, 3371, 1613, 1050, and 1036 cm-1 could be considered as the key factors to discriminate them. More significant differences were exhibited in their SD-IR, particularly for the peaks around 1080, 1144, 695, 665, 800, 1610, 1510, 1450, 1117 and 1077 cm-1. The visual 2D-IR spectra provided dynamic chemical structure information of the six Danshen samples with presenting different particular auto-peak clusters, respectively. Moreover, the contents of salvianolic acid B in all samples were measured quantitatively by a validated ultra performance liquid chromatography (UPLC), which was consistent with the FT-IR findings. This study provides a promising method for characteristics and quality control of the complicated and extremely similar herbal medicine like Danshen, which is more cost effective and time saving.
Qu, Lei; Chen, Jian-bo; Zhou, Qun; Zhang, Gui-jun; Sun, Su-qin; Guo, Yi-zhen
2016-11-01
As a kind of expensive perfume and valuable herb, the commercial Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy and two-dimensional (2D) correlation analysis are employed to establish a simple and quick identification method for the authentic and adulterated ALR. In the conventional infrared spectra, the standard ALR has a strong peak at 1658 cm-1 referring to the conjugated carbonyl of resin, while this peak is absent in the adulterated samples. The position, intensity, and shape of the auto-peaks and cross-peaks of the authentic and adulterated ALR are much different in the synchronous 2D correlation spectra with thermal perturbation. In the range of 1700-1500 cm-1, the standard ALR has four obvious auto-peaks, while the strongest one is at 1659 cm-1. The adulterated sample w-1 has three obvious auto-peaks and the strongest one is at 1647 cm-1. The adulterated sample w-2 has three obvious auto-peaks and the strongest one is at 1519 cm-1. The adulterated sample w-3 has four obvious auto-peaks and the strongest one is at 1690 cm-1. The above auto-peaks confirm that the standard ALR contains a certain content of resin compounds, while the three counterfeits contain little or different resins. The results show the potential of FT-IR spectroscopy and 2D correlation analysis in the simple and quick identification of authentic and adulterated ALR.
Theory of two-dimensional transformations
Kanayama, Yutaka J.; Krahn, Gary W.
1998-01-01
The article of record may be found at http://dx.doi.org/10.1109/70.720359 Robotics and Automation, IEEE Transactions on This paper proposes a new "heterogeneous" two-dimensional (2D) transformation group ___ to solve motion analysis/planning problems in robotics. In this theory, we use a 3×1 matrix to represent a transformation as opposed to a 3×3 matrix in the homogeneous formulation. First, this theory is as capable as the homogeneous theory, Because of the minimal size, its implement...
Boriakoff, Valentin
1994-01-01
The goal of this project was the feasibility study of a particular architecture of a digital signal processing machine operating in real time which could do in a pipeline fashion the computation of the fast Fourier transform (FFT) of a time-domain sampled complex digital data stream. The particular architecture makes use of simple identical processors (called inner product processors) in a linear organization called a systolic array. Through computer simulation the new architecture to compute the FFT with systolic arrays was proved to be viable, and computed the FFT correctly and with the predicted particulars of operation. Integrated circuits to compute the operations expected of the vital node of the systolic architecture were proven feasible, and even with a 2 micron VLSI technology can execute the required operations in the required time. Actual construction of the integrated circuits was successful in one variant (fixed point) and unsuccessful in the other (floating point).
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
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 sty
Lei, Yu; Zhou, Qun; Zhang, Yan-ling; Chen, Jian-bo; Sun, Su-qin; Noda, Isao
2010-06-01
Infrared (IR) spectroscopy is used in combination with two-dimensional (2D) correlation IR spectroscopy to conduct rapid non-destructive quantitative research in milk powder without additional separation steps. The experiments conducted in both FT-IR and 2D FT-IR spectra suggest that characteristic spectroscopic features of milk powder containing different carbohydrate can be detected, and then determine the type of carbohydrate. To predict the approximate content of lactose while the carbohydrate is lactose, different amount of crystallized lactose has been added to the reference milk powder. The correlation coefficient could be used to determine the content of crystallized lactose in milk powder. The method provides a rapid and convenient means for assessing the quality of milk powder.
Zhang, Chun-hui; Zhang, Gui-jun; Sun, Su-qin; Tu, Ya
2010-07-01
2D-IR correlation spectroscopy was used to do the research on crude and prepared drug of radix scutellariae and the extracts of them. The results show that the holistic shape of peaks among them are similar in the FTIR spectra. In second derivative spectra, the two absorption peaks: 1,745 and 1,411 cm(-1) of processed products move to the bigger wavenumber direction, while 1,357 cm(-1) of processed products moves to the smaller wavenumber direction; There are conspicuous differences in Two-dimensional infrared correlation spectroscopy among them: Four characteristic peaks are shown between 1,300 and 1,800 cm(-1). The intensity of peak at 1,575 cm(-1) is the strongest. There are three main districts about the autopeaks of sliced scutellariae. Wine-fried scutellariae has two auto-peak districts, in which all the auto-peaks are positively correlated. The FTIR spectra of total glycoside extract of different samples present characteristic peaks at 1,615, 1,585, 1,450 cm(-1) (vibration of phenyl framework) and 1,658 cm(-1) (=C-O ) respectively, therefore, the authors speculated that their mutual component is the compound of phenolic glycoside. The two-dimensional infrared correlation spectra present five automatic peaks (vibration of phenyl framework) in 800-1,800 cm(-1) (1,366, 1,420, 1,508, 1,585, 1,669 cm(-1)). So the authors can conclude that a lot of information can be provided by macro-fingerprint technology of infrared spectroscopy which can evaluate overall quality of radix scutellariae accurately and be used to study the characteristics of relevance of crude and prepared scutellariae.
Xu, Zheng; Li, Haoran; Wang, Congmin; Pan, Haihua; Han, Shijun
2006-06-28
Two-dimensional correlation spectroscopy was used to study the composition-dependent spectral variations of the CH-stretching bands of N,N-dimethylformamide (DMF)-water mixtures with X(DMF) ranging from 0.98 to 0.60. By a detailed correlation analysis of the spectral changes of the CH- and OH-stretching bands, it is found that the intensities of the CH and OH bands change in different ways when the water content is increased. It is also found that two different regions of the water content can be distinguished, in which the intensity changes have different signatures. A tentative explanation for how these phenomena might be related to structural changes in the mixture is proposed. The structural change of DMF induced by the water hydrogen bonded on the carbonyl group is supposed to be the possible origin of the methyl C-H blueshift instead of the direct C-H...O interactions before the hydrophobic hydration takes place.
The convolution theorem for two-dimensional continuous wavelet transform
Institute of Scientific and Technical Information of China (English)
ZHANG CHI
2013-01-01
In this paper , application of two -dimensional continuous wavelet transform to image processes is studied. We first show that the convolution and correlation of two continuous wavelets satisfy the required admissibility and regularity conditions ,and then we derive the convolution and correlation theorem for two-dimensional continuous wavelet transform. Finally, we present numerical example showing the usefulness of applying the convolution theorem for two -dimensional continuous wavelet transform to perform image restoration in the presence of additive noise.
Unger, Miriam; Siesler, Heinz W
2009-12-01
In the present study, the orientation of a poly(3-hydroxybutyrate) (PHB)/poly(epsilon-caprolactone) (PCL) blend was monitored during uniaxial elongation by rheo-optical Fourier transform infrared (FT-IR) spectroscopy and analyzed by generalized two-dimensional correlation spectroscopy (2D-COS). The dichroism of the delta(CH(2)) absorption bands of PHB and PCL was employed to determine the polymer chain orientation in the PHB/PCL blend during the elongation up to 267% strain. From the PHB and PCL specific orientation functions it was derived that the PCL chains orient into the drawing direction while the PHB chains orient predominantly perpendicular to the applied strain. To extract more detailed information about the polymer orientation during uniaxial elongation, 2D-COS analysis was employed for the dichroic difference of the polarization spectra recorded during the drawing process. In the corresponding synchronous and asynchronous 2D correlation plots, absorption bands characteristic of the crystalline and amorphous regions of PHB and PCL were separated. Furthermore, the 2D-COS analysis revealed that during the mechanical treatment the PCL domains orient before the PHB domains.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Sastry, V. S. S.; Polimeno, Antonino; Crepeau, Richard H.; Freed, Jack H.
1996-10-01
Two-dimensional Fourier transform (2D-FT)-electron spin resonance (ESR) studies on the small globular spin probe perdeuterated tempone (PDT) in the liquid crystal solvent 4O,8 (butoxy benzylidene octylaniline) are reported. These experiments, over the temperature range of 95 °C to 24 °C, cover the isotropic (I), nematic (N), smectic A (SA), smectic B (SB), and crystal (C) phases. The 2D-ELDOR (two-dimensional electron-electron double resonance) spectra confirm the anomalously rapid reorientation of PDT, especially in the lower temperature phases. The model of a slowly relaxing local structure (SRLS) leads to generally very good non-linear least squares (NLLS) global fits to the sets of 2D-ELDOR spectra obtained at each temperature. These fits are significantly better than those achieved by the standard model of Brownian reorientation in a macroscopic orienting potential. The SRLS model is able to account for anomalies first observed in an earlier 2D-ELDOR study on PDT in a different liquid crystal in its smectic phases. Although it is instructional to extract the various spectral densities from the COSY (correlation spectroscopy) and 2D-ELDOR spectra, the use of NLLS global fitting to a full set of 2D-ELDOR spectra is shown to be more reliable and convenient for obtaining optimum model parameters, especially in view of possible (incipient) slow motional effects from the SRLS or dynamic cage. The cage potential is found to remain fairly constant at about kBT over the various phases (with only a small drop in the SB phase), but its asymmetry increases with decreasing temperature T. This value is significantly larger than the weak macroscopic orienting potential which increases from 0.1 to 0.3kBT with decreasing T. The cage relaxation rate, given by Rc is about 3×107 s-1 in the I phase, but increases to about 108 s-1 in the SA, SB, and C phases. The rotational diffusion tensor for PDT shows only a small T-independent asymmetry, and its mean rotational diffusion
Fourier transformation for pedestrians
Butz, Tilman
2006-01-01
Meant to serve an "entertaining textbook," this book belongs to a rare genre. It is written for all students and practitioners who deal with Fourier transformation. Fourier series as well as continuous and discrete Fourier transformation are covered, and particular emphasis is placed on window functions. Many illustrations and easy-to-solve exercises make the book especially accessible, and its humorous style will add to the pleasure of learning from it.
Sastry, V. S. S.; Polimeno, Antonino; Crepeau, Richard H.; Freed, Jack H.
1996-10-01
Two-dimensional Fourier transform (2D-FT) electron spin resonance (ESR) studies on the rigid rodlike cholestane (CSL) spin-label in the liquid crystal solvent 4O,8 (butoxy benzylidene octylaniline) are reported. These experiments were performed over a wide temperature range: 96 °C to 25 °C covering the isotropic (I), nematic (N), smectic A (SA), smectic B (SB), and crystal (C) phases. It is shown that 2D-FT-ESR, especially in the form of 2D-ELDOR (two-dimensional electron-electron double resonance) provides greatly enhanced sensitivity to rotational dynamics than previous cw-ESR studies on this and related systems. This sensitivity is enhanced by obtaining a series of 2D-ELDOR spectra as a function of mixing time, Tm, yielding essentially a three-dimensional experiment. Advantage is taken of this sensitivity to study the applicability of the model of a slowly relaxing local structure (SRLS). In this model, a dynamic cage of solvent molecules, which relaxes on a slower time scale than the CSL solute, provides a local orienting potential in addition to that of the macroscopic aligning potential in the liquid crystalline phase. The theory of Polimeno and Freed for SRLS in the ESR slow motional regime is extended by utilizing the theory of Lee et al. to include 2D-FT-ESR experiments, and it serves as the basis for the analysis of the 2D-ELDOR experiments. It is shown that the SRLS model leads to significantly improved non-linear least squares fits to experiment over those obtained with the standard model of Brownian reorientation in a macroscopic aligning potential. This is most evident for the SA phase, and the use of the SRLS model also removes the necessity of fitting with the unreasonably large CSL rotational asymmetries in the smectic phases that are required in both the cw-ESR and 2D-ELDOR fits with the standard model. The cage potential is found to vary from about kBT in the isotropic phase to greater than 2kBT in the N and SA phases, with an abrupt drop to
Fourier and Laplace Transforms
Beerends, R.J.; Morsche, ter H.G.; Berg, van den J.C.
2003-01-01
This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the a
Fourier transform mass spectrometry.
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-07-01
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.
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
Error analysis for satellite gravity field determination based on two-dimensional Fourier methods
Cai, Lin; Hsu, Houtse; Gao, Fang; Zhu, Zhu; Luo, Jun
2012-01-01
The time-wise and space-wise approaches are generally applied to data processing and error analysis for satellite gravimetry missions. But both the approaches, which are based on least-squares collocation, address the whole effect of measurement errors and estimate the resolution of gravity field models mainly from a numerical point of indirect view. Moreover, requirement for higher accuracy and resolution gravity field models could make the computation more difficult, and serious numerical instabilities arise. In order to overcome the problems, this study focuses on constructing a direct relationship between power spectral density of the satellite gravimetry measurements and coefficients of the Earth's gravity potential. Based on two-dimensional Fourier transform, the relationship is analytically concluded. By taking advantage of the analytical expression, it is efficient and distinct for parameter estimation and error analysis of missions. From the relationship and the simulations, it is analytically confir...
Fourier transformation for pedestrians
Butz, Tilman
2015-01-01
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
Fourier transforms principles and applications
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.
Generic Quantum Fourier Transforms
Moore, Cristopher; Russell, A; Moore, Cristopher; Rockmore, Daniel; Russell, Alexander
2003-01-01
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the separation of variables technique that has been so successful in the study of classical Fourier transform computations. Specifically, this framework applies the existence of computable Bratteli diagrams, adapted factorizations, and Gel'fand-Tsetlin bases to offer efficient quantum circuits for the QFT over a wide variety a finite Abelian and non-Abelian groups, including all group families for which efficient QFTs are currently known and many new group families. Moreover, the method gives rise to the first subexponential-size quantum circuits for the QFT over the linear groups GL_k(q), SL_k(q), and the finite groups of Lie type, for any fixed prime power q.
Real Clifford Windowed Fourier Transform
Institute of Scientific and Technical Information of China (English)
Mawardi BAHRI; Sriwulan ADJI; Ji Man ZHAO
2011-01-01
We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation,reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform (WFT) and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Fourier transforms in spectroscopy
Kauppinen, Jyrki
2000-01-01
This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi
Fast Fourier transform telescope
Tegmark, Max; Zaldarriaga, Matias
2009-04-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore’s law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog2N rather than N2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Fourier Transform Spectrometer System
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.
Scarfone, A. M.
2017-08-01
We present a new formulation of Fourier transform in the picture of the κ-algebra derived in the framework of the κ-generalized statistical mechanics. The κ-Fourier transform is obtained from a κ-Fourier series recently introduced by Scarfone (2013). The kernel of this transform, that reduces to the usual exponential phase in the κ → 0 limit, is composed by a κ-deformed phase and a damping factor that gives a wavelet-like behaviour. We show that the κ-Fourier transform is isomorph to the standard Fourier transform through a changing of time and frequency variables. Nevertheless, the new formalism is useful to study, according to Fourier analysis, those functions defined in the realm of the κ-algebra. As a relevant application, we discuss the central limit theorem for the κ-sum of n-iterate statistically independent random variables.
Kuiper, Logan K
2016-01-01
An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.
Wang, Shouyu; Yan, Keding; Xue, Liang
2017-01-01
In order to obtain high contrast images and detailed descriptions of label free samples, quantitative interferometric microscopy combining with phase retrieval is designed to obtain sample phase distributions from fringes. As accuracy and efficiency of recovered phases are affected by phase retrieval methods, thus approaches owning higher precision and faster processing speed are still in demand. Here, two dimensional Hilbert transform based phase retrieval method is adopted in cellular phase imaging, it not only reserves more sample specifics compared to classical fast Fourier transform based method, but also overcomes disadvantages of traditional algorithm according to Hilbert transform which is a one dimensional processing causing phase ambiguities. Both simulations and experiments are provided, proving the proposed phase retrieval approach can acquire quantitative sample phases with high accuracy and fast speed.
Wavelet-fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
Qi, Wei; Ishimaru, Ichiro
2010-02-01
We propose an image-producing Fourier spectroscopic technology that enables two-dimensional spectroscopic images to be obtained within the focusing plane alone. This technology incorporates auto-correlational phase-shift interferometry that uses only object light generated by the bright points that optically make up the object. We are currently involved in studies of non-invasive technologies used to measure blood components such as glucose and lipids, which are measured for use in daily living. Previous studies have investigated non-invasive technologies that measure blood glucose levels by utilizing near-infrared light that permeates the skin well. It has been confirmed that subtle changes in the concentration of a glucose solution, a sample used to measure the glucose level, can be measured by analyzing the spectroscopic characteristics of near-infrared light; however, when applied to a biomembrane, technology such as this is incapable of precisely measuring the glucose level because light diffusion within the skin disturbs the measurement. Our proposed technology enables two-dimensional spectroscopy to a limited depth below the skin covered by the measurement. Specifically, our technology concentrates only on the vascular territory near the skin surface, which is only minimally affected by light diffusion, as discussed previously; the spectroscopic characteristics of this territory are obtained and the glucose level can be measured with good sensitivity. In this paper we propose an image-producing Fourier spectroscopy method that is used as the measuring technology in producing a three-dimensional spectroscopic image.
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.
Institute of Scientific and Technical Information of China (English)
卢明倩; 黄桂媛; 王巧贞; 许超; 黄庶识
2016-01-01
Abtract:[Objective]The aim of this study is to analyze the interaction between the different groups ofβ-carotene in the heating process.[Methods]Two-dimensional correlation spectrosco-py was applied to study the dynamic spectral changes ofβ-carotene from 30℃ to 100℃.[Re-sults]The changes of absorption characteristic peaks ofβ-carotene were inconspicuous in the conventional FTIR spectra and second derivative FTIR spectra during 30℃ to 100℃,which in-dicated that they had no oxidation reation.Two-dimensional correlation analysis showed that the changes of absorption peaks at 968 cm-1 ,1 442 cm-1 ,2 9 6 6 cm-1 and 3 0 1 2 cm-1 were more sen-sitive to temperature.Meanwhile,the order of different groups changes induced by temperature were as follows:the spectral changes of methyl-ene were faster than methyl,the spectral changes of methyl C-H symmetric stretching vibration in low wavenumber were faster than methyl anti-symmetric stretching vibration in high wavenumber,and olefin hydrocarbon symmetric stretching vibration were prior to olefin hydrocarbon anti-symmetric stretching vibration.[Con-clusion]This provides experimental basis for the mechanism of the conformational change ofβ-carotene in heating process.%【目的】了解在升温过程中β-胡萝卜素分子内不同基团之间的相互影响。【方法】采用二维相关红外光谱分析技术,研究β-胡萝卜素在30~100℃变温微扰过程中的动态光谱变化。【结果】β-胡萝卜素分子的吸收特征峰在一维红外光谱和二阶导数谱上变化不明显,表明其没有发生氧化反应。二维相关分析表明,反式共轭烯烃C—H 面外弯曲振动的968 cm-1,烯烃C—H 基团反对称弯曲振动的1442cm-1,甲基C—H 反对称伸缩振动的2966 cm-1和烯烃C—H 的对称伸缩振动的3012 cm-1,这些吸收峰的光谱变化对温度比较敏感。同时在微扰过程中,不同基团变化的先后顺序：亚甲基热运动引起的光谱变化快于
Directory of Open Access Journals (Sweden)
A. Aghili
2011-12-01
Full Text Available In this work,we present new theorems on two-dimensional Laplace transformation. We also develop some applications based on these results. The two-dimensional Laplace transformation is useful in the solution of non-homogeneous partial differential equations. In the last section a boundary value problem is solved by using the double Laplace-Carson transform.
Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography.
Wang, Yimin; Huang, David; Su, Ya; Yao, X Steve
2016-11-14
For phase-related imaging modalities using interferometric techniques, it is important to develop effective method to recover phase information that is mathematically wrapped. In this paper, we propose and demonstrate a two-dimensional (2D) method to achieve effective phase unwrapping in Doppler Fourier-domain (FD) optical coherence tomography (OCT), and recover the discontinuous phase distribution in retinal blood flow successfully for the first time in Doppler OCT studies. The proposed method is based on phase gradient approach in the axial dimension, with phase denoising performed through 2D window moving average in the sampled phase image using complex Doppler OCT data. The 2D unwrapping is carried out to correct phase discontinuities in the wrapped Doppler phase map, and the abrupt phase changes can be identified and corrected accurately. The proposed algorithm is computationally efficient and easy to be implemented.
APPLICATION OF TWO-DIMENSIONAL WAVELET TRANSFORM IN NEAR-SHORE X-BAND RADAR IMAGES
Institute of Scientific and Technical Information of China (English)
FENG Xiang-bo; YAN Yi-xin; ZHANG Wei
2011-01-01
Among existing remote sensing applications, land-based X-band radar is an effective technique to monitor the wave fields,and spatial wave information could be obtained from the radar images.Two-dimensional Fourier Transform (2-D FT) is the common algorithm to derive the spectra of radar images.However, the wave field in the nearshore area is highly non-homogeneous due to wave refraction, shoaling, and other coastal mechanisms.When applied in nearshore radar images, 2-D FT would lead to ambiguity of wave characteristics in wave number domain.In this article, we introduce two-dimensional Wavelet Transform (2-D WT) to capture the non-homogeneity of wave fields from nearshore radar images.The results show that wave number spectra by 2-D WT at six parallel space locations in the given image clearly present the shoaling of nearshore waves.Wave number of the peak wave energy is increasing along the inshore direction, and dominant direction of the spectra changes from South South West (SSW) to West South West (WSW).To verify the results of2-D WT, wave shoaling in radar images is calculated based on dispersion relation.The theoretical calculation results agree with the results of 2-D WT on the whole.The encouraging performance of 2-D WT indicates its strong capability of revealing the non-homogeneity of wave fields in nearshore X-band radar images.
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Static Fourier transform infrared spectrometer.
Schardt, Michael; Murr, Patrik J; Rauscher, Markus S; Tremmel, Anton J; Wiesent, Benjamin R; Koch, Alexander W
2016-04-01
Fourier transform spectroscopy has established itself as the standard method for spectral analysis of infrared light. Here we present a robust and compact novel static Fourier transform spectrometer design without any moving parts. The design is well suited for measurements in the infrared as it works with extended light sources independent of their size. The design is experimentally evaluated in the mid-infrared wavelength region between 7.2 μm and 16 μm. Due to its large etendue, its low internal light loss, and its static design it enables high speed spectral analysis in the mid-infrared.
A More Accurate Fourier Transform
Courtney, Elya
2015-01-01
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals (EI) that define Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric $\\mathrm{CO_2}$ concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT's FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability t...
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…
Novel Micro Fourier Transform Spectrometers
Institute of Scientific and Technical Information of China (English)
KONG Yan-mei; LIANG Jing-qiu; LIANG Zhong-zhu; WANG-Bo; ZHANG Jun
2008-01-01
The miniaturization of spectrometer opens a new application area with real-time and on-site measurements. The Fourier transform spectrometer(FTS) is much attractive considering its particular advantages among the approaches. This paper reviews the current status of micro FTS in worldwide and describes its developments; In addition, analyzed are the key problems in designing and fabricating FTS to be settled during the miniaturization. Finally, a novel model of micro FTS with no moving parts is proposed and analyzed, which may provide new concepts for the design of spectrometers.
Fourier-transform optical microsystems
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
JPL Fourier transform ultraviolet spectrometer
Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.
1994-01-01
The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.
Fourier-Transform Infrared Spectrometer
Schindler, R. A.
1986-01-01
Fourier-transform spectrometer provides approximately hundredfold increase in luminosity at detector plane over that achievable with older instruments of this type. Used to analyze such weak sources as pollutants and other low-concentration substances in atmosphere. Interferometer creates fringe patterns on two distinct arrays of light detectors, which observe different wavelength bands. Objective lens focuses scene on image plane, which contains optical chopper. To make instrument less susceptible to variations in scene under observation, field and detector lenses focus entrance aperture, rather that image, onto detector array.
Fourier Transform Methods. Chapter 4
Kaplan, Simon G.; Quijada, Manuel A.
2015-01-01
This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..
10th International Conference on Progress in Fourier Transform Spectroscopy
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.
Chen, Cao; Chu, Xinzhao
2017-09-01
Waves in the atmosphere and ocean are inherently intermittent, with amplitudes, frequencies, or wavelengths varying in time and space. Most waves exhibit wave packet-like properties, propagate at oblique angles, and are often observed in two-dimensional (2-D) datasets. These features make the wavelet transforms, especially the 2-D wavelet approach, more appealing than the traditional windowed Fourier analysis, because the former allows adaptive time-frequency window width (i.e., automatically narrowing window size at high frequencies and widening at low frequencies), while the latter uses a fixed envelope function. This study establishes the mathematical formalism of modified 1-D and 2-D Morlet wavelet transforms, ensuring that the power of the wavelet transform in the frequency/wavenumber domain is equivalent to the mean power of its counterpart in the time/space domain. Consequently, the modified wavelet transforms eliminate the bias against high-frequency/small-scale waves in the conventional wavelet methods and many existing codes. Based on the modified 2-D Morlet wavelet transform, we put forward a wave recognition methodology that automatically identifies and extracts 2-D quasi-monochromatic wave packets and then derives their wave properties including wave periods, wavelengths, phase speeds, and time/space spans. A step-by-step demonstration of this methodology is given on analyzing the lidar data taken during 28-30 June 2014 at McMurdo, Antarctica. The newly developed wave recognition methodology is then applied to two more lidar observations in May and July 2014, to analyze the recently discovered persistent gravity waves in Antarctica. The decomposed inertia-gravity wave characteristics are consistent with the conclusion in Chen et al. (2016a) that the 3-10 h waves are persistent and dominant, and exhibit lifetimes of multiple days. They have vertical wavelengths of 20-30 km, vertical phase speeds of 0.5-2 m/s, and horizontal wavelengths up to several
Moment-based method for computing the two-dimensional discrete Hartley transform
Dong, Zhifang; Wu, Jiasong; Shu, Huazhong
2009-10-01
In this paper, we present a fast algorithm for computing the two-dimensional (2-D) discrete Hartley transform (DHT). By using kernel transform and Taylor expansion, the 2-D DHT is approximated by a linear sum of 2-D geometric moments. This enables us to use the fast algorithms developed for computing the 2-D moments to efficiently calculate the 2-D DHT. The proposed method achieves a simple computational structure and is suitable to deal with any sequence lengths.
Curvature effects in two-dimensional optical devices inspired by transformation optics
Yuan, Shuhao
2016-11-14
Light transport in curved quasi two-dimensional waveguides is considered theoretically. Within transformation optics and tensor theory, a concise description of curvature effects on transverse electric and magnetic waves is derived. We show that the curvature can induce light focusing and photonic crystal properties, which are confirmed by finite element simulations. Our results indicate that the curvature is an effective parameter for designing quasi two-dimensional optical devices in the fields of micro and nano photonics. Â© 2016 Author(s).
The multiple-parameter fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
LANG Jun; TAO Ran; RAN QiWen; WANG Yue
2008-01-01
The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in frac-tional operator. A new source for the multiplicity of the weight-type fractional Fou-rier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters MN,∈ZM. Therefore a generalized frac-tional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.
The Fourier Transform on Quantum Euclidean Space
Directory of Open Access Journals (Sweden)
Kevin Coulembier
2011-05-01
Full Text Available We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.
Two modified discrete chirp Fourier transform schemes
Institute of Scientific and Technical Information of China (English)
樊平毅; 夏香根
2001-01-01
This paper presents two modified discrete chirp Fourier transform (MDCFT) schemes.Some matched filter properties such as the optimal selection of the transform length, and its relationship to analog chirp-Fourier transform are studied. Compared to the DCFT proposed previously, theoretical and simulation results have shown that the two MDCFTs can further improve the chirp rate resolution of the detected signals.
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
Two-dimensional shape classification using generalized Fourier representation and neural networks
Chodorowski, Artur; Gustavsson, Tomas; Mattsson, Ulf
2000-04-01
A shape-based classification method is developed based upon the Generalized Fourier Representation (GFR). GFR can be regarded as an extension of traditional polar Fourier descriptors, suitable for description of closed objects, both convex and concave, with or without holes. Explicit relations of GFR coefficients to regular moments, moment invariants and affine moment invariants are given in the paper. The dual linear relation between GFR coefficients and regular moments was used to compare shape features derive from GFR descriptors and Hu's moment invariants. the GFR was then applied to a clinical problem within oral medicine and used to represent the contours of the lesions in the oral cavity. The lesions studied were leukoplakia and different forms of lichenoid reactions. Shape features were extracted from GFR coefficients in order to classify potentially cancerous oral lesions. Alternative classifiers were investigated based on a multilayer perceptron with different architectures and extensions. The overall classification accuracy for recognition of potentially cancerous oral lesions when using neural network classifier was 85%, while the classification between leukoplakia and reticular lichenoid reactions gave 96% (5-fold cross-validated) recognition rate.
Fully phase encrypted memory using cascaded extended fractional Fourier transform
Nishchal, Naveen K.; Joseph, Joby; Singh, Kehar
2003-11-01
In this paper, we implement a fully phase encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The fully phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, conjugate of encrypted image. The decrypted phase image is converted into an amplitude image by using phase contrast technique. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the phase image, alleviating the need of alignment in the Fourier plane, thereby making the system rugged.
A Two-Dimensional Cloud Model for Condition Assessment of HVDC Converter Transformers
Directory of Open Access Journals (Sweden)
Linjie Zhao
2012-01-01
Full Text Available Converter transformers are the key and the most important components in high voltage direct current (HVDC power transmission systems. Statistics show that the failure rate of HVDC converter transformers is approximately twice of that of transformers in AC power systems. This paper presents an approach integrated with a two-dimensional cloud model and an entropy-based weight model to evaluate the condition of HVDC converter transformers. The integrated approach can describe the complexity of HVDC converter transformers and achieve an effective assessment of their condition. Data from electrical testing, DGA, oil testing, and visual inspection were chosen to form the double-level assessment index system. Analysis results show that the integrated approach is capable of providing a relevant and effective assessment which in turn, provides valuable information for the maintenance of HVDC converter transformers.
Shift sampling theory of Fourier transform computation
Institute of Scientific and Technical Information of China (English)
柴玉璞
1997-01-01
The DFT transform us extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFTξη A-E equation) is established, and the minimization property of discrete effect and the oscillation property of truncation effect are demonstrated. All these construct the shift sampling theory——a new theory about Fourier transform computation.
A new twist to fourier transforms
Meikle, Hamish D
2004-01-01
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Fourier transforms in radar and signal processing
Brandwood, David
2011-01-01
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit
Quantum Fourier transform in computational basis
Zhou, S. S.; Loke, T.; Izaac, J. A.; Wang, J. B.
2017-03-01
The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ɛ for each Fourier coefficient. Its time complexity depends polynomially on log (N), where N is the problem size, and linearly on 1/δ and 1/ɛ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
Mathematical description of the two-dimensional Gabor transform. Application to image encryption
Perez, Ronal; Vilardy, Juan M.; Torres, Cesar O.
2017-01-01
Information security with optical processing, such as the double random phase encoding and the Gabor transform (GT) has been investigated by various researchers. We present a two-dimensional (2-D) generalization of the one-dimensional GT. This 2-D GT is applied to encrypt digital images in this paper. The scaling factors of the GT can be used as new keys, providing a new encryption system with a high security characteristics. This method can encrypt and protect the information of the digital images with a high security for information processing systems.
Composite Cyclotomic Fourier Transforms with Reduced Complexities
Wu, Xuebin; Chen, Ning; Yan, Zhiyuan; Wang, Ying
2010-01-01
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic fast Fourier transforms (CFFTs) are promising due to their low multiplicative complexities. Unfortunately, there are two issues with CFFTs: (1) they rely on efficient short cyclic convolution algorithms, which has not been investigated thoroughly yet, and (2) they have very high additive complexities when directly implemented. In this paper, we address both issues. One of the main contributions of this paper is efficient bilinear 11-point cyclic convolution algorithms, which allow us to construct CFFTs over GF$(2^{11})$. The other main contribution of this paper is that we propose composite cyclotomic Fourier transforms (CCFTs). In comparison to previously proposed fast Fourier transforms, our CCFTs achieve lower overall complexities for moderate to long lengths, and the imp...
Electronically-Scanned Fourier-Transform Spectrometer
Breckinridge, J. B.; Ocallaghan, F. G.
1984-01-01
Instrument efficient, lightweight, and stable. Fourier-transform spectrometer configuration uses electronic, instead of mechanical, scanning. Configuration insensitive to vibration-induced sampling errors introduced into mechanically scanned systems.
Two-dimensional cylindrical thermal cloak designed by implicit transformation method
Yuan, Xuebo; Lin, Guochang; Wang, Youshan
2016-07-01
As a new-type technology of heat management, thermal metamaterials have attracted more and more attentions recently and thermal cloak is a typical case. Thermal conductivity of thermal cloak designed by coordinate transformation method is usually featured by inhomogeneity, anisotropy and local singularity. Explicit transformation method, which is commonly used to design thermal cloak with the coordinate transformation known in advance, has insufficient flexibility, making it hard to proactively reduce the difficulty of device fabrication. In this work, we designed the thermal conductivity of two-dimensional (2D) cylindrical thermal cloak using the implicit transformation method without knowledge of the coordinate transformation in advance. With two classes of generation functions taken into consideration, this study adopted full-wave simulations to analyze the thermal cloaking performances of designed thermal cloaks. Material distributions and simulation results showed that the implicit transformation method has high flexibility. The form of coordinate transformation not only influences the homogeneity and anisotropy but also directly influences the thermal cloaking performance. An improved layered structure for 2D cylindrical thermal cloak was put forward based on the generation function g(r) = r15, which reduces the number of the kinds of constituent materials while guaranteeing good thermal cloaking performance. This work provides a beneficial guidance for reducing the fabrication difficulty of thermal cloak.
A DISTRIBUTION SPACE FOR FOURIER TRANSFORM
Institute of Scientific and Technical Information of China (English)
Zhou Chaoying; Yang Lihua; Huang Daren
2007-01-01
A space DF is constructed and some characterizations of space DF are given. Itis shown that the classical Fourier transform is extended to the distribution space D'F, whichcan be embedded into the Schwartz distribution space D' continuously. It is also shown thatD'F is the biggest embedded subspace of D' on which the extended Fourier transform, F, is ahomeomorphism of D'F onto itself.
Fractional Fourier transform of Lorentz beams
Institute of Scientific and Technical Information of China (English)
Zhou Guo-Quan
2009-01-01
This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.
Energy Technology Data Exchange (ETDEWEB)
Patino, A [Universidad Technologica de Bolivar, Cartagena de Indias (Colombia); Durand, P-E; Fogret, E; Pellat-Finet, P, E-mail: alberto.patino-vanegas@univ-ubs.fr [Laboratoire de mathematiques et applications des mathematiques, Universite de Bretagne Sud, B P 92116, 56321 Lorient cedex (France)
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.
Glasser, L.
1987-01-01
This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…
Ghlaifan, Abdulatef; Tounsi, Yassine; Zada, Sara; Muhire, Desire; Nassim, Abdelkrim
2016-12-01
A method for optical phase extraction based on two-dimensional discrete wavelets transform (2-DWT) decomposition is shown. From modulated fringe pattern, phase distribution is extracted by the ratio between detail and approximation. Modulation process is realized digitally by introducing high-frequency spatial carrier, and this process needs two π/2-shifted fringe patterns. We propose to use only single fringe and generate its quadrature by spiral phase transform (SPT). After validation by computer simulation, we apply the 2-DWT algorithm on experimental speckle fringe correlation taken for hard disk surface. The extracted phase using SPT quadrature was compared with that given using this time experimental quadrature, and we show a good performance by multiscale structural similarity metric.
Weng, Jiawen; Zhong, Jingang; Hu, Cuiying
2009-06-20
We describe a numerical reconstruction technique for digital holography by means of the two-dimensional Gabor wavelet transform (2D-GWT). Applying the 2D-GWT to digital holography, the object wave can be reconstructed by calculating the wavelet coefficients of the hologram at the peak of the 2D-GWT automatically. At the same time the effect of the zero-order diffraction image and the twin image are eliminated without spatial filtering. Comparing the numerical reconstruction of a holographic image by the analysis of the one-dimensional Gabor wavelet transform (1D-GWT) with the 2D-GWT, we show that the 2D-GWT method is superior to the 1D-GWT method, especially when the fringes of the hologram are not just along the y direction. The theory and the results of a simulation and experiments are shown.
From Complex Fractional Fourier Transform to Complex Fractional Radon Transform
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; JIANG Nian-Quan
2004-01-01
We show that for n-dimensional complex fractional Fourier transform the corresponding complex fractional Radon transform can also be derived, however, it is different from the direct product of two n-dimensional real fractional Radon transforms. The complex fractional Radon transform of two-mode Wigner operator is calculated.
On the Scaled Fractional Fourier Transformation Operator
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; HU Li-Yun
2008-01-01
Based on our previous study [Chin.Phys.Lett.24(2007)2238]in which the Fresnel operator corresponding to classical Fresnel transform was introduced,we derive the fractional Fourier transformation operator,and the optical operator method is then enriched.
Directory of Open Access Journals (Sweden)
Ze-yu MAO
2014-01-01
Full Text Available River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.
Finite Element Analysis of Electromagnetic Waves in Two-Dimensional Transformed Bianisotropic Media
Liu, Yan; Guenneau, Sebastien
2015-01-01
We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations (PDEs) for longitudinal electric and magnetic field components. Perfectly Matched Layers (PMLs) are discussed to model such unbounded media. We implement these PDEs and PMLs in a finite element software. We apply transformation optics in order to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. We propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magneto-electric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that well-known metamaterials can be transposed to bianisotropic media.
Institute of Scientific and Technical Information of China (English)
Ushangi GOGINAVA
2011-01-01
The main aim of this paper is to prove that for any 0 ＜ p ≤ 2/3 there exists a martingale f ∈ Hp such that Marcinkiewicz-Fejér means of the two-dimensional conjugate Walsh-Fourier series of the martingale f is not uniformly bounded in the space Lp.
High order generalized permutational fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Ran Qi-Wen; Yuan Lin; Tan Li-Ying; Ma Jing; Wang Qi
2004-01-01
We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT),is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +∞,M = 4k (k is a natural number), and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
Fourier transforms and convolutions for the experimentalist
Jennison, RC
1961-01-01
Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t
Fast Fourier Transform algorithm design and tradeoffs
Kamin, Ray A., III; Adams, George B., III
1988-01-01
The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.
Clifford Fourier transform on vector fields.
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.
Casero, Ramón; Siedlecka, Urszula; Jones, Elizabeth S; Gruscheski, Lena; Gibb, Matthew; Schneider, Jürgen E; Kohl, Peter; Grau, Vicente
2017-05-01
Traditional histology is the gold standard for tissue studies, but it is intrinsically reliant on two-dimensional (2D) images. Study of volumetric tissue samples such as whole hearts produces a stack of misaligned and distorted 2D images that need to be reconstructed to recover a congruent volume with the original sample's shape. In this paper, we develop a mathematical framework called Transformation Diffusion (TD) for stack alignment refinement as a solution to the heat diffusion equation. This general framework does not require contour segmentation, is independent of the registration method used, and is trivially parallelizable. After the first stack sweep, we also replace registration operations by operations in the space of transformations, several orders of magnitude faster and less memory-consuming. Implementing TD with operations in the space of transformations produces our Transformation Diffusion Reconstruction (TDR) algorithm, applicable to general transformations that are closed under inversion and composition. In particular, we provide formulas for translation and affine transformations. We also propose an Approximated TDR (ATDR) algorithm that extends the same principles to tensor-product B-spline transformations. Using TDR and ATDR, we reconstruct a full mouse heart at pixel size 0.92µm×0.92µm, cut 10µm thick, spaced 20µm (84G). Our algorithms employ only local information from transformations between neighboring slices, but the TD framework allows theoretical analysis of the refinement as applying a global Gaussian low-pass filter to the unknown stack misalignments. We also show that reconstruction without an external reference produces large shape artifacts in a cardiac specimen while still optimizing slice-to-slice alignment. To overcome this problem, we use a pre-cutting blockface imaging process previously developed by our group that takes advantage of Brewster's angle and a polarizer to capture the outline of only the topmost layer of wax
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Replica Fourier Transform: Properties and applications
Directory of Open Access Journals (Sweden)
A. Crisanti
2015-02-01
Full Text Available The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically.
Robust Video Watermarking Based on Discrete Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
NIU Xiamu; SUN Shenghe
2001-01-01
A video watermarking techniquebased on discrete fractional Fourier transform(DFRFT) is proposed. Each frame of an original videois first decomposed into two-dimensional (2-D) mul-tiresolution representations by 2-D discrete wavelettransforms (DWT) along the spatial axis. Then thewavelet coefficient frames in each group of pictures(GOP, each GOP has 16 frames) are transformed intoDFRFT coefficient frames by one-dimensional (1-D)DFRFT along the temporal axis. The watermark isembedded into each DFRFT coefficient frame in theGOP, and the angular parameter of the DFRFT canbe changed to adapt itself to the original video. Experimental results show that the proposed techniqueis robust enough against the attacks of frame dropping, averaging and lossy compression.
Ultrafast Fourier-transform parallel processor
Energy Technology Data Exchange (ETDEWEB)
Greenberg, W.L.
1980-04-01
A new, flexible, parallel-processing architecture is developed for a high-speed, high-precision Fourier transform processor. The processor is intended for use in 2-D signal processing including spatial filtering, matched filtering and image reconstruction from projections.
Fourier transforms on an amalgam type space
Liflyand, E
2012-01-01
We introduce an amalgam type space, a subspace of $L^1(\\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the integrability of trigonometric series.
Fourier transform infrared spectrometery: an undergraduate experiment
Lerner, L.
2016-11-01
Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory.
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Image encryption techniques based on the fractional Fourier transform
Hennelly, B. M.; Sheridan, J. T.
2003-11-01
The fractional Fourier transform, (FRT), is a generalisation of the Fourier transform which allows domains of mixed spatial frequency and spatial information to be examined. A number of method have recently been proposed in the literature for the encryption of two dimensional information using optical systems based on the FRT. Typically, these methods require random phase screen keys to decrypt the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. We have proposed a new technique based on a random shifting or Jigsaw transformation. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in various FRT domains. The new method has been compared numerically with existing methods and shows comparable or superior robustness to blind decryption. An optical implementation is also proposed and the sensitivity of the various encryption keys to blind decryption is quantified. We also present a second image encryption technique, which is based on a recently proposed method of optical phase retrieval using the optical FRT and one of its discrete counterparts. Numerical simulations of the new algorithm indicates that the sensitivity of the keys is much greater than any of the techniques currently available. In fact the sensitivity appears to be so high that optical implementation, based on existing optical signal processing technology, may be impossible. However, the technique has been shown to be a powerful method of 2-D image data encryption.
Fourier Transform Fabry-Perot Interferometer
Snell, Hilary E.; Hays, Paul B.
1992-01-01
We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.
Fourier Transform Infrared Spectroscopic Studies in Flotation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Fourier transform infrared (FTIR) spectroscopy has been extensively employed in flotation research.The work done by the author and co-workers has been reported.A comparison has been made among the different FTIR spectroscopic techniques,e.g.,transmission FTIR spectroscopy,diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy,and attenuated total reflectance (ATR) FTIR spectroscopy.FTIR spectroscopy has been used to study the mechanism of interaction between the collector and the surfaces of different minerals,the mechanism of action of the depressant in improving the selectivity of flotation,and the mechanism of adsorption of the polymeric modifying reagent on mineral surfaces.The interaction between particles in mineral suspension has also been studied by FTIR spectroscopy.
Fourier-transform spectroscopy instrumentation engineering
Saptari, Vidi
2003-01-01
Many applications today require the Fourier-transform (FT) spectrometer to perform close to its limitations, such as taking many quantitative measurements in the visible and in the near infrared wavelength regions. In such cases, the instrument should not be considered as a perfect ""black box."" Knowing where the limitations of performance arise and which components must be improved are crucial to obtaining repeatable and accurate results. One of the objectives of this book is to help the user identify the instrument's bottleneck.
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.
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.
How to tickle spins with a fourier transform NMR spectrometer.
Segawa, Takuya F; Carnevale, Diego; Bodenhausen, Geoffrey
2013-02-01
In the long bygone days of continuous-wave nuclear magnetic resonance (NMR) spectroscopy, a selected transition within a multiplet of a high-resolution spectrum could be irradiated by a highly selective continuous-wave (CW) radio-frequency (rf) field with a very weak amplitude ω(2)/(2π)≤J. This causes splittings of connected transitions, allowing one to map the connectivities of all transitions within the energy-level diagram of the spin system. Such "tickling" experiments stimulated the invention of two-dimensional spectroscopy, but seem to have been forgotten for nearly 50 years. We show that tickling can readily be achieved in homonuclear systems with Fourier transform spectrometers by applying short pulses in the intervals between the sampling points. Extensions to heteronuclear systems are even more straightforward since they can be carried out using very weak CW rf fields.
Matrix isolation studies with Fourier transform IR
Energy Technology Data Exchange (ETDEWEB)
Green, David W.; Reedy, Gerald T.
1977-01-01
The combination of Fourier transform infrared (FT-IR) spectroscopy with the matrix-isolation techniques has advantages compared with the use of more conventional grating spectroscopy. Furthermore, the recent commercial availability of Fourier transform spectrometers has made FT-IR a practical alternative. Some advantages of the FT-IR spectrometer over the grating spectrometer are the result of the computerized data system that is a necessary part of the FT-IR spectrometer; other advantages are a consequence of the difference in optical arrangements and these represent the inherent advantages of the FT-IR method. In most applications with the matrix-isolation technique, the use of FT-IR spectroscopy results in either an improved signal-to-noise ratio or a shorter time for data collection compared with grating infrared spectroscopy. Fourier transform infrared spectroscopy has been used in the laboratory to study several molecular species in low-temperature matrices. Some species have been produced by high-temperature vaporization from Knudsen cells and others by sputtering. By sputtering, Ar and Kr matrices have been prepared which contain U atoms, UO, UO/sub 2/, UO/sub 3/, PuO, PuO/sub 2/, UN, or UN/sub 2/, depending upon the composition of the gas used to sputter as well as the identity of the metallic cathode. Infrared spectra of matrices containing these compounds are presented and discussed. (JRD)
A two-dimensional Stockwell transform for gravity wave analysis of AIRS measurements
Hindley, Neil P.; Smith, Nathan D.; Wright, Corwin J.; Rees, D. Andrew S.; Mitchell, Nicholas J.
2016-06-01
Gravity waves (GWs) play a crucial role in the dynamics of the earth's atmosphere. These waves couple lower, middle and upper atmospheric layers by transporting and depositing energy and momentum from their sources to great heights. The accurate parameterisation of GW momentum flux is of key importance to general circulation models but requires accurate measurement of GW properties, which has proved challenging. For more than a decade, the nadir-viewing Atmospheric Infrared Sounder (AIRS) aboard NASA's Aqua satellite has made global, two-dimensional (2-D) measurements of stratospheric radiances in which GWs can be detected. However, one problem with current one-dimensional methods for GW analysis of these data is that they can introduce significant unwanted biases. Here, we present a new analysis method that resolves this problem. Our method uses a 2-D Stockwell transform (2DST) to measure GW amplitudes, horizontal wavelengths and directions of propagation using both the along-track and cross-track dimensions simultaneously. We first test our new method and demonstrate that it can accurately measure GW properties in a specified wave field. We then show that by using a new elliptical spectral window in the 2DST, in place of the traditional Gaussian, we can dramatically improve the recovery of wave amplitude over the standard approach. We then use our improved method to measure GW properties and momentum fluxes in AIRS measurements over two regions known to be intense hotspots of GW activity: (i) the Drake Passage/Antarctic Peninsula and (ii) the isolated mountainous island of South Georgia. The significance of our new 2DST method is that it provides more accurate, unbiased and better localised measurements of key GW properties compared to most current methods. The added flexibility offered by the scaling parameter and our new spectral window presented here extend the usefulness of our 2DST method to other areas of geophysical data analysis and beyond.
Optical Planar Discrete Fourier and Wavelet Transforms
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2007-10-01
We present all-optical architectures to perform discrete wavelet transform (DWT), wavelet packet (WP) decomposition and discrete Fourier transform (DFT) using planar lightwave circuits (PLC) technology. Any compact-support wavelet filter can be implemented as an optical planar two-port lattice-form device, and different subband filtering schemes are possible to denoise, or multiplex optical signals. We consider both parallel and serial input cases. We design a multiport decoder/decoder that is able to generate/process optical codes simultaneously and a flexible logarithmic wavelength multiplexer, with flat top profile and reduced crosstalk.
Vélez-Rábago, Rodrigo; Solorza-Calderón, Selene; Jordan-Aramburo, Adina
2016-12-01
This work presents an image pattern recognition system invariant to translation, scale and rotation. The system uses the Fourier transform to achieve the invariance to translation and the analytical Forier-Mellin transform for the invariance to scale and rotation. According with the statistical theory of box-plots, the pattern recognition system has a confidence level at least of 95.4%.
Truong, T. K.; Liu, K. Y.; Reed, I. S.
1983-01-01
It is pointed out that the two-dimensional cyclic convolution is a useful tool for many two-dimensional digital signal processing applications. Two important applications are related to spaceborne high-resolution synthetic aperture radar (SAR) processing and image processing. Nussbaumer and Quandalle (1978) showed that a radix-2 polynomial transform analogous to the conventional radix-2 FFT algorithm can be used to compute a two-dimensional cyclic convolution. On the basis of results reported by Arambepola and Rayner (1979), a radix-2 polynomial transform can be defined to compute a multidimensional cyclic convolution. Truong et al. (1981) used the considered ideas together with the Chinese Theorem to further reduce the complexity of the radix-2 fast polynomial transform (FPT). Reed et al. (1981) demonstrated that such a new FPT algorithm is significantly faster than the FFT algorithm for computing a two-dimensional convolution. In the present investigation, a parallel-pipeline architecture is considered for implementing the FPT developed by Truong et al.
Laser Field Imaging Through Fourier Transform Heterodyne
Energy Technology Data Exchange (ETDEWEB)
Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.
1999-04-05
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.
Wavelets for approximate Fourier transform and data compression
Guo, Haitao
This dissertation has two parts. In the first part, we develop a wavelet-based fast approximate Fourier transform algorithm. The second part is devoted to the developments of several wavelet-based data compression techniques for image and seismic data. We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The classical Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. The main advantage of our algorithm is that the good time and frequency localization of wavelets can be exploited to approximate the Fourier transform for many classes of signals, resulting in much less computation. Thus the new algorithm provides an efficient complexity versus accuracy tradeoff. When approximations are allowed, under certain sparsity conditions, the algorithm can achieve linear complexity, i.e. O(N). The proposed algorithm also has built-in noise reduction capability. For waveform and image compression, we propose a novel scheme using the recently developed Burrows-Wheeler transform (BWT). We show that the discrete wavelet transform (DWT) should be used before the Burrows-Wheeler transform to improve the compression performance for many natural signals and images. We demonstrate that the simple concatenation of the DWT and BWT coding performs comparably as the embedded zerotree wavelet (EZW) compression for images. Various techniques that significantly improve the performance of our compression scheme are also discussed. The phase information is crucial for seismic data processing. However, traditional compression schemes do not pay special attention to preserving the phase of the seismic data, resulting in the loss of critical information. We propose a lossy compression method that preserves the phase as much as possible. The method is based on the self-adjusting wavelet transform that adapts to the locations of the significant signal components
National Research Council Canada - National Science Library
Robert M. Pasternack; Zhen Qian; Jing-Yi Zheng; Dimitris N. Metaxas; Nada N. Boustany
2009-01-01
.... The method consists of applying an optical Fourier filter bank consisting of Gabor-like filters of varying periods and extracting the optimum filter period that maximizes the filtered object signal...
DEFF Research Database (Denmark)
Kretschmer, Silvan; Komsa, Hannu-Pekka; Bøggild, Peter
2017-01-01
The polymorphism of two-dimensional (w2D) transition-metal dichalcogenides (TMDs) and different electronic properties of the polymorphs make TMDs particularly promising materials in the context of applications in electronics. Recently, local transformations from the semiconducting trigonal prisma...... development and optimization of electron-beam-mediated engineering of the atomic structure and electronic properties of 2D TMDs with subnanometer resolution.......The polymorphism of two-dimensional (w2D) transition-metal dichalcogenides (TMDs) and different electronic properties of the polymorphs make TMDs particularly promising materials in the context of applications in electronics. Recently, local transformations from the semiconducting trigonal...... prismatic H phase to the metallic octahedral T phase in 2D MoS2 have been induced by electron irradiation [Nat. Nanotech. 2014, 9, 391], but the mechanism of the transformations remains elusive. Using density functional theory calculations, we study the energetics of the stable and metastable phases of 2D...
Fourier transforms in the complex domain
Wiener, N
1934-01-01
With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of MÃ¼nz and SzÃ¡sz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,
Fourier transforms in generalized Fock spaces
Directory of Open Access Journals (Sweden)
John Schmeelk
1990-01-01
Full Text Available A classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…,where ϕ0∈C and ϕq∈L2(R3q, q≥1. We will replace the ϕq, q≥1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.
FFTW: Fastest Fourier Transform in the West
Frigo, Matteo; Johnson, Steven G.
2012-01-01
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST). Benchmarks performed on a variety of platforms show that FFTW's performance is typically superior to that of other publicly available FFT software, and is even competitive with vendor-tuned codes. In contrast to vendor-tuned codes, however, FFTW's performance is portable: the same program will perform well on most architectures without modification. The FFTW library is required by other codes such as StarCrash and Hammurabi.
Research progress on discretization of fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
TAO Ran; ZHANG Feng; WANG Yue
2008-01-01
As the fractional Fourier transform has attracted a considerable amount of atten-tion in the area of optics and signal processing,the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier trans-form.Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain,the discre-tization of the fractional Fourier transform has been investigated recently.A sum-mary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper.The discretizations include sampling in the fractional Fourier domain,discrete-time fractional Fourier transform,frac-tional Fourier series,discrete fractional Fourier transform (including 3 main types:linear combination-type;sampling-type;and eigen decomposition-type),and other discrete fractional signal transform.It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.
The Fourier transform of tubular densities
Prior, C B
2012-05-18
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.
JCE Online: Interactive Fourier Transform Activities
Zielinski, Theresa Julia
1999-02-01
In our vigorous teaching of concepts and skills to students, we may cover (hide) more than we uncover, obscuring significant relationships between mathematical models and their associated chemical concepts with excessive mathematical derivations. To set the record straight, I find that mathematical treatments of physical phenomena are beautiful and elegant. Students should know from where the equations and simplifications leading to them arise. They should know the limits of the equations in order to use them properly. However, this can be the Siren's song. For example, the mathematical representation of the Fourier transform and its significance as presented in most texts are too brief to convey understanding to the typical undergraduate student. Furthermore, a few hand calculations would not permit deeper probing of the method and its intimate link to spectroscopy. The Fourier transform is a very good example of how symbolic equation software can help to uncover the science by making the mathematical manipulations easier and the mathematical concepts more accessible. The complete articles and Mathcad documents described in these abstracts are available from JCE Online at http://jchemed.chem.wisc.edu/JCEWWW/Columns/McadInChem/.
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…
Tajahuerce, E; Saavedra, G; Furlan, W D; Sicre, E E; Andrés, P
2000-01-10
An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.
From fractional Fourier transformation to quantum mechanical fractional squeezing transformation
Institute of Scientific and Technical Information of China (English)
吕翠红; 范洪义; 李东韡
2015-01-01
By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hy-perbolic function, i.e., tanα→tanhα, sinα→sinhα, we find quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within ordered product of operators (IWOP) wederive the unitary operator responsible for the FrST, which is composite and is made of eiπa†a/2 and exp[ iα2 (a2+a†2)]. The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.
Fourier transform inequalities for phylogenetic trees.
Matsen, Frederick A
2009-01-01
Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.
Multicomplementary operators via finite Fourier transform
Energy Technology Data Exchange (ETDEWEB)
Klimov, Andrei B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico); Sanchez-Soto, Luis L [Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1 (Canada); Guise, Hubert de [Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1 (Canada)
2005-03-25
A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.
Fourier transform spectroscopy for future planetary missions
Brasunas, John; Kolasinski, John; Kostiuk, Ted; Hewagama, Tilak
2017-01-01
Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system. Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, we have developed CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. We discuss the roadmap for making CIRS-lite a viable candidate for future planetary missions, including the recent increased emphasis on ocean worlds (Europa, Encelatus, Titan) and also on smaller payloads such as CubeSats and SmallSats.
Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform
Lang, Jun
2012-05-01
In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by using the fractional Fourier transform, but most of their encryptions are complex values and need digital hologram technique to record information, which is inconvenient for digital transmission. In this paper, we propose a new approach for image encryption based on the real-valuedness and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission. In the proposed scheme, the original and encrypted images are respectively in the spatial domain and the reality-preserving multiple-parameter fractional Fourier transformed domain determined by the encryption keys. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.
Applying Quaternion Fourier Transforms for Enhancing Color Images
Directory of Open Access Journals (Sweden)
M.I. Khalil
2012-03-01
Full Text Available The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.
Integrability of the Fourier transform: functions of bounded variation
Liflyand, E
2012-01-01
Certain relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. The widest subspaces of the space of functions of bounded variation are indicated in which the cosine and sine Fourier transforms are integrable.
Geometric interpretations of the Discrete Fourier Transform (DFT)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
Quantum copying and simplification of the quantum Fourier transform
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.
Pasternack, Robert M; Qian, Zhen; Zheng, Jing-Yi; Metaxas, Dimitris N; Boustany, Nada N
2009-07-06
We use optical Gabor-like filtering implemented with a digital micromirror device to achieve nanoscale sensitivity to changes in the size of finite and periodic objects imaged at low resolution. The method consists of applying an optical Fourier filter bank consisting of Gabor-like filters of varying periods and extracting the optimum filter period that maximizes the filtered object signal. Using this optimum filter period as a measure of object size, we show sensitivity to a 7.5 nm change in the period of a chirped phase mask with period around 1 microm. We also show 30 nm sensitivity to change in the size of polystyrene spheres with diameters around 500 nm. Unlike digital post-processing our optical processing method retains its sensitivity when implemented at low magnification in undersampled images. Furthermore, the optimum Gabor filter period found experimentally is linearly related to sphere diameter over the range 0.46 microm-1 microm and does not rely on a predictive scatter model such as Mie theory. The technique may have applications in high throughput optical analysis of subcellular morphology to study organelle function in living cells.
Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms
Directory of Open Access Journals (Sweden)
Kokilashvili V
1997-01-01
Full Text Available As is well known, invariant operators with a shift can be bounded from into only if . We show that the case might also hold for weighted spaces. We derive the sufficient conditions for the validity of strong (weak type inequalities for the Hilbert transform when . The examples of couple of weights which guarantee the fulfillness of two-weighted strong (weak type inequalities for singular integrals are presented. The method of proof of the main results allows us to generalize the results of this paper to the singular integrals which are defined on homogeneous groups. The Fourier multiplier theorem is also proved.
Fully phase-encrypted memory using cascaded extended fractional Fourier transform
Nishchal, Naveen Kumar; Joseph, Joby; Singh, Kehar
2004-08-01
In this paper, we implement a fully phase-encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The full phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, the conjugate of the encrypted image. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the decrypted phase image, alleviating the need of alignment in the Fourier plane making the system rugged.
Hulse, George
2014-01-01
An optical approach using confocal parabolic reflectors is used to transform 2D input data based on spatial position to a 1D sequenced serial string. The optical input data are set up as a 2D array. Individual channels are established between the input array and the final output detector, which reads the data as a time based serial data. The transformation is achieved by changing the optical path length associated with each pixel and its channel to the output detector. The 2D data can be images or individual sources but the light must be parallel. This paper defines how to establish the channels and the calculations required to achieve the desired transformation.
Stepwise Iterative Fourier Transform: The SIFT
Benignus, V. A.; Benignus, G.
1975-01-01
A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.
Realization of quantum discrete Fourier transform with NMR
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The pulse sequences of the logic operations used in quantum discrete Fourier transform are designed for the experiment of nuclear magnetic resonance(NMR), and 2-qubit discrete Fourier transforms are implemented experimentally with NMR. The experimental errors are examined and methods for reducing the errors are proposed.
AN ANOMALY INTRUSION DETECTION METHOD USING FOURIER TRANSFORM
Institute of Scientific and Technical Information of China (English)
Yue Bing; Zhao Yuexia; Xu Zhoujun; Fu Hongjuan; Ma Fengning
2004-01-01
A set of discrete points obtained from audit records on a behavior session is processed with Fourier transform. The criterion of selecting Fourier transform coefficients is introduced, and is used to find a unified value from the set of coefficients. This unified value is compared with a threshold to determine whether the session is abnormal. Finally simple test results are reported.
Fiber Optic Fourier Transform White-Light Interferometry
Institute of Scientific and Technical Information of China (English)
Yi Jiang; Cai-Jie Tang
2008-01-01
Fiber optic Fourier transform white-light inter-fereometry is presented to interrogate the absolute optical path difference of an Mach-Zehnder inter-ferometer. The phase change of the interferometer caused by scanning wavelength can be calculated by a Fourier transform-based phase demodulation technique. A linear output is achieved.
Crystalline-crystalline phase transformation in two-dimensional In2Se3 thin layers.
Tao, Xin; Gu, Yi
2013-08-14
We report, for the first time, the fabrication of single-crystal In2Se3 thin layers using mechanical exfoliation and studies of crystalline-crystalline (α → β) phase transformations as well as the corresponding changes of the electrical properties in these thin layers. Particularly, using electron microscopy and correlative in situ micro-Raman and electrical measurements, we show that, in contrast to bulk single crystals, the β phase can persist in single-crystal thin layers at room temperature (RT). The single-crystal nature of the layers before and after the phase transition allows for unambiguous determination of changes in the electrical resistivity. Specifically, the β phase has an electrical resistivity about 1-2 orders of magnitude lower than the α phase. Furthermore, we find that the temperature of the α → β phase transformation increases by as much as 130 K with the layer thickness decreasing from ~87 nm to ~4 nm. These single-crystal thin layers are ideal for studying the scaling behavior of the phase transformations and associated changes of the electrical properties. For these In2Se3 thin layers, the accessibility of the β phase at RT, with distinct electrical properties than the α phase, provides the basis for multilevel phase-change memories in a single material system.
Thermal stabilization of static single-mirror Fourier transform spectrometers
Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.
2017-05-01
Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.
Fractional Fourier transform of apertured paraboloid refracting system
Institute of Scientific and Technical Information of China (English)
Jiannong Chen; Jinliang Yan; Defa Wang; Yongjiang Yu
2007-01-01
The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier transform acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
Energy Technology Data Exchange (ETDEWEB)
Layton, E.G. (Joint Inst. for Lab. Astrophysics, Boulder, CO (United States)); Stade, E. (Colorado Univ., Boulder, CO (United States). Dept. of Mathematics)
1993-08-28
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author).
Cryogenic Scan Mechanism for Fourier Transform Spectrometer
Brasunas, John C.; Francis, John L.
2011-01-01
A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses
Directory of Open Access Journals (Sweden)
Lucy Lim
2016-01-01
Full Text Available Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices.
A discrete Fourier transform for virtual memory machines
Galant, David C.
1992-01-01
An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.
A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis
Ioup, G. E.
1980-01-01
Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.
Image restoration based on the discrete fraction Fourier transform
Yan, Peimin; Mo, Yu L.; Liu, Hong
2001-09-01
The fractional Fourier transform is the powerful tool for time-variant signal analysis. For space-variant degradation and non-stationary processes the filtering in fractional Fourier domains permits reduction of the error compared with ordinary Fourier domain filtering. In this paper the concept of filtering in fractional Fourier domains is applied to the problem of estimating degraded images. Efficient digital implementation using discrete Hermite eigenvectors can provide similar results to match the continuous outputs. Expressions for the 2D optimal filter function in fractional domains will be given for transform domains characterized by the two rotation angle parameters of the 2D fractional Fourier transform. The proposed method is used to restore images that have several degradations in the experiments. The results show that the method presented in this paper is valid.
Research progress of the fractional Fourier transform in signal processing
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.
Barnett, Patrick D; Strange, K Alicia; Angel, S Michael
2016-12-12
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.
Imaging Analysis by Means of Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Starting from the diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.
Electro-Optic Imaging Fourier Transform Spectral Polarimeter Project
National Aeronautics and Space Administration — Boulder Nonlinear Systems, Inc. (BNS) proposes to develop an Electro-Optic Imaging Fourier Transform Spectral Polarimeter (E-O IFTSP). The polarimetric system is...
On the physical relevance of the discrete Fourier transform
CSIR Research Space (South Africa)
Greben, JM
1991-11-01
Full Text Available This paper originated from the author's dissatisfaction with the way the discrete Fourier transform is usually presented in the literature. Although mathematically correct, the physical meaning of the common representation is unsatisfactory...
Embolic Doppler ultrasound signal detection via fractional Fourier transform.
Gençer, Merve; Bilgin, Gökhan; Aydın, Nizamettin
2013-01-01
Computerized analysis of Doppler ultrasound signals can aid early detection of asymptomatic circulating emboli. For analysis, physicians use informative features extracted from Doppler ultrasound signals. Time -frequency analysis methods are useful tools to exploit the transient like signals such as Embolic signals. Detection of discriminative features would be the first step toward automated analysis of embolic Doppler ultrasound signals. The most problematic part of setting up emboli detection system is to differentiate embolic signals from confusing similar wave-like patterns such as Doppler speckle and artifacts caused by tissue movement, probe tapping, speaking etc. In this study, discrete version of fractional Fourier transform is presented as a solution in the detection of emboli in digitized Doppler ultrasound signals. An accurate set of parameters are extracted using short time Fourier transform and fractional Fourier transform and the results are compared to reveal detection quality. Experimental results prove the efficiency of fractional Fourier transform in which discriminative features becomes more evident.
Marko, H.
1978-01-01
A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.
Quantum Fourier Transform and Phase Estimation in Qudit System
Institute of Scientific and Technical Information of China (English)
CAO Ye; PENG Shi-Guo; ZHENG Chao; LONG Gui-Lu
2011-01-01
The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc.In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case.They can be seen as subroutines in a main program run in a qudit quantum computer, and the quantum circuits are given.
Simple optical setup implementation for digital Fourier transform holography
Energy Technology Data Exchange (ETDEWEB)
De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passo da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); Rodrigues, D M C; Dos Santos, P A M, E-mail: pams@if.uff.br [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)
2011-01-01
In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.
Fourier transform spectroscopy in the visible and ultraviolet range.
Luc, P; Gerstenkorn, S
1978-05-01
In cases where the photon noise is the limiting factor, the multiplex gain is not always conserved; however the throughput (Jacquinot's advantage) is not affected. Therefore extension of Fourier transform spectroscopy to higher frequencies has great possibilities. Studies at high resolution, both in emission and in absorption, show that the performance achieved by Fourier transform spectroscopy in the visible and uv range is comparable with that reached in the ir.
Rotation-invariant texture analysis using Radon and Fourier transforms
Institute of Scientific and Technical Information of China (English)
Songshan Xiao; Yongxing Wu
2007-01-01
@@ Texture analysis is a basic issue in image processing and computer vision, and how to attain the rotationinvariant texture characterization is a key problem. This paper proposes a rotation-invariant texture analysis technique using Radon and Fourier transforms. This method uses Radon transform to convert rotation to translation, then utilizes Fourier transform and takes the moduli of the Fourier transform of these functions to make the translation invariant. A k-nearest-neighbor rule is employed to classify texture images. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. Experiment results show the feasibility of the proposed method and its robustness to additive white noise.
Dynamic measurement of deformation using Fourier transform digital holographic interferometry
Gao, Xinya; Wu, Sijin; Yang, Lianxiang
2013-10-01
Digital holographic interferometry (DHI) is a well-established optical technique for measurement of nano-scale deformations. It has become more and more important due to the rapid development of applications in aerospace engineering and biomedicine. Traditionally, phase shift technique is used to quantitatively measure the deformations in DHI. However, it cannot be applied in dynamic measurement. Fourier transform phase extraction method, which can determine the phase distribution from only a single hologram, becomes a promising method to extract transient phases in DHI. This paper introduces a digital holographic interferometric system based on 2D Fourier transform phase extraction method, with which deformations of objects can be measured quickly. In the optical setup, the object beam strikes a CCD via a lens and aperture, and the reference beam is projected on the CCD through a single-mode fiber. A small inclination angle between the diverging reference beam and optical axial is introduced in order to physically separate the Fourier components in frequency domain. Phase maps are then obtained by the utilization of Fourier transform and windowed inverse Fourier transform. The capability of the Fourier transform DHI is discussed by theoretical discussion as well as experiments.
Imaginary angle fractional Fourier transform and its optical implementation
Institute of Scientific and Technical Information of China (English)
华建文; 刘立人; 李国强
1997-01-01
The concept of imaginary angle fractional Fourier transform is proposed. Its existence and additive operation are proved. With this concept, FRT is expanded to the optical transform of convex lens outside the range of double focal length and that of concave lens.
SAW chirp Fourier transform for MB-OFDM UWB receiver
Institute of Scientific and Technical Information of China (English)
HE Peng-fei; L(U) Ying-hua; ZHANG Hong-xin; WANG Ye-qiu; XU Yong
2006-01-01
In the conventional multiband orthogonal frequency division multiplexing ultra wideband (MB-OFDM UWB )receiver, the fast Fourier transform (FFT) algorithm is realized by the expensive and power-consuming digital signal processor (DSP) chips. In this article, the lower power, lower cost, and lower complexity real-time analog surface acoustic wave (SAW)chirp Fourier transform devices were used to replace the DSP part. A MB-OFDM UWB receiver based on the M-C-M SAW chirp Fourier transform was presented, and the step of signal transformation from input signals was also depicted. The simulation results show that the proposed receiver provides similar bit error performance compared to the fully digital receiver when used in the channel environments proposed by the IEEE 802.15SG3a.
[Analysis of cell arrangements in Biota orientalis using Fourier transformation].
Duo, Hua-Qiong; Wang, Xi-Ming
2009-10-01
Fourier transform image-processing technology is applied for determining the cross section cell arrangement of early-wood in Biota orientalis. In this method, the disc-convoluted dot map from each cell radius with 10 pixels is transformed by Fourier transform, generating the angle distribution function in the power spectral pattern. The maximum value is the arrangement of the cell. The results of Fourier transform image-processing technology indicated that the arrangements of the cell of Biota orientalis are 15 degrees in oblique direction, respectively. This method provides a new basis for the digitized identification of the wood, and also the new theoretical research direction for the digitized identification and examination of the wood species.
Directory of Open Access Journals (Sweden)
Sarunya Kanjanawattana
2017-07-01
Full Text Available Image classification plays a vital role in many areas of study, such as data mining and image processing; however, serious problems collectively referred to as the course of dimensionality have been encountered in previous studies as factors that reduce system performance. Furthermore, we also confront the problem of different graph characteristics even if graphs belong to same types. In this study, we propose a novel method of graph-type classification. Using our approach, we open up a new solution of high-dimensional images and address problems of different characteristics by converting graph images to one dimension with a discrete Fourier transformation and creating numeric datasets using wavelet and Hough transformations. Moreover, we introduce a new classifier, which is a combination between artificial neuron networks (ANNs and support vector machines (SVMs, which we call ANNSVM, to enhance accuracy. The objectives of our study are to propose an effective graph-type classification method that includes finding a new data representative used for classification instead of two-dimensional images and to investigate what features make our data separable. To evaluate the method of our study, we conducted five experiments with different methods and datasets. The input dataset we focused on was a numeric dataset containing wavelet coefficients and outputs of a Hough transformation. From our experimental results, we observed that the highest accuracy was provided using our method with Coiflet 1, which achieved a 0.91 accuracy.
Three-dimensional adaptive coordinate transformations for the Fourier modal method.
Küchenmeister, Jens
2014-01-27
The concepts of adaptive coordinates and adaptive spatial resolution have proved to be a valuable tool to improve the convergence characteristics of the Fourier Modal Method (FMM), especially for metallo-dielectric systems. Yet, only two-dimensional adaptive coordinates were used so far. This paper presents the first systematic construction of three-dimensional adaptive coordinate and adaptive spatial resolution transformations in the context of the FMM. For that, the construction of a three-dimensional mesh for a periodic system consisting of two layers of mutually rotated, metallic crosses is discussed. The main impact of this method is that it can be used with any classic FMM code that is able to solve the large FMM eigenproblem. Since the transformation starts and ends in a Cartesian mesh, only the transformed material tensors need to be computed and entered into an existing FMM code.
Electro-Optical Imaging Fourier-Transform Spectrometer
Chao, Tien-Hsin; Zhou, Hanying
2006-01-01
An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.
Methods of theme presentation "The Fourier transform of impulse functions"
Directory of Open Access Journals (Sweden)
Faniya Ahmetova
2016-09-01
Full Text Available The paper considers the Fourier transform of impulse functions, which is the mathematical basis of the tasks associated with the theory of reception and signal conversion in optoelectronic system. The method of calculating of two functions convolution, its Fourier image and the image of the Fourier-Bessel axisymmetric functions are demonstrated in details. A table, which summarizes the analytical expression for the shifted impulse functions and records their Fourier transforms, is provided. A wide range of examples of solving tasks, containing the graphic illustration, is analyzed. A structured approach to the presentation of the material, which combines basic theoretical information and analysis of typical tasks, will help second-year students of optoelectronic specialty in their independent work and homework.
COMPARISON OF FOURIER AND WAVELET TRANSFORMS IN GEOPHYSICAL APPLICATIONS
Directory of Open Access Journals (Sweden)
Hakan ALP
2008-01-01
Full Text Available In this study, it was compared Fourier Transformation using widely in analysing of geophysics data and image processing and Wavelet Transformation using in image processing, boundary analysis and recently years in use geophysical data analysis. It was applicated and compared two transformations in the both geophysical data and fundamental functions. Then the results obtained were evaluated. In this study it was compared two transformation using earthquake records and Bouger gravity anomalies map of Hatay region geophysical data. At the end of the our study it was clearly seen that wavelet transform can be used by geophysical data analysing.
Energy Technology Data Exchange (ETDEWEB)
Rodriguez G, A.; Bowtell, R.; Mansfield, P. [Area de Procesamiento Digital de Senales e Imagenes Biomedicas. Universidad Autonoma Metropolitana Iztapalapa. Mexico D.F. 09340 Mexico (Mexico)
1998-12-31
Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)
The Formalization of Discrete Fourier Transform in HOL
Directory of Open Access Journals (Sweden)
Zhiping Shi
2015-01-01
Full Text Available Traditionally, Discrete Fourier Transform (DFT is performed with numerical or symbolic computation, which cannot guarantee 100% accurate analysis which may be necessary for safety-critical applications. Machine theorem proving is one of the formal methods that perform accurate analysis with completeness to some extent. This paper proposes the formalization of DFT in a higher-order logic theorem prover named HOL. We propose the formal definition of DFT and verify the fundamental properties of DFT. Two case studies are presented to illustrate usefulness and correctness of the formalized DFT, including formal verifications of Fast Fourier Transform (FFT and cosine frequency shift.
Fourier transform infrared spectra applications to chemical systems
Ferraro, John R
1985-01-01
The final and largest volume to complete this four-volume treatise is published in response to the intense commercial and research interest in Fourier Transform Interferometry.Presenting current information from leading experts in the field, Volume 4 introduces new information on, for example, applications of Diffuse Reflectance Spectroscopy in the Far-Infrared Region. The editors place emphasis on surface studies and address advances in Capillary Gas Chromatography - Fourier Transform Interferometry.Volume 4 especially benefits spectroscopists and physicists, as well as researchers
Recording Fractional Fourier Transform Hologram Using Holographic Zone Plate
Institute of Scientific and Technical Information of China (English)
高峰; 曾阳素; 张怡霄; 杨静; 高福华; 郭永康
2002-01-01
FRTH(fractional Fourier transform hologram) is a new kind of hologram that differs from common Fresnel holograms and Fourier transform holograms. Due to the flexibility of zone plate. A method that uses the -1 order diffraction wave of zone plate as the object wave and the 0 order diffraction wave as the reference wave to record FRTH is presented. It provides a new simple way to record FRTH. In this paper, the theory of achieving FRT and recording FRTH using holographic zone plate is presented and experimental results are given.
Multifractional Fourier Transform Method and Its Applications to Image Encryption
Institute of Scientific and Technical Information of China (English)
RANQiwen; WANGQi; MAJing; TANLiying
2003-01-01
The multiplicity of the fractional Fourier transform(FRFT),which is intrinsic in any fractional operator,has been claimed by several authors,but never across-the-board developed.Particularly,the weight-type FRFT(WFRFT) has not been investigated.Starting with defining the multifractional Fourier transform (MFRFT),we gained the generalization permutation matrix group (GPMG)representation and multiplicity of the MFRFT,and the relationships among the MFRFT the standard WFRFT and the standard CFRFT.Finally,as a application,a novel image encryption method hased on the MFRFT is propounded.Similation results show that this method is safe,practicable and impactful.
Phase retrieval for attacking fractional Fourier transform encryption.
Kong, Dezhao; Shen, Xueju; Cao, Liangcai; Jin, Guofan
2017-04-20
An advanced iterative phase retrieval algorithm is applied to perform a ciphertext-only attack on the fractional Fourier transform-based double random phase encryption system. With the given complex amplitude of ciphertext and definite support of the object image, the original object image can be recovered by estimating the energy of support area in the recovered image. The encryption system can be attacked by analyzing the sensibility of fractional Fourier transform order keys and evaluating the energy of the object image support area. The proposed algorithm can obtain encrypted fractional order and retrieve two random phase keys. Numerical results demonstrate the efficacy of the proposed attacking method.
Fourier-transform and global contrast interferometer alignment methods
Goldberg, Kenneth A.
2001-01-01
Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.
Fourier transform infrared spectra applications to chemical systems
Ferraro, John R
1978-01-01
Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems presents the chemical applications of the Fourier transform interferometry (FT-IR).The book contains discussions on the applications of FT-IR in the fields of chromatography FT-IR, polymers and biological macromolecules, emission spectroscopy, matrix isolation, high-pressure interferometry, and far infrared interferometry. The final chapter is devoted to the presentation of the use of FT-IR in solving national technical problems such as air pollution, space exploration, and energy related subjects.Researc
Discrete Fourier Transform in a Complex Vector Space
Dean, Bruce H. (Inventor)
2015-01-01
An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.
Discrete Fourier Transform Analysis in a Complex Vector Space
Dean, Bruce H.
2009-01-01
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
Zhao, An-Xin; Tang, Xiao-Jun; Zhang, Zhong-Hua; Liu, Jun-Hua
2014-10-01
The generalized two-dimensional correlation spectroscopy and Fourier transform infrared were used to identify hydrocarbon isomers in the mixed gases for absorption spectra resolution enhancement. The Fourier transform infrared spectrum of n-butane and iso-butane and the two-dimensional correlation infrared spectrum of concentration perturbation were used for analysis as an example. The all band and the main absorption peak wavelengths of Fourier transform infrared spectrum for single component gas showed that the spectra are similar, and if they were mixed together, absorption peaks overlap and peak is difficult to identify. The synchronous and asynchronous spectrum of two-dimensional correlation spectrum can clearly identify the iso-butane and normal butane and their respective characteristic absorption peak intensity. Iso-butane has strong absorption characteristics spectrum lines at 2,893, 2,954 and 2,893 cm(-1), and n-butane at 2,895 and 2,965 cm(-1). The analysis result in this paper preliminary verified that the two-dimensional infrared correlation spectroscopy can be used for resolution enhancement in Fourier transform infrared spectrum quantitative analysis.
Fourier and Hadamard transform spectrometers - A limited comparison
Tai, M. H.; Harwit, M.
1976-01-01
An encoding figure of merit is established for a detector-noise limited Fourier transform spectrometer (FTS) and compared to the comparable figure for a Hadamard transform spectrometer (HTS). The limitation of the Fourier system is partly that it does not truly Fourier analyze the radiation. Instead a cosine squared modulation is imposed on the different spectral frequencies. An additional difficulty is that neither the cosine nor the cosine squared functions form an orthonormal set. This makes the Fellgett's advantage (root-mean-squared figure of merit) for a single detector Michelson interferometer a factor of the square root of (N/8) greater than for a conventional grating instrument - rather than the square root of (N/2). The theoretical limit would be the square root of N.
Application of fast Fourier transformation in thermoluminescence thermogram reconstruction
Pla, C.; Podgorsak, E. B.
1984-03-01
A thermoluminescence (TL) thermogram reconstruction technique based on fast Fourier transformation (FFT) techniques is presented. Only the first few terms of the real and imaginary ``frequency arrays,'' representing the thermogram in the frequency domain, are used for thermogram reconstruction by an inverse transformation. A method to determine the optimum number of FFT terms is discussed and a reconstruction study performed on six commonly used TL materials.
SPICA/SAFARI fourier transform spectrometer mechanism evolutionary design
Dool, T.C. van den; Kruizinga, B.; Braam, B.C.; Hamelinck, R.F.M.M.; Loix, N.; Loon, D. van; Dams, J.
2012-01-01
TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme in 2022. JAXA leads the development o
Optical correlation based on the fractional Fourier transform.
Granieri, S; Arizaga, R; Sicre, E E
1997-09-10
Some properties of optical correlation based on the fractional Fourier transform are analyzed. For a particular set of fractional orders, a filter is obtained that becomes insensitive to scale variations of the object. An optical configuration is also proposed to carry out the fractional correlation in a flexible way, and some experimental results are shown.
Coupling of column liquid chromatography and Fourier transform infrared spectrometry
Somsen, G.W; Gooijer, C; Velthorst, N.H; Brinkman, U.A Th
1998-01-01
This paper provides an extensive overview of the literature on the coupling of column liquid chromatography (LC) and Fourier transform infrared spectrometry (FT-IR). Flow-cell-based FT-IR detection and early solvent-elimination interfaces for LC-FT-IR are discussed in brief. A comprehensive descript
Quantum Discrete Fourier Transform in an Ion Trap System
Institute of Scientific and Technical Information of China (English)
ZHENG Shi-Biao
2007-01-01
We propose two schemes for the implementation of quantum discrete Fourier transform in the ion trap system. In each scheme we design a tunable two-qubit phase gate as the main ingredient. The experimental implementation of the schemes would be an important step toward complex quantum computation in the ion trap system.
Fourier transformation methods in the field of gamma spectrometry
Indian Academy of Sciences (India)
A Abdel-Hafiez
2006-09-01
The basic principles of a new version of Fourier transformation is presented. This new version was applied to solve some main problems such as smoothing, and denoising in gamma spectroscopy. The mathematical procedures were first tested by simulated data and then by actual experimental data.
Quaternion Fourier transforms for signal and image processing
Ell, Todd A; Sangwine, Stephen J
2014-01-01
Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book's attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.
AN ASYMPTOTIC ORDER OF FOURIER TRANSFORM ON SL(2,R)
Institute of Scientific and Technical Information of China (English)
Wang Xinsong; Zheng Weixing
2003-01-01
In this paper, a better asymptotic order of Fourier transform on SL(2 ,R) is obtained by using classicalanalysis and Lie analysis comparing with that of [5]、 [6], and the Plancherel theorem on Cc2 (SL (2, R)) isalso obtained as an application.
Quasi- Chun- Ching Shih's Fractional Fourier Transform with Periodicity of 2,3 and M
Institute of Scientific and Technical Information of China (English)
FAN Xi-zhi
2004-01-01
Based on Chun-Ching Shih's idea, the basic transform was substituted and the quasi-ChunChing Shih's fractional Fourier transform with periodicity of 2, 3 and M was deduced. The two former transforms and the Chun-Ching Shih's fractional Fourier transform were only the particular cases of quasiChun-Ching Shih's fractional Fourier transform with periodicity of M.
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
Dean, Bruce H. (Inventor)
2012-01-01
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
DEFF Research Database (Denmark)
Vandekerckhove, J; Bauw, G; Vancompernolle, K
1990-01-01
A systematic comparison of the protein synthesis patterns of cultured normal and transformed human fibroblasts and epithelial cells, using two-dimensional gel protein analysis combined with computerized imaging and data acquisition, identified a 90-kD protein (SSP 5714) as one of the most striking...... downregulated markers typical of the transformed state. Using the information stored in the comprehensive human cellular protein database, we found this protein strongly expressed in several fetal tissues and one of them, epidermis, served as a source for preparative two-dimensional gel electrophoresis. Partial...... and by coelectrophoresis with purified human gelsolin. These results suggest that an important regulatory protein of the microfilament system may play a role in defining the phenotype of transformed human fibroblast and epithelial cells in culture. Udgivelsesdato: 1990-Jul...
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
On the finite Fourier transforms of functions with infinite discontinuities
Directory of Open Access Journals (Sweden)
Branko Saric
2002-01-01
Full Text Available The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.
An introduction to Laplace transforms and Fourier series
Dyke, Phil
2014-01-01
Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...
Ultrafast ranging lidar based on real-time Fourier transformation.
Xia, Haiyun; Zhang, Chunxi
2009-07-15
Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the time delay between the two signals. The temporal interferograms are transformed from the time domain into the frequency domain using a time-to-frequency conversion function obtained in the calibration process. The Fourier transform is used in the data processing. A range resolution of 334 nm at a sampling rate of 48.6 MHz over a distance of 16 cm is demonstrated in the laboratory.
The Discrete Fourier Transform on hexagonal remote sensing image
Li, Yalu; Ben, Jin; Wang, Rui; Du, Lingyu
2016-11-01
Global discrete grid system will subdivide the earth recursively to form a multi-resolution grid hierarchy with no Overlap and seamless which help build global uniform spatial reference datum and multi-source data processing mode which takes the position as the object and in the aspect of data structure supports the organization, process and analysis of the remote sensing big data. This paper adopts the base transform to realize the mutual transformation of square pixel and hexagonal pixel. This paper designs the corresponding discrete Fourier transform algorithm for any lattice. Finally, the paper show the result of the DFT of the remote sensing image of the hexagonal pixel.
Transfer Functions Via Laplace- And Fourier-Borel Transforms
Can, Sumer; Unal, Aynur
1991-01-01
Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.
A Student's Guide to Fourier Transforms - 2nd Edition
James, J. F.
2002-09-01
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science. Expanded to include more emphasis on applications An established successful textbook for undergraduate and graduate students Includes worked examples and copious diagrams throughout
A VLSI architecture for simplified arithmetic Fourier transform algorithm
Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.
1992-01-01
The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.
Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie
2015-10-20
In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.
Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition
Directory of Open Access Journals (Sweden)
Yufeng Lu
2012-01-01
Full Text Available A fractional fourier transform (FrFT based chirplet signal decomposition (FrFT-CSD algorithm is proposed to analyze ultrasonic signals for NDE applications. Particularly, this method is utilized to isolate dominant chirplet echoes for successive steps in signal decomposition and parameter estimation. FrFT rotates the signal with an optimal transform order. The search of optimal transform order is conducted by determining the highest kurtosis value of the signal in the transformed domain. A simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chirp rate parameter in the simulated ultrasonic echoes. Benchmark and ultrasonic experimental data are used to evaluate the FrFT-CSD algorithm. Signal processing results show that FrFT-CSD not only reconstructs signal successfully, but also characterizes echoes and estimates echo parameters accurately. This study has a broad range of applications of importance in signal detection, estimation, and pattern recognition.
Novel fringe scanning/Fourier transform method of synthetic imaging
Energy Technology Data Exchange (ETDEWEB)
Crawford, T.M.; Albano, R.K.
1993-08-01
We have developed a one-dimensional theory and a computer model for synthetically imaging scenes using a novel fringe scanning/Fourier transform technique. Our method probes a scene using two interfering beams of slightly different frequency. These beams form a moving fringe pattern which scans the scene and resonates with any spatial frequency components having the same spatial frequency as the scanning fringe pattern. A simple, non-imaging detector above the scene observes any scattered radiation from the scene falling onto it. If a resonance occurs between the scanning fringe pattern and the scene, then the scattered radiation will be modulated at the difference frequency between the two probing beams. By changing the spatial period of the fringe pattern and then measuring the amplitude and phase of the modulated radiation that is scattered from the scene, the Fourier amplitudes and phases of the different spatial frequency components making up the scene can be measured. A synthetic image of the scene being probed can be generated from this Fourier amplitude and phase data by taking the inverse Fourier transform of this information. This technique could be used to image objects using light, ultrasonic, or other electromagnetic or acoustic waves.
Fourier transform approach in modulation technique of experimental measurements.
Khazimullin, M V; Lebedev, Yu A
2010-04-01
An application of Fourier transform approach in modulation technique of experimental studies is considered. This method has obvious advantages compared with traditional lock-in amplifiers technique--simple experimental setup, a quickly available information on all the required harmonics, high speed of data processing using fast Fourier transform algorithm. A computationally simple, fast and accurate Fourier coefficients interpolation (FCI) method has been implemented to obtain a useful information from harmonics of a multimode signal. Our analysis shows that in this case FCI method has a systematical error (bias) of a signal parameters estimation, which became essential for the short data sets. Hence, a new differential Fourier coefficients interpolation (DFCI) method has been suggested, which is less sensitive to a presence of several modes in a signal. The analysis has been confirmed by simulations and measurements of a quartz wedge birefringence by means of the photoelastic modulator. The obtained bias, noise level, and measuring speed are comparable and even better than in lock-in amplifier technique. Moreover, presented DFCI method is expected to be promised candidate for using in actively developing imaging systems based on the modulation technique requiring fast digital signal processing of large data sets.
Institute of Scientific and Technical Information of China (English)
宋丽娜; 王维国
2012-01-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Song, Li-Na; Wang, Wei-Guo
2012-08-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Prediction of Tide Height Using the Discrete Fourier Transform
Directory of Open Access Journals (Sweden)
Md. Towhiduzzaman
2016-12-01
Full Text Available In this study, I have investigated some aspects of astronomical tide and predicted tide time and height by different methods. This thesis deals with the prediction of height and time for both high and low waters of the ports set up in several places by discrete Fourier transform. I computed the tide height using Discrete Fourier Transform (DFT. The results are found to be in an agreement with the predicted data of others. By this work, we can predict the tide height of overall stations if the sample observed data are available for any kind of stations. I think that my work could be helpful to predict the tides over all stations where the observed data are available.
A simple scanning mirror mechanism for a Fourier transform spectrometer
Brasunas, John C.; Cushman, G. Mark
1998-04-01
We present a simple scanning mirror mechanism for a Fourier transform spectrometer, consisting of a voice coil actuator, a ball-bearing slide, and a single cube corner mirror or retroreflector. The use of a single cube corner reduces significantly the sensitivity of the Fourier transform spectrometer to the tilt of its moving mirror, enabling the simple mechanism. With simple velocity feedback using a linear velocity transducer, we achieve a scan speed stability of 2%-5% (root-mean-square) for scan speeds from 40 to 440 μm/s for a travel of 2.2 cm, corresponding to a spectral resolution of 0.06 cm-1. Fringe amplitude stability is about 5%. This scan mechanism was operated at standard temperature and pressure, but the relatively minute amount of lubricant in the ball-bearing slide may indicate possible operation under vacuum and/or cryogenic conditions.
Implementing quantum Fourier transform with integrated photonic devices
Tabia, Gelo Noel
2014-03-01
Many quantum algorithms that exhibit exponential speedup over their classical counterparts employ the quantum Fourier transform, which is used to solve interesting problems such as prime factorization. Meanwhile, nonclassical interference of single photons achieved on integrated platforms holds the promise of achieving large-scale quantum computation with multiport devices. An optical multiport device can be built to realize any quantum circuit as a sequence of unitary operations performed by beam splitters and phase shifters on path-encoded qudits. In this talk, I will present a recursive scheme for implementing quantum Fourier transform with a multimode interference photonic integrated circuit. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Fourier transform spectrometer based on Fabry-Perot interferometer.
Al-Saeed, Tarek A; Khalil, Diaa A
2016-07-10
We analyze the Fourier transform spectrometer based on a symmetric/asymmetric Fabry-Perot interferometer. In this spectrometer, the interferogram is obtained by recording the intensity as a function of the interferometer length. Then, we recover the spectrum by applying the discrete Fourier transform (DFT) directly on the interferogram. This technique results in spectral harmonic overlap and fictitious wavenumber components outside the original spectral range. For this purpose, in this work, we propose a second method to recover the spectrum. This method is based on expanding the DFT of the interferogram and the spectrum by a Haar or box function. By this second method, we recovered the spectrum and got rid of the fictitious spectral components and spectral harmonic overlap.
Perfect vortex beam: Fourier transformation of a Bessel beam.
Vaity, Pravin; Rusch, Leslie
2015-02-15
We derive a mathematical description of a perfect vortex beam as the Fourier transformation of a Bessel beam. Building on this development, we experimentally generate Bessel-Gauss beams of different orders and Fourier transform them to form perfect vortex beams. By controlling the radial wave vector of a Bessel-Gauss beam, we can control the ring radius of the generated beam. Our theoretical predictions match with the experimental results and also provide an explanation for previous published works. We find the perfect vortex resembles that of an orbital angular momentum (OAM) mode supported in annular profiled waveguides. Our prefect vortex beam generation method can be used to excite OAM modes in an annular core fiber.
Multiparty Quantum Secret Sharing Using Quantum Fourier Transform
Institute of Scientific and Technical Information of China (English)
HUANG Da-Zu; CHEN Zhi-Gang; GUO Ying
2009-01-01
A (n, n )-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform.In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert.Furthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant.Security analysis shows that our scheme is secure.Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.
On the Fourier transform of the greatest common divisor
van der Kamp, Peter H
2012-01-01
The discrete Fourier transform of the greatest common divisor is a multiplicative function that generalises both the gcd-sum function and Euler's totient function. On the one hand it is the Dirichlet convolution of the identity with Ramanujan's sum, and on the other hand it can be written as a generalised convolution product of the identity with the totient function. We show that this arithmetic function of two integers (a,m) counts the number of elements in the set of ordered pairs (i,j) such that i*j is equivalent to a modulo m. Furthermore we generalise a dozen known identities for the totient function, to identities which involve the discrete Fourier transform of the greatest common divisor, including its partial sums, and its Lambert series.
Scalable Fourier transform system for instantly structured illumination in lithography.
Ye, Yan; Xu, Fengchuan; Wei, Guojun; Xu, Yishen; Pu, Donglin; Chen, Linsen; Huang, Zhiwei
2017-05-15
We report the development of a unique scalable Fourier transform 4-f system for instantly structured illumination in lithography. In the 4-f system, coupled with a 1-D grating and a phase retarder, the ±1st order of diffracted light from the grating serve as coherent incident sources for creating interference patterns on the image plane. By adjusting the grating and the phase retarder, the interference fringes with consecutive frequencies, as well as their orientations and phase shifts, can be generated instantly within a constant interference area. We demonstrate that by adapting this scalable Fourier transform system into lithography, the pixelated nano-fringe arrays with arbitrary frequencies and orientations can be dynamically produced in the photoresist with high variation resolution, suggesting its promising application for large-area functional materials based on space-variant nanostructures in lithography.
On-chip photonic Fourier transform with surface plasmon polaritons
Institute of Scientific and Technical Information of China (English)
Shan Shan Kou; Guanghui Yuan; Qian wang; Luping Du; Eugeniu Balaur; Daohua Zhang; Dingyuan Tang
2016-01-01
The Fourier transform (FT),a cornerstone of optical processing,enables rapid evaluation of fundamental mathematical operations,such as derivatives and integrals.Conventionally,a converging lens performs an optical FT in free space when light passes through it.The speed of the transformation is limited by the thickness and the focal length of the lens.By usingthe wave nature of surface plasmon polaritons (SPPs),here we demonstrate that the FT can be implemented in a planar configuration with a minimal propagation distance of around 10 μm,resulting in an increase of speed by four to five orders of magnitude.The photonic FT was tested by synthesizing intricate SPP waves with their Fourier components.The reduced dimensionality in the minuscule device allows the future development of an ultrafast on-chip photonic information processing platform for large-scale optical computing.
Matrix-Vector Based Fast Fourier Transformations on SDR Architectures
Directory of Open Access Journals (Sweden)
Y. He
2008-05-01
Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.
Time-frequency representation measurement based on temporal Fourier transformation
Suen, Yifan; Xiao, Shaoqiu; Hao, Sumin; Zhao, Xiaoxiang; Xiong, Yigao; Liu, Shenye
2016-10-01
We propose a new scheme to physically realize the short-time Fourier transform (STFT) of chirped optical pulse using time-lens array that enables us to get time-frequency representation without using FFT algorithm. The time-lens based upon the four-wave mixing is used to perform the process of temporal Fourier transformation. Pump pulse is used for both providing the quadratic phase and being the window function of STFT. The idea of STFT is physically realized in our scheme. Simulations have been done to investigate performance of the time-frequency representation scheme (TFRS) in comparison with STFT using FFT algorithm. Optimal measurement of resolution in time and frequency has been discussed.
Magnetic suspension based Fourier Transform Infrared Spectrometer mechanism (FTIS)
Köker, Ingo; Langenbach, Harald; Schmid, Manfred; Lautier, Jean-Michel
2005-07-01
In the frame of an ESTEC technology contract the development of a Magnetically Suspended Fourier Transform Spectrometer Mechanism (FTIS) was carried out. The aim of the development is to avoid the issues found in mechanically suspended systems and to provide an active alignment and disturbance rejection capability for spectrometer applications. In the frame of FTIS an actively controlled suspension system based on the use of magnetic bearings was defined, developed and built as a demonstration model.
Homology of balanced complexes via the Fourier transform
Meshulam, Roy
2011-01-01
Let G_0,...,G_k be finite abelian groups and let G_0*...*G_k be the join of the 0-dimensional complexes G_i. We give a characterization of the integral k-coboundaries of subcomplexes of G_0*...*G_k in terms of the Fourier transform on the group G_0 \\times ... \\times G_k. This leads to an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.
Scaled Fractional Fourier Transform for Partially Coherent Beams
Institute of Scientific and Technical Information of China (English)
蔡阳健; 林强
2003-01-01
The definition of scaled fractional Fourier transform (SFRT) is extended to partially coherent beams based directly on the cross-spectral density. Based on this formula, an equivalent tensor ABCD law for the SFRT of partially coherent twisted anisotropic Gaussian-Schell model beams is derived. The derived formulae provide a powerful tool for analysing and calculating the SFRT of partially coherent beams. An application example is provided.
Fourier spectroscopy with a one-million-point transformation
Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.
1972-01-01
A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.
Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation
Institute of Scientific and Technical Information of China (English)
QIAN Xiao-Qing; SONG Tong-Qiang
2006-01-01
We deduce entangled fractional Fourier transformation (EFFT) for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n-mode entangled states of continuum variables in n-mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n-mode squeezed state.
CONCURRENT SPEECHES SEPARATION USING WRAPPED DISCRETE FOURIER TRANSFORM
Institute of Scientific and Technical Information of China (English)
Zhang Xichun; Li Yunjie; Zhang Jun; Wei Gang
2005-01-01
This letter proposes a new method for concurrent voiced speech separation. Firstly the Wrapped Discrete Fourier Transform (WDFT) is used to decompose the harmonic spectra of the mixed speeches. Then the individual speech is reconstructed by using the sinusoidal speech model. By taking advantage of the non-uniform frequency resolution of WDFT, harmonic spectra parameters can be estimated and separated accurately. Experimental results on mixed vowels separation show that the proposed method can recover the original speeches effectively.
Label-free identification of individual bacteria using Fourier transform light scattering
Jo, YoungJu; Kim, Min-hyeok; Park, HyunJoo; Kang, Suk-Jo; Park, YongKeun
2015-01-01
Rapid identification of bacterial species is crucial in medicine and food hygiene. In order to achieve rapid and label-free identification of bacterial species at the single bacterium level, we propose and experimentally demonstrate an optical method based on Fourier transform light scattering (FTLS) measurements and statistical classification. For individual rod-shaped bacteria belonging to four bacterial species (Listeria monocytogenes, Escherichia coli, Lactobacillus casei, and Bacillus subtilis), two-dimensional angle-resolved light scattering maps are precisely measured using FTLS technique. The scattering maps are then systematically analyzed, employing statistical classification in order to extract the unique fingerprint patterns for each species, so that a new unidentified bacterium can be identified by a single light scattering measurement. The single-bacterial and label-free nature of our method suggests wide applicability for rapid point-of-care bacterial diagnosis.
Fourier-transform Ghost Imaging with Hard X-rays
Yu, Hong; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming
2016-01-01
Knowledge gained through X-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. Atomic details of sample structures is achievable by X-ray crystallography, however, it is only applied to crystalline structures. Imaging techniques based on X-ray coherent diffraction or zone plates are capable of resolving the internal structure of non-crystalline materials at nanoscales, but it is still a challenge to achieve atomic resolution. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudo-thermal hard X-rays by measuring the second-order intensity correlation function of the light. We show that high resolution Fourier-transform diffraction pattern of a complex structure can be achieved at Fresnel region, and the amplitude and phase distributions of a sample in spatial domain can be retrieved successfully. The method of lensless X-ray Fourier-transform ghost imaging extends X-ray...
Mass spectral peak distortion due to Fourier transform signal processing.
Rockwood, Alan L; Erve, John C L
2014-12-01
Distortions of peaks can occur when one uses the standard method of signal processing of data from the Orbitrap and other FT-based methods of mass spectrometry. These distortions arise because the standard method of signal processing is not a linear process. If one adds two or more functions, such as time-dependent signals from a Fourier transform mass spectrometer and performs a linear operation on the sum, the result is the same as if the operation was performed on separate functions and the results added. If this relationship is not valid, the operation is non-linear and can produce unexpected and/or distorted results. Although the Fourier transform itself is a linear operator, the standard algorithm for processing spectra in Fourier transform-based methods include non-linear mathematical operators such that spectra processed by the standard algorithm may become distorted. The most serious consequence is that apparent abundances of the peaks in the spectrum may be incorrect. In light of these considerations, we performed theoretical modeling studies to illustrate several distortion effects that can be observed, including abundance distortions. In addition, we discuss experimental systems where these effects may manifest, including suggested systems for study that should demonstrate these peak distortions. Finally, we point to several examples in the literature where peak distortions may be rationalized by the phenomena presented here.
Fourier transform light scattering angular spectroscopy using digital inline holography.
Kim, Kyoohyun; Park, YongKeun
2012-10-01
A simple and practical method for measuring the angle-resolved light scattering (ARLS) from individual objects is reported. Employing the principle of inline holography and a Fourier transform light scattering technique, both the static and dynamic scattering patterns from individual micrometer-sized objects can be effectively and quantitatively obtained. First, the light scattering measurements were performed on individual polystyrene beads, from which the refractive index and diameter of each bead were retrieved. Also, the measurements of the static and dynamic light scattering from intact human red blood cells are demonstrated. Using the present method, an existing microscope can be directly transformed into a precise instrument for ARLS measurements.
[Continuum based fast Fourier transform processing of infrared spectrum].
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.
A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp.
Barlow, Euan; Mulholland, Anthony J
2011-11-01
The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.
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
Twin image elimination in digital holography by combination of Fourier transformations
Choudhury, Debesh
2013-01-01
We present a new technique for removing twin image in in-line digital Fourier holography using a combination of Fourier transformations. Instead of recording only a Fourier transform hologram of the object, we propose to record a combined Fourier transform hologram by simultaneously recording the hologram of the Fourier transform and the inverse Fourier transform of the object with suitable weighting coefficients. Twin image is eliminated by appropriate inverse combined Fourier transformation and proper choice of the weighting coefficients. An optical configuration is presented for recording combined Fourier transform holograms. Simulations demonstrate the feasibility of twin image elimination. The hologram reconstruction is sensitive to phase aberrations of the object, thereby opening a way for holographic phase sensing.
Lang, Jun
2012-07-01
In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by use of the fractional Fourier transform, but most of their encryptions are complex value and need digital hologram technique to record their encrypted information, which is inconvenience for digital transmission. In this paper, we first propose a novel reality-preserving multiple-parameter fractional Fourier transform which share real-valuedness outputs as well as most of the properties required for a fractional transform. Then we propose a new approach for image encryption based on the real-valuedness of the reality-preserving multiple-parameter fractional Fourier transform and the decorrelation property of chaotic maps in order to meet the requirements of the secure image transmission. In the proposed scheme, the image is encrypted by juxtaposition of sections of the image in the reality-preserving multiple-parameter fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.
Improved Spectral Representation for Birdcall Based on Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A novel spectral representation based on fractional Fourier transform (FrFT) is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart, and the spectrum gathering method is used to show the energy distribution related to the pitch frequency. The fixed transform order and adaptive orders for FrFT are tested. The fixed order can be obtained empirically or calculated according to the known chirp rate. The adaptive optimal orders are determined by using ambiguity function. Experimental results with birdcalls show that the FrFT-based spectrogram with an optimal transform order has higher resolution than its STFT-based counterpart, and the better performance can be achieved if adaptive orders are used.
Partial differential equation transform - Variational formulation and Fourier analysis.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-12-01
Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform's controllable frequency localization obtained by adjusting the order of PDEs. The
Numerical Analysis of Inhomogeneous Dielectric Waveguide Using Periodic Fourier Transform
Directory of Open Access Journals (Sweden)
M. Moradian
2007-01-01
Full Text Available A general method is introduced to obtain the propagation constants of the inhomogeneous dielectric waveguide. The periodic Fourier transform is applied to the normalized Maxwell's equations and makes the field components periodic. Then they are expanded in Fourier series. Finally, the trapezoidal rule is applied to approximate the convolution integral which leads to a set of coupled second-order differential equations that can be solved as an eigenvalue-eigenvector problem. The normalized propagation constant can be obtained as the square roots of the eigenvalues of the coefficient matrices. The proposed method is applied to the dielectric waveguide with a two-layered dielectric profile in the transverse direction, and the first four-confined TE modes are obtained. The propagation constants for the mentioned dielectric waveguide are also derived analytically and are then compared with those derived by the proposed method. Comparison of results shows the efficacy of the proposed method.
A transformada de Fourier em basic The Fourier transform (FFT in basic
Directory of Open Access Journals (Sweden)
Mauricio Gomes Constantino
2000-06-01
Full Text Available In this paper we describe three computer programs in Basic language about the Fourier transform (FFT which are available in the Internet site http://artemis.ffclrp.usp.br/SoftwareE.htm (in English or http://artemis.ffclrp.usp.br/softwareP.htm (in Portuguese since October 1998. Those are addresses to the Web Page of our Laboratory of Organic Synthesis. The programs can be downloaded and used by anyone who is interested on the subject. The texts, menus and captions in the programs are written in English.
Denoise in the pseudopolar grid Fourier space using exact inverse pseudopolar Fourier transform
Wei, Fan Jun
2015-01-01
In this paper I show a matrix method to calculate the exact inverse pseudopolar grid Fourier transform, and use this transform to do noise removals in the k space of pseudopolar grids. I apply the Gaussian filter to this pseudopolar grid and find the advantages of the noise removals are very excellent by using pseudopolar grid, and finally I show the Cartesian grid denoise for comparisons. The results present the signal to noise ratio and the variance are much better when doing noise removals in the pseudopolar grid than the Cartesian grid. The noise removals of pseudopolar grid or Cartesian grid are both in the k space, and all these noises are added in the real space.
Directional short-time Fourier transform of distributions
Directory of Open Access Journals (Sweden)
Katerina Hadzi-Velkova Saneva
2016-04-01
Full Text Available Abstract In this paper we consider the directional short-time Fourier transform (DSTFT that was introduced and investigated in (Giv in J. Math. Anal. Appl. 399:100-107, 2013. We analyze the DSTFT and its transpose on test function spaces S ( R n $\\mathcal {S}(\\mathbb {R}^{n}$ and S ( Y 2 n $\\mathcal {S}(\\mathbb {Y}^{2n}$ , respectively, and prove the continuity theorems on these spaces. Then the obtained results are used to extend the DSTFT to spaces of distributions.
Fourier Transform Infrared Spectroscopic Analysis of Protein Secondary Structures
Institute of Scientific and Technical Information of China (English)
Jilie KONG; Shaoning YU
2007-01-01
Infrared spectroscopy is one of the oldest and well established experimental techniques for the analysis of secondary structure of polypeptides and proteins. It is convenient, non-destructive, requires less sample preparation, and can be used under a wide variety of conditions. This review introduces the recent developments in Fourier transform infrared (FTIR) spectroscopy technique and its applications to protein structural studies. The experimental skills, data analysis, and correlations between the FTIR spectroscopic bands and protein secondary structure components are discussed. The applications of FTIR to the secondary structure analysis, conformational changes, structural dynamics and stability studies of proteins are also discussed.
THREE-VARIABLE ALTERNATING TRIGONOMETRIC FUNCTIONS AND CORRESPONDING FOURIER TRANSFORMS
Directory of Open Access Journals (Sweden)
Agata Bezubik
2016-06-01
Full Text Available The common trigonometric functions admit generalizations to any higher dimension, the symmetric, antisymmetric and alternating ones. In this paper, we restrict ourselves to three dimensional generalization only, focusing on alternating case in detail. Many specific properties of this new class of special functions useful in applications are studied. Such are the orthogonalities, both the continuous one and the discrete one on the 3D lattice of any density, corresponding discrete and continuous Fourier transforms, and others. Rapidly increasing precision of the interpolation with increasing density of the 3D lattice is shown in an example.
The discrete Fourier transform theory, algorithms and applications
Sundaraajan, D
2001-01-01
This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and
Hyperspectral imaging using the single-pixel Fourier transform technique
Jin, Senlin; Hui, Wangwei; Wang, Yunlong; Huang, Kaicheng; Shi, Qiushuai; Ying, Cuifeng; Liu, Dongqi; Ye, Qing; Zhou, Wenyuan; Tian, Jianguo
2017-03-01
Hyperspectral imaging technology is playing an increasingly important role in the fields of food analysis, medicine and biotechnology. To improve the speed of operation and increase the light throughput in a compact equipment structure, a Fourier transform hyperspectral imaging system based on a single-pixel technique is proposed in this study. Compared with current imaging spectrometry approaches, the proposed system has a wider spectral range (400-1100 nm), a better spectral resolution (1 nm) and requires fewer measurement data (a sample rate of 6.25%). The performance of this system was verified by its application to the non-destructive testing of potatoes.
Parallel image registration method for snapshot Fourier transform imaging spectroscopy
Zhang, Yu; Zhu, Shuaishuai; Lin, Jie; Zhu, Feijia; Jin, Peng
2017-08-01
A fast and precise registration method for multi-image snapshot Fourier transform imaging spectroscopy is proposed. This method accomplishes registration of an image array using the positional relationship between homologous points in the subimages, which are obtained offline by preregistration. Through the preregistration process, the registration problem is converted to the problem of using a registration matrix to interpolate subimages. Therefore, the hardware interpolation of graphics processing unit (GPU) texture memory, which has speed advantages for its parallel computing, can be used to significantly enhance computational efficiency. Compared to a central processing unit, GPU performance showed ˜27 times acceleration in registration efficiency.
Atomic transition probabilities of Ce I from Fourier transform spectra
Lawler, J. E.; Chisholm, J.; Nitz, D. E.; Wood, M. P.; Sobeck, J.; Den Hartog, E. A.
2010-04-01
Atomic transition probabilities for 2874 lines of the first spectrum of cerium (Ce I) are reported. These data are from new branching fraction measurements on Fourier transform spectra normalized with previously reported radiative lifetimes from time-resolved laser-induced-fluorescence measurements (Den Hartog et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 085006). The wavelength range of the data set is from 360 to 1500 nm. Comparisons are made to previous investigations which are less extensive. Accurate Ce i transition probabilities are needed for lighting research and development on metal halide high-intensity discharge lamps.
Multi-band Image Registration Method Based on Fourier Transform
Institute of Scientific and Technical Information of China (English)
庹红娅; 刘允才
2004-01-01
This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features,they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.
A high-resolution Fourier-transform infrared spectrometer.
Johnson, H. L.; Forbes, F. F.; Thompson, R. I.; Steinmetz , D. L.; Harris, O.
1973-01-01
We have developed a Fourier-transform infrared spectrometer having a resolution of 0.5/cm over the range of wavelength from 1 to 5.5 microns. It has been used to observe the sun over this wavelength range from a Lear Jet flying at an altitude of 14 km, and to observe a number of stars from the ground, using the 229-cm telescope of the Steward Observatory and the 152-cm aluminum-mirror telescope at the Observatorio Astronomico Nacional in the Sierra de San Pedro Martir, Baja California, Mexico. The solar spectrum is given here, while the ground-based spectra are being published separately.
Fourier-transform Raman spectroscopic study of human hair
Akhtar, W.; Edwards, H. G. M.; Farwell, D. W.; Nutbrown, M.
1997-07-01
Fourier-transform Raman microscopic spectra of normal, untreated and bleached hair fibres are presented. Vibrational assignments are made and differences are ascribed to the production of cysteic acid from cysteine. Changes in conformation associated with the disulphide bond in the keratotic component are noted from the ν(CSSC) vibrational modes at wave numbers near 500 cm -1. Raman spectra of hair root ends have also been investigated with a diminution in cysteine content being observed. Application of the technique to the biomedical investigation of healthy and diseased hair is proposed.
Ash melting behavior by Fourier transform infrared spectroscopy
Institute of Scientific and Technical Information of China (English)
LI Han-xu; QIU Xiao-sheng; TANG Yong-xin
2008-01-01
A Fourier Transform Infrared Spectroscopic (FTIR) method involving a Fe2O3 flux was used to learn how China's coal ash melts. The relationship between ash fusion temperature and chemical composition, as well as the effects of Fe2O3 flux on the ash fusion temperature were studied. The relationship between ash fusion temperature and chemical composition, mineralogical phases and functional groups was analyzed with the FTIR method. The results show that the ash fusion temperature is related to the location and transmittance of certain absorption peaks, which is of great significance for the study of ash behavior.
Beam profile for the Herschel-SPIRE Fourier transform spectrometer.
Makiwa, Gibion; Naylor, David A; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H D
2013-06-01
One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile.
Double passing the Kitt Peak 1-m Fourier transform spectrometer
Jennings, D. E.; Hubbard, R.; Brault, J. W.
1985-01-01
Attention is given to a simple technique for performing the conversion of the Kitt Peak 1-m Fourier transform spectrometer's dual input/output optical configuration to a double pass configuration that improves spectral resolution by a factor of 2. The modification is made by placing a flat mirror in the output beam from each cat's eye, retroreflecting the beams back through the cat's eyes to the first beam splitter. A single detector is placed at the second input port, which then becomes the instrument's output.
Particle field holography data reduction by Fourier transform analysis
Hess, Cecil F.; Trolinger, James D.
1987-01-01
The size distribution of a particle field hologram is obtained with a Fourier transformation of the Fraunhofer diffraction pattern of the reconstructed hologram. Off-axis absorption holograms of particle fields with known characteristics were obtained and analyzed with a commercially available instrument. The mean particle size of the reconstructed hologram was measured with an error of + or - 5 percent, while the distribution broadening was estimated within + or - 15 percent. Small sections of a pulsed laser hologram of a synthetic fuel spray were analyzed with this method thus yielding a spatially resolved size distribution. The method yields fast and accurate automated analysis of particle field holograms.
Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions
Morelli, Eugene A.
2013-01-01
A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.
2014-09-26
Marine Research. IS. K3LXOROS (Centinue en reveree side it necessa.yad Identlfy by blek nmer) ’-"luorescence Malysis J) Chlorophyll Auorescencej Marine... chlorophylls , carotenoids, and phycobilins. Chlorophyll a provides the universal link between these three groups since it is the only pigment present in...accessory pigments ( chlorophylls b and c, carotenoids, and phycobilins) and channels it into the photosynthetic process. This allows photosynthesis to
The Non-uniform Fast Fourier Transform in Computed Tomography
Tang, Junqi
2016-01-01
This project is aimed at designing the fast forward projection algorithm and also the backprojection algorithm for cone beam CT imaging systems with circular X-ray source trajectory. The principle of the designs is based on utilizing the potential computational efficiency which the Fourier Slice Theorem and the Non-uniform Fast Fourier Transform (NUFFT) will bring forth. In this Masters report, the detailed design of the NUFFT based forward projector including a novel 3D (derivative of) Radon space resampling method will be given. Meanwhile the complexity of the NUFFT based forward projector is analysed and compared with the non-Fourier based CT projector, and the advantage of the NUFFT based forward projection in terms of the computational efficiency is demonstrated in this report. Base on the design of the forward algorithm, the NUFFT based 3D direct reconstruction algorithm will be derived. The experiments will be taken to test the performance of the forward algorithm and the backprojection algorithm to sh...
Ordered fast fourier transforms on a massively parallel hypercube multiprocessor
Tong, Charles; Swarztrauber, Paul N.
1989-01-01
Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine.
Fractional Fourier transform of Cantor sets: further numerical study
Institute of Scientific and Technical Information of China (English)
Gao Qiong; Liao tian-He; Cui Yuan-Feng
2008-01-01
This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.
A high-resolution Fourier Transform Spectrometer for planetary spectroscopy
Cruikshank, D. P.; Sinton, W. M.
1973-01-01
The employment of a high-resolution Fourier Transform Spectrometer (FTS) is described for planetary and other astronomical spectroscopy in conjunction with the 88-inch telescope at Mauna Kea Observatory. The FTS system is designed for a broad range of uses, including double-beam laboratory spectroscopy, infrared gas chromatography, and nuclear magnetic resonance spectroscopy. The data system is well-suited to astronomical applications because of its great speed in acquiring and transforming data, and because of the enormous storage capability of the magnetic tape unit supplied with the system. The basic instrument is outlined 2nd some of the initial results from the first attempted use on the Mauna Kea 88-inch telescope are reported.
A Matrix Formulation of Discrete Chirp Fourier Transform Algorithms
Institute of Scientific and Technical Information of China (English)
Juan Pablo Soto Quiros; Domingo Rodriguez
2014-01-01
This work presents a computational matrix framework in terms of tensor signal algebra for the formulation of discrete chirp Fourier transform algorithms. These algorithms are used in this work to estimate the point target functions (impulse response functions) of multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) systems. This estimation technique is being studied as an alternative to the estimation of point target functions using the discrete cross-ambiguity function for certain types of environmental surveillance applications. The tensor signal algebra is presented as a mathematics environment composed of signal spaces, finite dimensional linear operators, and special matrices where algebraic methods are used to generate these signal transforms as computational estimators. Also, the tensor signal algebra contributes to analysis, design, and implementation of parallel algorithms. An instantiation of the framework was performed by using the MATLAB Parallel Computing Toolbox, where all the algorithms presented in this paper were implemented.
Fourier transform for fermionic systems and the spectral tensor network.
Ferris, Andrew J
2014-07-01
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.
Fast Fourier Transform Co-Processor (FFTC)- Towards Embedded GFLOPs
Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Wite, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland
2012-08-01
Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co- Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment.In frame of the ESA activity “Fast Fourier Transform DSP Co-processor (FFTC)” (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following:Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP.The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance.The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT- based processing tasks.A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses.The presentation will give and overview on the project, including the results of the validation of the FFTC ASIC prototypes.
Fast Fourier Transform Co-processor (FFTC), towards embedded GFLOPs
Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Witte, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland; Kopp, Nicholas
2012-10-01
Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co-Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment. In frame of the ESA activity "Fast Fourier Transform DSP Co-processor (FFTC)" (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following: • Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP. • The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance. The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT-based processing tasks. A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses. The paper will give an overview on the project, including the results of the validation of the FFTC ASIC prototypes.
Quantum process tomography of the quantum Fourier transform.
Weinstein, Yaakov S; Havel, Timothy F; Emerson, Joseph; Boulant, Nicolas; Saraceno, Marcos; Lloyd, Seth; Cory, David G
2004-10-01
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive-although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors which occurred over the full quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cumulative effect of small errors in the single qubit gates.
High Etendue Imaging Fourier Transform Spectrometer: initial results
Horton, Richard F.; Conger, Chris A.; Pelligrino, L. S.
1997-10-01
At the Denver meeting, last year, we presented the High Etendue Imaging Fourier Transform Spectrometer, (HEIFTS), theory and optical design. This device uses a new 'image plane interferometer' geometry to produce 'autocorrelation function modulation' in the image plane of a 2D imaging array, such that the phase offset of the modulation varies linearly across the image. As a 2D image is pushbroomed across the imaging, array, the record of an individual scene pixel is recorded for each autocorrelation phase offset. The 3D array of this data is processed to yield an 'autocorrelation function' data cube, which is Fourier transformed to yield a 'wavenumber' hyperspectral data curve. A phase I device has been demonstrated in the laboratory and initial results are presented. The significant increase in signal to noise ratio, which the HEIFTS optical design promises over conventional hyperspectral imaging schemes, has been simulated, and results will be discussed. A Phase II system is being prepared for initial field deployment, and will be described.
Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy
Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks
2016-06-01
Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described.
Integrated optics in an electrically scanned imaging Fourier transform spectrometer
Breckinridge, James B. (Inventor); Ocallaghan, Fred G. (Inventor)
1982-01-01
An efficient, lightweight and stable, Fourier transform spectrometer was developed. The mechanical slide mechanism needed to create a path difference was eliminated by the use of retro-reflecting mirrors in a monolithic interferometer assembly in which the mirrors are not at 90 degrees to the propagation vector of the radiation, but rather at a small angle. The resulting plane wave fronts create a double-sided inteferogram of the source irradiance distribution which is detected by a charge-coupled device image sensor array. The position of each CCD pixel in the array is an indication of the path difference between the two retro-reflecting mirrors in the monolithic optical structure. The Fourier transform of the signals generated by the image sensor provide the spectral irradiance distribution of the source. For imaging, the interferometer assembly scans the source of irradiation by moving the entire instrument, such as would occur if it was fixedly mounted to a moving platform, i.e., a spacecraft. During scanning, the entrace slot to the monolithic optical structure sends different pixels to corresponding interferograms detected by adjacent columns of pixels of the image sensor.
[Fourier Transform Spectrometer Based on Rotating Parallel-Mirror-Pair].
Zhao, Bao-wei; Xiangli, Bin; Cai, Qi-sheng; Lü, Qun-bo; Zhou, Jin-song
2015-11-01
In the temporally-modulated Fourier transform spectroscopy, the translational moving mirror is difficult to drive accurately, causing tilt and shear problems. While, a rotational moving mirror can solve these problems. A rotary Fourier transform spectrometer is recommanded in this paper. Its principle is analyzed and the optical path difference is deduced. Also, the constrains for engineering realization are presented. This spectrometer consists of one beamsplitter, two fixed mirrors, one rotating parallel mirror pair, a collimating lens, a collecting lens, and one detector. From it's principle, this spectrometer show a simple structure, and it is assembled and adjustmented easily because the two split light are interfered with each other after reflected through the same plane mirror; By calculating the expression of it's optical path difference, the spectrometer is easy to realize large optical path difference, meaning high spectral resolution; Through analyzing it's engineering design constraints and computer simulation, it is known that the spectrometer should get the high resolution sample by high-speed spinning motor, so it is easy to achieve precise motion control, good stability, fast measurement speed.
Fourier-Transform Ghost Imaging with Hard X Rays
Yu, Hong; Lu, Ronghua; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming
2016-09-01
Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available.
Dai, Guang-Ming
2006-02-15
The set of Fourier series is discussed following some discussion of Zernike polynomials. Fourier transforms of Zernike polynomials are derived that allow for relating Fourier series expansion coefficients to Zernike polynomial expansion coefficients. With iterative Fourier reconstruction, Zernike representations of wavefront aberrations can easily be obtained from wavefront derivative measurements.
Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail
2016-11-14
We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.
A Two-dimensional Genetic Algorithm Based on the Eno-Haar Wavelet Transform%一种基于Eno-Haar小波变换二维遗传算法
Institute of Scientific and Technical Information of China (English)
宋锦萍; 赵晨萍; 李登峰
2007-01-01
A two-dimensional genetic algorithm of wavelet coefficient is presented by using the ENO wavelet transform and the decomposed characterization of the two-dimensional Haar wavelet. And simulated by the ENO interpolation the article shows the affectivity and the superiority of this algorithm.
Statistical study of approximations to two dimensional inviscid turbulence
Energy Technology Data Exchange (ETDEWEB)
Glaz, H.M.
1977-09-01
A numerical technique is developed for studying the ergodic and mixing hypotheses for the dynamical systems arising from the truncated Fourier transformed two-dimensional inviscid Navier-Stokes equations. This method has the advantage of exactly conserving energy and entropy (i.e., total vorticity) in the inviscid case except for numerical error in solving the ordinary differential equations. The development of the mathematical model as an approximation to a real physical (turbulent) flow and the numerical results obtained are discussed.
2014-10-09
Radon -Fractional Fourier Transform and Its Application to Radar Maneuvering Target Detection Xiaolong Chen*, Fuqing Cai, Yu Cong, Jian Guan...unit (ARU) and Doppler frequency migration (DFM) effects. In this paper, a novel transform called the Radon -fractional Fourier transform (RFRFT) is...are carried out and the performances of different methods including MTD, FRFT, and the Radon -Fourier transform (RFT) are compared, which demonstrate
Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Fridberger, Anders; Ren, Tianying; Wang, Ruikang; Jacques, Steven L.; Nuttall, Alfred L.
2015-02-01
In this study, we measure the in vivo apical-turn vibrations of the guinea pig organ of Corti in both axial and radial directions using phase-sensitive Fourier domain optical coherence tomography. The apical turn in guinea pig cochlea has best frequencies around 100 - 500 Hz which are relevant for human speech. Prior measurements of vibrations in the guinea pig apex involved opening the otic capsule, which has been questioned on the basis of the resulting changes to cochlear hydrodynamics. Here this limitation is overcome by measuring the vibrations through bone without opening the otic capsule. Furthermore, we have significantly reduced the surgery needed to access the guinea pig apex in the axial direction by introducing a miniature mirror inside the bulla. The method and preliminary data are discussed in this article.
Energy Technology Data Exchange (ETDEWEB)
Bartosch, T. [Erlanger-Nuernberg Univ., Erlanger (Germany). Lehrstul fuer Nachrichtentechnik I; Seidl, D. [Seismologisches Zentralobservatorium Graefenberg, Erlanegen (Greece). Bundesanstalt fuer Geiwissenschaften und Rohstoffe
1999-06-01
Among a variety of spectrogram methods short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were selected to analyse transients in non-stationary signals. Depending on the properties of the tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli (Italy).
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi
2004-01-01
We find quantum mechanical Fourier-Hankel representation transform for an electron moving in a uniform magnetic field. The physical meaning of Fourier decomposition states of electron's coordinate eigenstate and the momentum eigenstate are revealed.
Charge reversal Fourier transform ion cyclotron resonance mass spectrometry.
Lobodin, Vladislav V; Savory, Joshua J; Kaiser, Nathan K; Dunk, Paul W; Marshall, Alan G
2013-02-01
We report the first charge reversal experiments performed by tandem-in-time rather than tandem-in-space MS/MS. Precursor odd-electron anions from fullerene C(60), and even-electron ions from 2,7-di-tert-butylfluorene-9-carboxylic acid and 3,3'-bicarbazole were converted into positive product ions ((-)CR(+)) inside the magnet of a Fourier transform ion cyclotron resonance mass spectrometer. Charge reversal was activated by irradiating precursor ions with high energy electrons or UV photons: the first reported use of those activation methods for charge reversal. We suggest that high energy electrons achieve charge reversal in one step as double electron transfer, whereas UV-activated (-)CR(+) takes place stepwise through two single electron transfers and formally corresponds to a neutralization-reionization ((-)NR(+)) experiment.
Observing Extended Sources with the \\Herschel SPIRE Fourier Transform Spectrometer
Wu, Ronin; Etxaluze, Mireya; Makiwa, Gibion; Naylor, David A; Salji, Carl; Swinyard, Bruce M; Ferlet, Marc; van der Wiel, Matthijs H D; Smith, Anthony J; Fulton, Trevor; Griffin, Matt J; Baluteau, Jean-Paul; Benielli, Dominique; Glenn, Jason; Hopwood, Rosalind; Imhof, Peter; Lim, Tanya; Lu, Nanyao; Panuzzo, Pasquale; Pearson, Chris; Sidher, Sunil; Valtchanov, Ivan
2013-01-01
The Spectral and Photometric Imaging Receiver (SPIRE) on the European Space Agency's Herschel Space Observatory utilizes a pioneering design for its imaging spectrometer in the form of a Fourier Transform Spectrometer (FTS). The standard FTS data reduction and calibration schemes are aimed at objects with either a spatial extent much larger than the beam size or a source that can be approximated as a point source within the beam. However, when sources are of intermediate spatial extent, neither of these calibrations schemes is appropriate and both the spatial response of the instrument and the source's light profile must be taken into account and the coupling between them explicitly derived. To that end, we derive the necessary corrections using an observed spectrum of a fully extended source with the beam profile and the source's light profile taken into account. We apply the derived correction to several observations of planets and compare the corrected spectra with their spectral models to study the beam c...
Seismic Shear Energy Reflection By Radon-Fourier Transform
Directory of Open Access Journals (Sweden)
Malik Umairia
2016-01-01
Full Text Available Seismic waves split in an anisotropic medium, instead of rotating horizontal component to principal direction, Radon-Fourier is derived to observe the signature of shear wave reflection. Synthetic model with fracture is built and discretized using finite difference scheme for spatial and time domain. Common depth point (CDP with single shot gives traces and automatic gain is preprocessed before Radon Transform (RT, a filtering technique gives radon domain. It makes easier to observe fractures at specific incidence and improves its quality in some way by removing the noise. A comparison of synthetic data and BF-data is performed on the basis of root means square error (RMS values. The RMS error is minimum at the 10th trace in radon domain.
Mid-Infrared Frequency Comb Fourier Transform Spectrometer
Adler, Florian; Foltynowicz, Aleksandra; Cossel, Kevin C; Briles, Travis C; Hartl, Ingmar; Ye, Jun
2010-01-01
Optical frequency-comb-based-high-resolution spectrometers offer enormous potential for spectroscopic applications. Although various implementations have been demonstrated, the lack of suitable mid-infrared comb sources has impeded explorations of molecular fingerprinting. Here we present for the first time a frequency-comb Fourier transform spectrometer operating in the 2100-to-3700-cm-1 spectral region that allows fast and simultaneous acquisitions of broadband absorption spectra with up to 0.0056 cm-1 resolution. We demonstrate part-per-billion detection limits in 30 seconds of integration time for various important molecules including methane, ethane, isoprene, and nitrous oxide. Our system enables precise concentration measurements even in gas mixtures that exhibit continuous absorption bands, and it allows detection of molecules at levels below the noise floor via simultaneous analysis of multiple spectral features. This system represents a near real-time, high-resolution, high-bandwidth mid-infrared sp...
Persian Sign Language Recognition Using Radial Distance and Fourier Transform
Directory of Open Access Journals (Sweden)
Bahare Jalilian
2013-11-01
Full Text Available This paper provides a novel hand gesture recognition method to recognize 32 static signs of the Persian Sign Language (PSL alphabets. Accurate hand segmentation is the first and important step in sign language recognition systems. Here, we propose a method for hand segmentation that helps to build a better vision based sign language recognition system. The proposed method is based on YCbCr color space, single Gaussian model and Bayes rule. It detects region of hand in complex background and non-uniform illumination. Hand gesture features are extracted by radial distance and Fourier transform. Finally, the Euclidean distanceis used to compute the similarity between the input signs and all training feature vectors in the database. The system is tested on 480 posture images of the PSL, 15 images for each 32 signs. Experimental results show that our approach is capable to recognize all 32 PSL alphabets with 95.62% recognition rate.
A rheumatoid arthritis study by Fourier transform infrared spectroscopy
Carvalho, Carolina S.; Silva, Ana Carla A.; Santos, Tatiano J. P. S.; Martin, Airton A.; dos Santos Fernandes, Ana Célia; Andrade, Luís E.; Raniero, Leandro
2012-01-01
Rheumatoid arthritis is a systemic inflammatory disease of unknown causes and a new methods to identify it in early stages are needed. The main purpose of this work is the biochemical differentiation of sera between normal and RA patients, through the establishment of a statistical method that can be appropriately used for serological analysis. The human sera from 39 healthy donors and 39 rheumatics donors were collected and analyzed by Fourier Transform Infrared Spectroscopy. The results show significant spectral variations with p<0.05 in regions corresponding to protein, lipids and immunoglobulins. The technique of latex particles, coated with human IgG and monoclonal anti-CRP by indirect agglutination known as FR and CRP, was performed to confirm possible false-negative results within the groups, facilitating the statistical interpretation and validation of the technique.
Lamellar grating optimization for miniaturized fourier transform spectrometers.
Ferhanoglu, Onur; Seren, Hüseyin R; Lüttjohann, Stephan; Urey, Hakan
2009-11-09
Microfabricated Lamellar grating interferometers (LGI) require fewer components compared to Michelson interferotemeters and offer compact and broadband Fourier transform spectrometers (FTS) with good spectral resolution, high speed and high efficiency. This study presents the fundamental equations that govern the performance and limitations of LGI based FTS systems. Simulations and experiments were conducted to demonstrate and explain the periodic nature of the interferogram envelope due to Talbot image formation. Simulations reveal that the grating period should be chosen large enough to avoid Talbot phase reversal at the expense of mixing of the diffraction orders at the detector. Optimal LGI grating period selection depends on a number of system parameters and requires compromises in spectral resolution and signal-to-bias ratio (SBR) of the interferogram within the spectral range of interest. New analytical equations are derived for spectral resolution and SBR of LGI based FTS systems.
Spatially Resolved Fourier Transform Spectroscopy in the Extreme Ultraviolet
Jansen, G S M; Freisem, L; Eikema, K S E; Witte, S
2016-01-01
Coherent extreme ultraviolet (XUV) radiation produced by table-top high-harmonic generation (HHG) sources provides a wealth of possibilities in research areas ranging from attosecond physics to high resolution coherent imaging. However, it remains challenging to fully exploit the coherence of such sources for interferometry and Fourier transform spectroscopy (FTS). This is due to the need for a measurement system that is stable at the level of a wavelength fraction, yet allowing a controlled scanning of time delays. Here we demonstrate XUV interferometry and FTS in the 17-55 nm wavelength range using an ultrastable common-path interferometer suitable for high-intensity laser pulses that drive the HHG process. This approach enables the generation of fully coherent XUV pulse pairs with sub-attosecond timing variation, tunable time delay and a clean Gaussian spatial mode profile. We demonstrate the capabilities of our XUV interferometer by performing spatially resolved FTS on a thin film composed of titanium and...
The RC Circuit: An Approach with Fourier Transforms
Indian Academy of Sciences (India)
2016-11-01
In this article we shall mathematically analyse the Resistor-Capacitor (RC) circuit with the help of Fourier transforms(FT). This very general technique gives us a lot of insight intosolving first order differential equations with source terms dependingon time. In itself, the RC circuit is by far the mostcommonplace entity in modern electronics. But the method ofFT is not the accepted custom for an electronic engineer, whois probably more comfortable working with complex impedancesand phasors while solving problems in network analysis.In fact, what is used much more extensively is the Laplacetransform. But a lot of things, (including the complex impedanceitself, and some insight into complex analysis) can be understoodbetter if we use the FT approach to solve the differentialequations that come up in network analysis. The use of FTcomes smoothly from first principles – precisely what we setout to demonstrate here.
Initial Results from the USNO Dispersed Fourier Transform Spectrograph
Hajian, A R; Cenko, A T; Olling, R P; Mozurkewich, D; Armstrong, J T; Pohl, B; Petrossian, S; Knuth, K H; Hindsley, R B; Murison, M; Efroimsky, M; Dantowitz, R; Kozubal, M; Currie, D G; Nordgren, T E; Tycner, C; McMillan, R S; Hajian, Arsen R.; Behr, Bradford B.; Cenko, Andrew T.; Olling, Robert P.; Mozurkewich, David; Pohl, Brian; Petrossian, Sevan; Knuth, Kevin H.; Hindsley, Robert B.; Murison, Marc; Efroimsky, Michael; Dantowitz, Ronald; Kozubal, Marek; Currie, Douglas G.; Nordgren, Tyler E.; Tycner, Christopher; Millan, Robert S. Mc
2006-01-01
We have designed and constructed a ``dispersed Fourier Transform Spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity disadvantage of a conventional FTS for high resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a simple and inexpensive laser metrology system, which enables very precise calibration of the interferometer wavelength scale. The fusion of interferometric and dispersive technologies with a laser metrology system yields an instrument well-suited to stellar spectroscopy, velocimetry, and extrasolar planet detection, which is competitive with existing high-resolution, high accuracy stellar spectrometers. In this paper, we describe the design of our prototype dFTS, explain the algorithm we use to efficiently reconstruct a broadband spectrum from a sequence of narrowband i...
Wide-Field Detected Fourier Transform CARS Microscopy
Duarte, Alex Soares; Schnedermann, Christoph; Kukura, Philipp
2016-11-01
We present a wide-field imaging implementation of Fourier transform coherent anti-Stokes Raman scattering (wide-field detected FT-CARS) microscopy capable of acquiring high-contrast label-free but chemically specific images over the full vibrational ‘fingerprint’ region, suitable for a large field of view. Rapid resonant mechanical scanning of the illumination beam coupled with highly sensitive, camera-based detection of the CARS signal allows for fast and direct hyperspectral wide-field image acquisition, while minimizing sample damage. Intrinsic to FT-CARS microscopy, the ability to control the range of time-delays between pump and probe pulses allows for fine tuning of spectral resolution, bandwidth and imaging speed while maintaining full duty cycle. We outline the basic principles of wide-field detected FT-CARS microscopy and demonstrate how it can be used as a sensitive optical probe for chemically specific Raman imaging.
Microscope system with on axis programmable Fourier transform filtering
Martínez, José Luis; García-Martínez, Pascuala; Moreno, Ignacio
2017-02-01
We propose an on-axis microscope optical system to implement programmable optical Fourier transform image processing operations, taking advantage of phase and polarization modulation of a liquid crystal on silicon (LCOS) display. We use a Hamamatsu spatial light modulator (SLM), free of flickering, which therefore can be tuned to fully eliminate the zero order component of the encoded diffractive filter. This allows the realization of filtering operation on axis (as opposed to other systems in the literature that require operating off axis), therefore making use of the full space bandwidth provided by the SLM. The system is first demonstrated by implementing different optical processing operations based on phase-only blazed gratings such as phase contrast, band-pass filtering, or additive and substractive imaging. Then, a simple Differential interference contrast (DIC) imaging is obtained changing to a polarization modulation scheme, achieved simply by selecting a different incident state of polarization on the incident beam.
Motion saliency detection using a temporal fourier transform
Chen, Zhe; Wang, Xin; Sun, Zhen; Wang, Zhijian
2016-06-01
Motion saliency detection aims at detecting the dynamic semantic regions in a video sequence. It is very important for many vision tasks. This paper proposes a new type of motion saliency detection method, Temporal Fourier Transform, for fast motion saliency detection. Different from conventional motion saliency detection methods that use complex mathematical models or features, variations in the phase spectrum of consecutive frames are identified and extracted as the key to obtaining the location of salient motion. As all the calculation is made on the temporal frequency spectrum, our model is independent of features, background models, or other forms of prior knowledge about scenes. The benefits of the proposed approach are evaluated for various videos where the number of moving objects, illumination, and background are all different. Compared with some the state of the art methods, our method achieves both good accuracy and fast computation.
High-Throughput Screening Using Fourier-Transform Infrared Imaging
Directory of Open Access Journals (Sweden)
Erdem Sasmaz
2015-06-01
Full Text Available Efficient parallel screening of combinatorial libraries is one of the most challenging aspects of the high-throughput (HT heterogeneous catalysis workflow. Today, a number of methods have been used in HT catalyst studies, including various optical, mass-spectrometry, and gas-chromatography techniques. Of these, rapid-scanning Fourier-transform infrared (FTIR imaging is one of the fastest and most versatile screening techniques. Here, the new design of the 16-channel HT reactor is presented and test results for its accuracy and reproducibility are shown. The performance of the system was evaluated through the oxidation of CO over commercial Pd/Al2O3 and cobalt oxide nanoparticles synthesized with different reducer-reductant molar ratios, surfactant types, metal and surfactant concentrations, synthesis temperatures, and ramp rates.
Short-time Fourier transform laser Doppler holography
Atlan, Michael
2012-01-01
We report a demonstration of laser Doppler holography at a sustained acquisition rate of 250 Hz on a 1 Megapixel complementary metal-oxide-semiconductor (CMOS) sensor array and image display at 10 Hz frame rate. The holograms are optically acquired in off-axis configuration, with a frequency-shifted reference beam. Wide-field imaging of optical fluctuations in a 250 Hz frequency band is achieved by turning time-domain samplings to the dual domain via short-time temporal Fourier transformation. The measurement band can be positioned freely within the low radio-frequency spectrum by tuning the frequency of the reference beam in real-time. Video-rate image rendering is achieved by streamline image processing with commodity computer graphics hardware. This experimental scheme is validated by a non-contact vibrometry experiment.
Instrument concept of the imaging Fourier transform spectrometer GLORIA
Directory of Open Access Journals (Sweden)
F. Friedl-Vallon
2014-10-01
Full Text Available The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the upper troposphere/lower stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated into a gimbal. The assembly can be mounted in the belly pod of the German High Altitude and Long Range research aircraft (HALO and in instrument bays of the Russian M55 Geophysica. Measurements are made in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, and the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition, the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
Optical design of the ATMOS Fourier transform spectrometer
Abel, I. R.; Reynolds, B. R.; Breckinridge, J. B.; Pritchard, J.
1979-01-01
The optical system design of the ATMOS Fourier transform spectrometer to be operated from Spacelab for the measurement of stratospheric trace molecules is described. The design contains features which can achieve the required fringe contrast of 80% and spectral resolution of 0.02/cm over a spectral range of 2-16 microns. In particular, the design is based on the following features which alleviate the usual requirements for alignment precision: (1) 'cat's eye' mirror configuration in the two arms of the interferometer for retroreflection stability, (2) tilt-compensated system of beamsplitter, compensator, and fold mirrors for wavefront directional stability, (3) paraboloidal 'cat's eye' primary mirror for wavefront stability against shear, (4) rotatable compensator for matching chromatic dispersion, and (5) wedged refractive components to avoid channel spectra due to the Fabry-Perot effect.
Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)
Best, F. A.; Revercomb, H. E.; Bingham, G. E.; Knuteson, R. O.; Tobin, D. C.; LaPorte, D. D.; Smith, W. L.
2001-01-01
The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.
A direct digital synthesis chirped pulse Fourier transform microwave spectrometer.
Finneran, Ian A; Holland, Daniel B; Carroll, P Brandon; Blake, Geoffrey A
2013-08-01
Chirped pulse Fourier transform microwave (CP-FTMW) spectrometers have become the instrument of choice for acquiring rotational spectra, due to their high sensitivity, fast acquisition rate, and large bandwidth. Here we present the design and capabilities of a recently constructed CP-FTMW spectrometer using direct digital synthesis (DDS) as a new method for chirped pulse generation, through both a suite of extensive microwave characterizations and deep averaging of the 10-14 GHz spectrum of jet-cooled acetone. The use of DDS is more suited for in situ applications of CP-FTMW spectroscopy, as it reduces the size, weight, and power consumption of the chirp generation segment of the spectrometer all by more than an order of magnitude, while matching the performance of traditional designs. The performance of the instrument was further improved by the use of a high speed digitizer with dedicated signal averaging electronics, which facilitates a data acquisition rate of 2.1 kHz.
A Fourier transform Raman spectrometer with visible laser excitation
Dzsaber, S; Bernáth, B; Gyüre, B; Fehér, T; Kramberger, C; Pichler, T; Simon, F
2014-01-01
We present the development and performance of a Fourier transformation (FT) based Raman spectrometer working with visible laser (532 nm) excitation. It is generally thought that FT-Raman spectrometers are not viable in the visible range where shot-noise limits the detector performance and therein they are outperformed by grating based, dispersive ones. We show that contrary to this common belief, the recent advances of high-performance interference filters makes the FT-Raman design a valid alternative to dispersive Raman spectrometers for samples which do not luminesce. We critically compare the performance of our spectrometer to two dispersive ones: a home-built single channel and a state-of-the-art CCD based instruments. We demonstrate a similar or even better sensitivity than the CCD based dispersive spectrometer particularly when the laser power density is considered. The instrument possesses all the known advantages of the FT principle of spectral accuracy, high throughput, and economic design. We also d...
[Influence of collimation system on static Fourier transform spectrometer].
Jiang, Cheng-Zhi; Liang, Jing-Qiu; Liang, Zhong-Zhu; Sun, Qiang; Wang, Wei-Biao
2014-01-01
Collimation system provides collimated light for the static Fourier-transform spectroscopy (SFTS). Its quality is crucial to the signal to noise ratio (SNR) of SFTS. In the present paper, the physical model of SFTS was established based on the Fresnel diffraction theory by means of numerical software. The influence of collimation system on the SFTS was discussed in detail focusing on the aberrations of collimation lens and the quality of extended source. The results of simulation show that the influences of different kinds of aberrations on SNR take on obvious regularity, and in particular, the influences of off-axis aberrations on SNR are closely related to the location of off-axis point source. Finally the extended source's maximum radius allowed was obtained by simulation, which equals to 0.65 mm. The discussion results will be used for the design of collimation system.
Indirect Fourier transform in the context of statistical inference.
Muthig, Michael; Prévost, Sylvain; Orglmeister, Reinhold; Gradzielski, Michael
2016-09-01
Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.
OCTAD-S: digital fast Fourier transform spectrometers by FPGA
Iwai, Kazumasa; Kubo, Yûki; Ishibashi, Hiromitsu; Naoi, Takahiro; Harada, Kenichi; Ema, Kenji; Hayashi, Yoshinori; Chikahiro, Yuichi
2017-07-01
We have developed a digital fast Fourier transform spectrometer made of an analog-to-digital converter (ADC) and a field-programmable gate array (FPGA). The base instrument has independent ADC and FPGA modules, which allow us to implement different spectrometers in a relatively easy manner. Two types of spectrometers have been instrumented: one with 4.096 GS/s sampling speed and 2048 frequency channels and the other with 2.048 GS/s sampling speed and 32,768 frequency channels. The signal processing in these spectrometers has no dead time, and the accumulated spectra are recorded in external media every 8 ms. A direct sampling spectroscopy up to 8 GHz is achieved by a microwave track-and-hold circuit, which can reduce the analog receiver in front of the spectrometer. Highly stable spectroscopy with a wide dynamic range was demonstrated in a series of laboratory experiments and test observations of solar radio bursts.
Radix-3 Algorithm for Realization of Discrete Fourier Transform
Directory of Open Access Journals (Sweden)
M.Narayan Murty
2016-07-01
Full Text Available In this paper, a new radix-3 algorithm for realization of discrete Fourier transform (DFT of length N = 3m (m = 1, 2, 3,... is presented. The DFT of length N can be realized from three DFT sequences, each of length N/3. If the input signal has length N, direct calculation of DFT requires O (N 2 complex multiplications (4N 2 real multiplications and some additions. This radix-3 algorithm reduces the number of multiplications required for realizing DFT. For example, the number of complex multiplications required for realizing 9-point DFT using the proposed radix-3 algorithm is 60. Thus, saving in time can be achieved in the realization of proposed algorithm.
Transformed Fourier and Fick equations for the control of heat and mass diffusion
Directory of Open Access Journals (Sweden)
S. Guenneau
2015-05-01
Full Text Available We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves, the temperature (or mass concentration inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.
Otsuka, Makoto; Fukui, Yuya; Ozaki, Yukihiro
2009-03-01
The purpose of this study was to evaluate the enzymatic stability of colloidal trypsin powder during heating in a solid-state by using Fourier transform infrared (FT-IR) spectra with chemoinformatics and generalized two-dimensional (2D) correlation spectroscopy. Colloidal crystalline trypsin powders were heated using differential scanning calorimetry. The enzymatic activity of trypsin was assayed by the kinetic degradation method. Spectra of 10 calibration sample sets were recorded three times with a FT-IR spectrometer. The maximum intensity at 1634cm(-1) of FT-IR spectra and enzymatic activity of trypsin decreased as the temperature increased. The FT-IR spectra of trypsin samples were analyzed by a principal component regression analysis (PCR). A plot of the calibration data obtained was made between the actual and predicted trypsin activity based on a two-component model with gamma(2)=0.962. On the other hand, a 2D method was applied to FT-IR spectra of heat-treated trypsin. The result was consistent with that of the chemoinformetrical method. The results for deactivation of colloidal trypsin powder by heat-treatment indicated that nano-structure of crystalline trypsin changed by heating reflecting that the beta-sheet was mainly transformed, since the peak at 1634cm(-1) decreased with dehydration. The FT-IR chemoinformetrical method allows for a solid-state quantitative analysis of the bioactivity of the bulk powder of trypsin during drying.
Transformed Fourier and Fick equations for the control of heat and mass diffusion
Guenneau, S.; Petiteau, D.; Zerrad, M.; Amra, C.; Puvirajesinghe, T.
2015-05-01
We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves, the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.
Adaptive Controller for Compact Fourier Transform Spectrometer with Space Applications
Keymeulen, D.; Yiu, P.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.; Conroy, M.
2014-12-01
Here we present noise mitigation techniques developed as part of an adaptive controller for a very compact Compositional InfraRed Interferometric Spectrometer (CIRIS) implemented on a stand-alone field programmable gate array (FPGA) architecture with emphasis on space applications in high radiation environments such as Europa. CIRIS is a novel take on traditional Fourier Transform Spectrometers (FTS) and replaces linearly moving mirrors (characteristic of Michelson interferometers) with a constant-velocity rotating refractor to variably phase shift and alter the path length of incoming light. The design eschews a monochromatic reference laser typically used for sampling clock generation and instead utilizes constant time-sampling via internally generated clocks. This allows for a compact and robust device, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 µm) on planetary exploration missions. The instrument's embedded microcontroller is implemented on a VIRTEX-5 FPGA and a PowerPC with the aim of sampling the instrument's detector and optical rotary encoder in order to construct interferograms. Subsequent onboard signal processing provides spectral immunity from the noise effects introduced by the compact design's removal of a reference laser and by the radiation encountered during space flight to destinations such as Europa. A variety of signal processing techniques including resampling, radiation peak removal, Fast Fourier Transform (FFT), spectral feature alignment, dispersion correction and calibration processes are applied to compose the sample spectrum in real-time with signal-to-noise-ratio (SNR) performance comparable to laser-based FTS designs in radiation-free environments. The instrument's FPGA controller is demonstrated with the FTS to characterize its noise mitigation techniques and highlight its suitability for implementation in space systems.
Institute of Scientific and Technical Information of China (English)
Chujun Zheng; Peng Han; Hongsen Chang
2006-01-01
@@ A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π,and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.
A Two-Dimensional Double Dispersed Hadamard Transform Spectrometer%双色散二维阿达玛变换光谱仪
Institute of Scientific and Technical Information of China (English)
刘佳; 石磊; 李凯; 郑信文; 曾立波; 吴琼水
2012-01-01
设计了一种双色散二维调制的阿达玛变换光谱仪,利用光栅在水平方向的谱级色散和棱镜在垂直方向的谱线色散进行二维分光.与传统的二维光谱CCD探测方法不同,该设计独辟蹊径,采用面阵数字微镜对二维光谱进行阿达玛调制,并利用单点式检测器进行光信号的检测.理论计算及光学仿真表明,与传统的二维光谱探测仪器相比,该光谱仪不仅具有高的分辨率,同时还具有很高的信噪比.%A kind of two-dimensional hadamard transform spectrometer was developed. A grating was used for chromatic dispersion of orders and a prism was used for spectral dispersion. Quite different from traditional CCD detection method, a digital micromirror device (DMD) was applied for optical modulation, and a simple point detector was used as the sensor. Compared with traditional two-dimensional spectrometer, it has the advantage of high resolution and signal-noise-ratio, which was proved by theoretical calculation and computer simulation.
仿射变换对二维蕨类形状控制的研究%Affine Transformation for Two-dimensional Fern Shape Control
Institute of Scientific and Technical Information of China (English)
包晔
2012-01-01
通过对仿射变换矩阵系数进行调节分析，研究仿射变换矩阵对二维蕨类形状控制的作用，并分析仿射变换矩阵的各个系数对二维蕨类植物生成的形状和弯曲方向的影响，给出了蕨类植物形状控制方法，证明能较好地控制蕨类植物叶片的生长方向和形状，但还不能够控制叶片生成的精确角度和叶片的精确大小．%In this paper, affine transformation matrix of two-dimensional fern shape control is analyzed, and the affine trans- formation matrix coefficients on the shape generated by the two-dimensional ferns are adjusted and the bending directions are given. Better controlling approaches to the direction and shape of fern leaves are put forward in detail.
2014-09-18
DEVELOPMENT OF IMAGING FOURIER -TRANSFORM SPECTROSCOPY FOR THE CHARACTERIZATION OF TURBULENT JET FLAMES DISSERTATION Jacob L. Harley, Captain, USAF...work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENP-DS-14-S-13 DEVELOPMENT OF IMAGING FOURIER -TRANSFORM...DISTRIBUTION UNLIMITED AFIT-ENP-DS-14-S-13 DEVELOPMENT OF IMAGING FOURIER -TRANSFORM SPECTROSCOPY FOR THE CHARACTERIZATION OF TURBULENT JET FLAMES Jacob L
Fourier transform Raman approach to structural correlation in hemoglobin derivatives.
Venkatesh, B; Ramasamy, S; Mylrajan, M; Asokan, R; Manoharan, P T; Rifkind, J M
1999-07-01
In order to obtain information on the structural aspects of hemoglobin (Hb), Fourier transform Raman (FT-R) measurements on various ferrous, ferric derivatives and nickel reconstituted Hb (NiHb) has been made. FT-R spectra for these derivatives were obtained by laser excitation in the near infrared region (NIR) (1064 nm) whereby the wave-number region (600-1700 cm-1) related to both porphyrin ring modes and some globin modes were monitored. Comparison of various modes was made based on previous resonance Raman (RR) results. The wave-number shifts with respect to changes in oxidation state and spin state are very similar to those observed by RR. Additional bands at 1654, 1459, and 1003 cm-1 for deoxyHb and at 1656, 1454, and 1004 cm-1 for oxy Hb can be correlated to globin modes. The shift in the position of these bands for the binding of oxygen can be related to changes in conformation during the transformation. The presence of two distinct sites in NiHb could be monitored by the use of FT-R technique.
[Biological Process Oriented Online Fourier Transform Infrared Spectrometer].
Xie, Fei; Wu, Qiong-shui; Zeng, Li-bo
2015-08-01
An online Fourier Transform Infrared Spectrometer and an ATR (Attenuated Total Reflection) probe, specifically at the application of real time measurement of the reaction substrate concentration in biological processes, were designed. (1) The spectrometer combined the theories of double cube-corner reflectors and flat mirror, which created a kind of high performance interferometer system. The light path folding way was utilized to makes the interferometer compact structure. Adopting double cube-corner reflectors, greatly reduces the influence of factors in the process of moving mirror movement such as rotation, tilt, etc. The parallelogram oscillation flexible support device was utilized to support the moving mirror moves. It cancelled the friction and vibration during mirror moving, and ensures the smooth operation. The ZnSe splitter significantly improved the hardware reliability in high moisture environment. The method of 60° entrance to light splitter improves the luminous flux. (2) An ATR in situ measuring probe with simple structure, large-flux, economical and practical character was designed in this article. The transmission of incident light and the light output utilized the infrared pipe with large diameter and innerplanted-high plating membrane, which conducted for the infrared transmission media of ATR probe. It greatly reduced the energy loss of infrared light after multiple reflection on the inner wall of the light pipe. Therefore, the ATR probe obtained high flux, improved the signal strength, which make the signal detected easily. Finally, the high sensitivity of MCT (Mercury Cadmium Telluride) detector was utilized to realize infrared interference signal collection, and improved the data quality of detection. The test results showed that the system yields the advantages of perfect moisture-proof performance, luminous flux, online measurement, etc. The designed online Fourier infrared spectrometer can real-time measured common reactant substrates
Institute of Scientific and Technical Information of China (English)
Wang Chuandan; Zhang Zhongpei; Li Shaoqian
2007-01-01
The method of FRactional Fourier Transform (FRFT) is introduced to Transform Domain Communication System (TDCS) for signal transforming in the paper after theoretical analysis. The method yields optimal Basis Function (BF) by FRFT with optimal transform angle. The TDCS using the proposed method has wider usable spectrum, stronger robustness and better ability of anti non-stationary jamming than using usual methods, such as Fourier Transform (FT), Auto Regressive (AR), Wavelet Transform (WT), etc. The main simulation results are as follows. First, the Bit Error Rate (BER) Pb is close to theoretical bound of no jamming no matter in single tone or in linear chirp interference. Second, the interference-to-signal ratio J/E is at least 12dB more than that of Direct Spread Spectrum System (DSSS) under the same BER if the spectrum hopping-to-signal ratio is 1:20 in chirp plus hopping interfering. Third, the Eb/No (when estimation difference is 90% between transmitter and receiver) is about 3.5dB or about 0.5dB (when estimation difference is 10% between transmitter and receiver) more than that of theoretical result when no estimation difference under Pb = 10-2.
Institute of Scientific and Technical Information of China (English)
魏鑫宇; 冯立新; 张国艳
2012-01-01
Based on the trigonometric interpolation theory, a function is approximated by its trigonometric interpolation function. By the properties of Dirac distribution function, the analytic expressions of the Fourier transform and inverse Fourier transform for the trigonometric interpolation function are derived to approximate the Fourier transform and inverse Fourier transform for the original function. The numerical formulations for calculating the Fourier transforms and the inverse Fourier transforms of the functions with one variable and two variables are derived, respectively. Comparing with the algorithm using rectangular formula of numerical integration, the numerical examples show that the proposed method achieves higher accuracy.%基于三角插值理论,用函数的三角插值函数代替函数本身,并借助Dirac广义函数的性质写出三角插值函数的Fourier变换、逆变换的解析表达式,将之作为函数的Fourier变换、逆变换的近似.基于这种想法,分别推导一元函数、二元函数的Fourier变换和Fourier逆变换的计算公式.数值实验表明,这种方法比通常基于矩形求积公式计算连续Fourier变换、逆变换的精度要高.
Directory of Open Access Journals (Sweden)
D. Seidl
1999-06-01
Full Text Available Among a variety of spectrogram methods Short-Time Fourier Transform (STFT and Continuous Wavelet Transform (CWT were selected to analyse transients in non-stationary tremor signals. Depending on the properties of the tremor signal a more suitable representation of the signal is gained by CWT. Three selected broadband tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli.
Logan, T. L.; Huning, J. R.; Glackin, D. L.
1983-01-01
The use of two dimensional Fast Fourier Transforms (FFTs) subjected to pattern recognition technology for the identification and classification of low altitude stratus cloud structure from Geostationary Operational Environmental Satellite (GOES) imagery was examined. The development of a scene independent pattern recognition methodology, unconstrained by conventional cloud morphological classifications was emphasized. A technique for extracting cloud shape, direction, and size attributes from GOES visual imagery was developed. These attributes were combined with two statistical attributes (cloud mean brightness, cloud standard deviation), and interrogated using unsupervised clustering amd maximum likelihood classification techniques. Results indicate that: (1) the key cloud discrimination attributes are mean brightness, direction, shape, and minimum size; (2) cloud structure can be differentiated at given pixel scales; (3) cloud type may be identifiable at coarser scales; (4) there are positive indications of scene independence which would permit development of a cloud signature bank; (5) edge enhancement of GOES imagery does not appreciably improve cloud classification over the use of raw data; and (6) the GOES imagery must be apodized before generation of FFTs.
Fractional Fourier Transform Applied to Digital Images Encryption
Vilardy, Juan M.; Torres, Cesar O.; Mattos, Lorenzo
2008-04-01
In the present paper a digital algorithm was developed to make phase encryption of digital indexed images to color using the fractional Fourier transform (the images in RGB are converted to indexed before to encrypt). The indexed images are represented by a matrix of M×N pixels (where M defines the height and N is the Width of the image) and a color map (it's a matrix of C×3 elements, where C indicates the colors number of the image and the number 3 indicates the three columns associated with the color components: Red, Green and Blue of each pixel of the matrix of M×N) associated to the matrix of pixels to suitably represent the color information of the image. The indexed image (matrix of M×N pixels) to encrypt is placed as the phase of a complex exponential, then is transformed three times and multiplied in intermediate steps by two random phase masks statistically independent thus to obtain the encrypted image, for decrypt the coding image the encryption procedure is applied in the inverse sense to the conjugated complex of the encrypted image, then is taken the negative of the phase of the resulting function of the decryption process and the original image is obtained this way that had been encrypted; For the color map equal procedure is applied in the encryption/decryption process described previously for the matrix of M×N pixels. In the implemented cryptographic algorithm five keys are used, constituted by three fractional orders and two random phase masks, all these keys are necessary for a correct decryption providing a dependability to the transference of images by means of the communications nets.
Calibration of the Herschel SPIRE Fourier Transform Spectrometer
Swinyard, B M; Hopwood, R; Valtchanov, I; Lu, N; Fulton, T; Benielli, D; Imhof, P; Marchili, N; Baluteau, J -P; Bendo, G J; Ferlet, M; Griffin, M J; Lim, T L; Makiwa, G; Naylor, D A; Orton, G S; Papageorgiou, A; Pearson, C P; Schulz, B; Sidher, S D; Spencer, L D; van der Wiel, M H D; Wu, R
2014-01-01
The Herschel SPIRE instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of 450-1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a spatially extended source and uses the Herschel telescope as primary calibrator. Conversion from extended to point-source calibration is carried out using observations of the planet Uranus. The model of the telescope emission is shown to be accurate to within 6% and repeatable to better than 0.06% and, by comparison with models of Mars and Neptune, the Uranus model is shown to be accurate to within 3%. Multiple observations of a number of point-like sources show that the repeatability of the calibration is better than 1%, if the effects of the satellite absolu...
Fourier transform infrared absorption spectroscopy of jet-cooled radicals
Rohrs, Henry W.; Wickham-Jones, C. Tom; Ellison, G. Barney; Berry, David; Argrow, Brian M.
1995-03-01
We describe an experiment that couples a high-resolution Fourier transform spectrometer (FTS) to a supersonic jet of radicals. A 1-mm-i.d. cylindrical SiC nozzle is resistively heated to 1500 K in order to decompose organic precursors and generate expansions of jet-cooled radicals. We have used this apparatus to pyrolyze alkyl nitrites to make alkoxy and nitric oxide radicals. The residence time of radicals in this hot nozzle is roughly 20 μs RONO→ΔRO+NO. We use the FTS to detect the IR absorption of the product NO (ν0=1876.1 cm-1) at resolutions as fine as 0.005 cm-1 FWHM. We observe the product NO from the pyrolysis of CH3CH2ONO to be rotationally cooled to roughly 50 K. The IR spectra indicate that the optical path length is about 3/4 cm and that the nitrites pyrolyze to produce approximately 1014 NO radicals cm-3 some 9 mm downstream from the nozzle. Our spectrometer is capable of detecting an absorption signal of 0.1% over a bandwidth of 100 cm-1 at 0.005 cm-1 resolution. Depending on the infrared cross section of the radical, this implies that we are able to monitor diatomic radical densities of roughly 5×1012 cm-3 (quantum state)-1.
External Second Gate-Fourier Transform Ion Mobility Spectrometry.
Energy Technology Data Exchange (ETDEWEB)
Tarver, Edward E., III
2005-01-01
Ion mobility spectrometry (IMS) is recognized as one of the most sensitive and versatile techniques for the detection of trace levels of organic vapors. IMS is widely used for detecting contraband narcotics, explosives, toxic industrial compounds and chemical warfare agents. Increasing threat of terrorist attacks, the proliferation of narcotics, Chemical Weapons Convention treaty verification as well as humanitarian de-mining efforts has mandated that equal importance be placed on the analysis time as well as the quality of the analytical data. (1) IMS is unrivaled when both speed of response and sensitivity has to be considered. (2) With conventional (signal averaging) IMS systems the number of available ions contributing to the measured signal to less than 1%. Furthermore, the signal averaging process incorporates scan-to-scan variations decreasing resolution. With external second gate Fourier Transform ion mobility spectrometry (FT-IMS), the entrance gate frequency is variable and can be altered in conjunction with other data acquisition parameters to increase the spectral resolution. The FT-IMS entrance gate operates with a 50% duty cycle and so affords a 7 to 10-fold increase in sensitivity. Recent data on high explosives are presented to demonstrate the parametric optimization in sensitivity and resolution of our system.
Transmission fourier transform Raman spectroscopy of pharmaceutical tablet cores.
Pelletier, Michael J; Larkin, Peter; Santangelo, Matthew
2012-04-01
Transmission Fourier transform (FT) Raman spectroscopy of pharmaceutical tablet cores is demonstrated using traditional, unmodified commercial instrumentation. The benefits of improved precision over backscattering Raman spectroscopy due to increased sample volume are demonstrated. Self-absorption effects on analyte band ratios and sample probe volume are apparent, however. A survey of near-infrared (NIR) absorption spectra in the FT-Raman spectral range (approximately 0 to 3500 wavenumber shift from 1064 nm, or 1064 to 1700 nm) of molecules with a wide range of NIR-active functional groups shows that although absorption at the laser wavelength (1064 nm) is relatively small, some regions of the Raman spectrum coincide with NIR absorbances of 0.5 per cm or greater. Fortunately, the pharmaceutically important regions of the Raman shift spectrum from 0 to 600 cm(-1) and from 1400 to 1900 cm(-1) exhibit low self-absorption for most organic materials. A statistical analysis of transmission FT-Raman noise in spectra collected from different regions of a pharmaceutical tablet provides insight into both spectral distortion and reduced sampling volume caused by self-absorption.
Spin Glass Field Theory with Replica Fourier Transforms
Pimentel, Iveta R.; De Dominicis, Cirano
We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas n and the number of replica symmetry breaking steps R generic integers. We show how the RFT applied to the two-replica fields allows to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows to express any i-replica vertex in the new RFT basis and hence enables to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi's solution for the free-energy of an Ising spin glass.
Resource requirements for a fault-tolerant quantum Fourier transform
Goto, Hayato; Nakamura, Satoshi; Kujiraoka, Mamiko; Ichimura, Kouichi
2015-03-01
The quantum Fourier transform (QFT) is a basic subroutine for most quantum algorithms providing an exponential speedup over classical ones. We investigate resource requirements for a fault-tolerant QFT. To implement single-qubit rotations for a QFT in a fault-tolerant manner, we examine three types of approaches: ancilla-free gate synthesis, ancilla-assisted gate synthesis, and state distillation. While the gate synthesis approximates single-qubit rotations with basic quantum operations, the state distillation enables to perform specific single-qubit rotations required for the QFT exactly. It is unknown, however, which approach is better for the QFT. We estimated the resource requirement for a QFT in each case, where the resource is measured by the total number of the π / 8 gates denoted by T, which is called the T count. Contrary to the initial expectation, the total T count for the state distillation is considerably larger than those for the ancilla-free and ancilla-assisted gate synthesis. Thus, we conclude that the ancilla-assisted gate synthesis is the best for a fault-tolerant QFT so far.
Online Botnet Detection Based on Incremental Discrete Fourier Transform
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Xiaocong Yu
2010-05-01
Full Text Available Botnet detection has attracted lots of attention since botnet attack is becoming one of the most serious threats on the Internet. But little work has considered the online detection. In this paper, we propose a novel approach that can monitor the botnet activities in an online way. We define the concept of “feature streams” to describe raw network traffic. If some feature streams show high similarities, the corresponding hosts will be regarded as suspected bots which will be added into the suspected bot hosts set. After activity analysis, bot hosts will be confirmed as soon as possible. We present a simple method by computing the average Euclidean distance for similarity measurement. To avoid huge calculation among feature streams, classical Discrete Fourier Transform (DFT technique is adopted. Then an incremental calculation of DFT coefficients is introduced to obtain the optimal execution time. The experimental evaluations show that our approach can detect both centralized and distributed botnet activities successfully with high efficiency and low false positive rate.
SAR-based vibrometry using the fractional Fourier transform
Campbell, Justin B.; Wang, Qi; Ade-Bello, Jelili; Caudana, Humberto; Trujillo, Nicole B.; Bhatta, Ishwor; Dunkel, Ralf; Atwood, Thomas; Doerry, Armin; Gerstle, Walter H.; Santhanam, Balu; Hayat, Majeed M.
2015-05-01
A fundamental assumption when applying Synthetic Aperture Radar (SAR) to a ground scene is that all targets are motionless. If a target is not stationary, but instead vibrating in the scene, it will introduce a non-stationary phase modulation, termed the micro-Doppler effect, into the returned SAR signals. Previously, the authors proposed a pseudosubspace method, a modification to the Discrete Fractional Fourier Transform (DFRFT), which demonstrated success for estimating the instantaneous accelerations of vibrating objects. However, this method may not yield reliable results when clutter in the SAR image is strong. Simulations and experimental results have shown that the DFRFT method can yield reliable results when the signal-to-clutter ratio (SCR) > 8 dB. Here, we provide the capability to determine a target's frequency and amplitude in a low SCR environment by presenting two methods that can perform vibration estimations when SCR < 3 dB. The first method is a variation and continuation of the subspace approach proposed previously in conjunction with the DFRFT. In the second method, we employ the dual-beam SAR collection architecture combined with the extended Kalman filter (EKF) to extract information from the returned SAR signals about the vibrating target. We also show the potential for extending this SAR-based capability to remotely detect and classify objects housed inside buildings or other cover based on knowing the location of vibrations as well as the vibration histories of the vibrating structures that house the vibrating objects.
Improved Fast Fourier Transform Based Method for Code Accuracy Quantification
Energy Technology Data Exchange (ETDEWEB)
Ha, Tae Wook; Jeong, Jae Jun [Pusan National University, Busan (Korea, Republic of); Choi, Ki Yong [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-10-15
The capability of the proposed method is discussed. In this study, the limitations of the FFTBM were analyzed. The FFTBM produces quantitatively different results due to its frequency dependence. Because the problem is intensified by including a lot of high frequency components, a new method using a reduced cut-off frequency was proposed. The results of the proposed method show that the shortcomings of FFTBM are considerably relieved. Among them, the fast Fourier transform based method (FFTBM) introduced in 1990 has been widely used to evaluate a code uncertainty or accuracy. Prosek et al., (2008) identified its drawbacks, the so-called 'edge effect'. To overcome the problems, an improved FFTBM by signal mirroring (FFTBM-SM) was proposed and it has been used up to now. In spite of the improvement, the FFTBM-SM yielded different accuracy depending on the frequency components of a parameter, such as pressure, temperature and mass flow rate. Therefore, it is necessary to reduce the frequency dependence of the FFTBMs. In this study, the deficiencies of the present FFTBMs are analyzed and a new method is proposed to mitigate its frequency dependence.
Analysis of ovarian tumor pathology by Fourier Transform Infrared Spectroscopy
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Mehrotra Ranjana
2010-12-01
Full Text Available Abstract Background Ovarian cancer is the second most common cancer among women and the leading cause of death among gynecologic malignancies. In recent years, infrared (IR spectroscopy has gained attention as a simple and inexpensive method for the biomedical study of several diseases. In the present study infrared spectra of normal and malignant ovarian tissues were recorded in the 650 cm-1 to 4000 cm-1 region. Methods Post surgical tissue samples were taken from the normal and tumor sections of the tissue. Fourier Transform Infrared (FTIR data on twelve cases of ovarian cancer with different grades of malignancy from patients of different age groups were analyzed. Results Significant spectral differences between the normal and the ovarian cancerous tissues were observed. In particular changes in frequency and intensity in the spectral region of protein, nucleic acid and lipid vibrational modes were observed. It was evident that the sample-to-sample or patient-to-patient variations were small and the spectral differences between normal and diseased tissues were reproducible. Conclusion The measured spectroscopic features, which are the spectroscopic fingerprints of the tissues, provided the important differentiating information about the malignant and normal tissues. The findings of this study demonstrate the possible use of infrared spectroscopy in differentiating normal and malignant ovarian tissues.
Screening cervical lesions with Fourier transform infrared spectroscopy
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The screening results were reported based on the Fourier transform infrared spectroscopy (FTIR) analysis of the samples of exfoliated cervical cells from 354 women. Their spectra can be sorted into two types based on the emerging or not of the absorption bands near 970 cm-1 and 1 170 cm-1: T1 (83.1%) type without emerging, and T2 (16.9%) type with obviously emerging. All of the samples assigned to T1 were cytologically diagnosed as normal or within normal limits (PapⅠ). 28.9% and 71.1% of samples exhibiting T2 profile, were cytologically evaluated as Pap Ⅰand abnormal respectively. 3 women in the abnormal group were diagnosed as to have cervical cells with changes associated with high grade of inflammation, cervical scar and cervical erosion. Furthermore, based on the progressive change of the relative intensities of the absorption bands, both T1 and T2 profiles can be categorized into 6 subtypes. The observed heterogeneous spectra and the progressive changes in the absorption frequencies and the relative intensities exhibit features suggestive of the progressive process of cervical lesion. The FTIR method has the potential to complement the cytological smear for large-volume screening of cervical lesions.
Chiral Process Monitoring Using Fourier Transform Microwave Spectroscopy
Neill, Justin L.; Muckle, Matt; Pate, Brooks
2017-06-01
We present the application of Fourier transform microwave (FTMW) spectroscopy in monitoring the chiral purity of components in a reaction mixture. This is of particular interest due to the increasing use of continuous pharmaceutical manufacturing processes, in which a number of attributes (including the chiral purity of the product) can change on short time scales. Therefore, new techniques that can accomplish this measurement rapidly are desired. The excellent specificity of FTMW spectroscopy, coupled with newly developed techniques for measuring enantiomeric excess in a mixture, have motivated this work. In collaboration with B. Frank Gupton (Virginia Commonwealth University), we are testing this application first with the synthesis of artemisinin. Artemisinin, a common drug for malaria treatment, is of high global health interest and subject to supply shortages, and therefore a strong candidate for continuous manufacturing. It also has moderately high molecular weight (282 amu) and seven chiral centers, making it a good candidate to test the capabilities of FTMW spectroscopy. Using a miniature cavity-enhanced FTMW spectrometer design, we aim to demonstrate selective component quantification in the reaction mixture. Future work that will be needed to fully realize this application will be discussed. R.D. Suenram, J.U. Grabow, A.Zuban, and I.Leonov, Rev. Sci. Instrum. 70, 2127 (1999).
Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS)
Sromovsky, L. A.
2002-01-01
This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).
Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability
Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.
2007-01-01
The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.
Fourier transform infrared microspectroscopy and multivariate methods for radiobiological dosimetry.
Meade, A D; Clarke, C; Byrne, H J; Lyng, F M
2010-02-01
The scientific literature contains an ever-growing number of reports of applications of vibrational spectroscopy as a multivariate non-invasive tool for analysis of biological effects at the molecular level. Recently, Fourier transform infrared microspectroscopy (FTIRM) has been demonstrated to be sensitive to molecular events occurring in cells and tissue after exposure to ionizing radiation. In this work the application of FTIRM in the examination of dose-dependent molecular effects occurring in skin cells after exposure to ionizing radiation with the use of partial least-squares regression (PLSR) and generalized regression neural networks (GRNN) was studied. The methodology is shown to be sensitive to molecular events occurring with radiation dose and time after exposure. The variation in molecular species with dose and time after irradiation is shown to be non-linear by virtue of the higher modeling efficiency yielded from the non-linear algorithms. Dose prediction efficiencies of approximately +/-10 mGy were achieved at 96 h after irradiation, highlighting the potential applications of the methodology in radiobiological dosimetry.
Fourier transform ion cyclotron resonance mass spectrometry: a primer.
Marshall, A G; Hendrickson, C L; Jackson, G S
1998-01-01
This review offers an introduction to the principles and generic applications of FT-ICR mass spectrometry, directed to readers with no prior experience with the technique. We are able to explain the fundamental FT-ICR phenomena from a simplified theoretical treatment of ion behavior in idealized magnetic and electric fields. The effects of trapping voltage, trap size and shape, and other nonidealities are manifested mainly as perturbations that preserve the idealized ion behavior modified by appropriate numerical correction factors. Topics include: effect of ion mass, charge, magnetic field, and trapping voltage on ion cyclotron frequency; excitation and detection of ICR signals; mass calibration; mass resolving power and mass accuracy; upper mass limit(s); dynamic range; detection limit, strategies for mass and energy selection for MSn; ion axialization, cooling, and remeasurement; and means for guiding externally formed ions into the ion trap. The relation of FT-ICR MS to other types of Fourier transform spectroscopy and to the Paul (quadrupole) ion trap is described. The article concludes with selected applications, an appendix listing accurate fundamental constants needed for ultrahigh-precision analysis, and an annotated list of selected reviews and primary source publications that describe in further detail various FT-ICR MS techniques and applications.
Single beam Fourier transform digital holographic quantitative phase microscopy
Energy Technology Data Exchange (ETDEWEB)
Anand, A., E-mail: arun-nair-in@yahoo.com; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V. [Optics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390001 (India); Faridian, A.; Pedrini, G.; Osten, W. [Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart (Germany); Dubey, S. K. [Siemens Technology and Services Pvt. Ltd, Corporate Technology—Research and Technology Centre, Bangalore 560100 (India); Javidi, B. [Department of Electrical and Computer Engineering, U-4157, University of Connecticut, Storrs, Connecticut 06269-2157 (United States)
2014-03-10
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
High-resolution wide-band Fast Fourier Transform spectrometers
Klein, Bernd; Krämer, Ingo; Bell, Andreas; Meyer, Klaus; Güsten, Rolf
2012-01-01
We describe the performance of our latest generations of sensitive wide-band high-resolution digital Fast Fourier Transform Spectrometer (FFTS). Their design, optimized for a wide range of radio astronomical applications, is presented. Developed for operation with the GREAT far infrared heterodyne spectrometer on-board SOFIA, the eXtended bandwidth FFTS (XFFTS) offers a high instantaneous bandwidth of 2.5 GHz with 88.5 kHz spectral resolution and has been in routine operation during SOFIA's Basic Science since July 2011. We discuss the advanced field programmable gate array (FPGA) signal processing pipeline, with an optimized multi-tap polyphase filter bank algorithm that provides a nearly loss-less time-to-frequency data conversion with significantly reduced frequency scallop and fast sidelobe fall-off. Our digital spectrometers have been proven to be extremely reliable and robust, even under the harsh environmental conditions of an airborne observatory, with Allan-variance stability times of several 1000 se...
Fourier transform optical profilometry using fiber optic Lloyd's mirrors.
Kart, Türkay; Kösoğlu, Gülşen; Yüksel, Heba; İnci, Mehmet Naci
2014-12-10
A fiber optic Lloyd's mirror assembly is used to obtain various optical interference patterns for the detection of 3D rigid body shapes. Two types of fiber optic Lloyd's systems are used in this work. The first consists of a single-mode optical fiber and a highly reflecting flat mirror to produce bright and dark strips. The second is constructed by locating a single-mode optical fiber in a v-groove, which is formed by two orthogonal flat mirrors to allow the generation of square-type interference patterns for the desired applications. The structured light patterns formed by these two fiber Lloyd's techniques are projected onto 3D objects. Fringe patterns are deformed due to the object's surface topography, which are captured by a digital CCD camera and processed with a Fourier transform technique to accomplish 3D surface topography of the object. It is demonstrated that the fiber-optic Lloyd's technique proposed in this work is more compact, more stable, and easier to configure than other existing surface profilometry systems, since it does not include any high-cost optical tools such as aligners, couplers, or 3D stages. The fringe patterns are observed to be more robust against environmental disturbances such as ambient temperature and vibrations.
Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.
Mikkonen, Jopi J W; Raittila, Jussi; Rieppo, Lassi; Lappalainen, Reijo; Kullaa, Arja M; Myllymaa, Sami
2016-09-01
Saliva provides a valuable tool for assessing oral and systemic diseases, but concentrations of salivary components are very small, calling the need for precise analysis methods. In this work, Fourier transform infrared (FT-IR) spectroscopy using transmission and photoacoustic (PA) modes were compared for quantitative analysis of saliva. The performance of these techniques was compared with a calibration series. The linearity of spectrum output was verified by using albumin-thiocyanate (SCN(-)) solution at different SCN(-) concentrations. Saliva samples used as a comparison were obtained from healthy subjects. Saliva droplets of 15 µL were applied on the silicon sample substrate, 6 drops for each specimen, and dried at 37 ℃ overnight. The measurements were carried out using an FT-IR spectrometer in conjunction with an accessory unit for PA measurements. The findings with both transmission and PA modes mirror each other. The major bands presented were 1500-1750 cm(-1) for proteins and 1050-1200 cm(-1) for carbohydrates. In addition, the distinct spectral band at 2050 cm(-1) derives from SCN(-) anions, which is converted by salivary peroxidases to hypothiocyanate (OSCN(-)). The correlation between the spectroscopic data with SCN(-) concentration (r > 0.990 for transmission and r = 0.967 for PA mode) was found to be significant (P < 0.01), thus promising to be utilized in future applications.
Multi-channel sampling theorems for band-limited signals with fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
2008-01-01
Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies.
Localization Operators and an Uncertainty Principle for the Discrete Short Time Fourier Transform
Directory of Open Access Journals (Sweden)
Carmen Fernández
2014-01-01
Full Text Available Localization operators in the discrete setting are used to obtain information on a signal f from the knowledge on the support of its short time Fourier transform. In particular, the extremal functions of the uncertainty principle for the discrete short time Fourier transform are characterized and their connection with functions that generate a time-frequency basis is studied.
An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.
Eastman, M. P.; And Others
1986-01-01
Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.
Sui, Liansheng; Liu, Benqing; Wang, Qiang; Li, Ye; Liang, Junli
2015-12-01
A color image encryption scheme is proposed based on Yang-Gu mixture amplitude-phase retrieval algorithm and two-coupled logistic map in gyrator transform domain. First, the color plaintext image is decomposed into red, green and blue components, which are scrambled individually by three random sequences generated by using the two-dimensional Sine logistic modulation map. Second, each scrambled component is encrypted into a real-valued function with stationary white noise distribution in the iterative amplitude-phase retrieval process in the gyrator transform domain, and then three obtained functions are considered as red, green and blue channels to form the color ciphertext image. Obviously, the ciphertext image is real-valued function and more convenient for storing and transmitting. In the encryption and decryption processes, the chaotic random phase mask generated based on logistic map is employed as the phase key, which means that only the initial values are used as private key and the cryptosystem has high convenience on key management. Meanwhile, the security of the cryptosystem is enhanced greatly because of high sensitivity of the private keys. Simulation results are presented to prove the security and robustness of the proposed scheme.
Topochemical Transformations of CaX2 (X=C, Si, Ge) to Form Free-Standing Two-Dimensional Materials.
Pratik, Saied Md; Nijamudheen, A; Datta, Ayan
2015-12-01
Topochemical transformations of layered materials CaX2 (X=Si, Ge) are the method of choice for the high-yield synthesis of pristine, defect-free two-dimensional systems silicane and germanane, which have advanced electronic properties. Based on solid-state dispersion-corrected calculations, mechanisms for such transformations are elucidated that provide an in-depth understanding of phase transition in these layered materials. While formation of such layered materials is highly favorable for silicane and germanane, a barrier of 1.2 eV in the case of graphane precludes its synthesis from CaC2 topochemically. The energy penalty required for distorting linear acetylene into a trans-bent geometry accounts for this barrier. In contrast it is highly favorable in the heavier analogues, resulting in barrierless topochemical generation of silicane and germanane. Photochemical generation of the trans-bent structure of acetylene in its first excited state (S1 ) can directly generate graphane through a barrierless condensation. Unlike the buckled structure of silicene, the phase-h of CaSi2 with perfectly planar silicene layers exhibits the Dirac cones at the high symmetry points K and H. Interestingly, topochemical acidification of the cubic phase of calcium carbide is predicted to generate the previously elusive platonic hydrocarbon, tetrahedrane.
Precise and fast spatial-frequency analysis using the iterative local Fourier transform.
Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook
2016-09-19
The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.
Ogawa, Takahiro; Haseyama, Miki
2013-03-01
A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.
Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments
Nemeth, Alexandra; Mancal, Tomas; Lukes, Vladimir; Hauer, Juergen; Kauffmann, Harald F; Sperling, Jaroslaw
2010-01-01
This is the first in a series of two papers investigating the effect of electron-phonon coupling in two-dimensional Fourier transformed electronic spectroscopy. We present a series of one- and two-dimensional nonlinear spectroscopic techniques for studying a dye molecule in solution. Ultrafast laser pulse excitation of an electronic transition coupled to vibrational modes induces a propagating vibrational wave packet that manifests itself in oscillating signal intensities and line-shapes. For the two-dimensional electronic spectra we can attribute the observed modulations to periodic enhancement and decrement of the relative amplitudes of rephasing and non-rephasing contributions to the total response. Different metrics of the two-dimensional signals are shown to relate to the frequency-frequency correlation function which provides the connection between experimentally accessible observations and the underlying microscopic molecular dynamics. A detailed theory of the time-dependent two-dimensional spectral li...
Institute of Scientific and Technical Information of China (English)
Pang Chao-Yang; Hu Ben-Qiong
2008-01-01
The discrete Fourier transform(DFT)is the base of modern signal processing.1-dimensional fast Fourier transform (1D FFT)and 2D FFT have time complexity O(N log N)and O(N2 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(1D 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,1D 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.
A Fourier transform infrared trace gas analyser for atmospheric applications
Directory of Open Access Journals (Sweden)
D. W. T. Griffith
2012-05-01
Full Text Available Concern in recent decades about human impacts on Earth's climate has led to the need for improved and expanded measurement capabilities for greenhouse gases in the atmosphere. In this paper we describe in detail an in situ trace gas analyser based on Fourier Transform Infrared (FTIR spectroscopy that is capable of simultaneous and continuous measurements of carbon dioxide (CO_{2}, methane (CH_{4}, carbon monoxide (CO, nitrous oxide (N_{2}O and ^{13}C in CO_{2} in air with high precision and accuracy. Stable water isotopes can also be measured in undried airstreams. The analyser is automated and allows unattended operation with minimal operator intervention. Precision and accuracy meet and exceed the compatibility targets set by the World Meteorological Organisation – Global Atmosphere Watch Programme for baseline measurements in the unpolluted troposphere for all species except ^{13}C in CO_{2}.
The analyser is mobile and well suited to fixed sites, tower measurements, mobile platforms and campaign-based measurements. The isotopic specificity of the optically-based technique and analysis allows application of the analyser in isotopic tracer experiments, for example ^{13}C in CO_{2} and ^{15}N in N_{2}O. We review a number of applications illustrating use of the analyser in clean air monitoring, micrometeorological flux and tower measurements, mobile measurements on a train, and soil flux chamber measurements.
Fourier Transform Spectrometer measurements of Atmospheric Carbon Dioxide and Methane
Kivi, Rigel; Heikkinen, Pauli; Chen, Huilin; Hatakka, Juha; Laurila, Tuomas
2016-04-01
Ground based remote sensing measurements of column CO2 and CH4 using Fourier Transform Spectrometers (FTS) within the Total Carbon Column Observing Network (TCCON) are known for high precision and accuracy. These measurements are performed at various locations globally and they have been widely used in carbon cycle studies and validation of space born measurements. The relevant satellite missions include the Orbiting Carbon Observatory-2 (OCO-2) by the National Aeronautics and Space Administration (NASA); the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) by the European Space Agency (ESA); the Greenhouse gases Observing SATellite (GOSAT) by the Japan Aerospace Exploration Agency (JAXA) and the upcoming Sentinel-5 Precursor mission, which is an ESA mission and scheduled for launch in 2016. Results of the column CO2 and CH4 measurements at Sodankylä in northern Finland (at 67.4° N, 26.6° E) are reported in this study. The measurements have been performed on regular basis since the beginning of the program in early 2009. We also present evaluation of the data quality of the ground based measurements and comparisons with the available satellite based retrievals. In case of comparisons between the GOSAT and ground based retrievals of CO2 and CH4 no significant biases were found. Sodankylä is one of the northernmost stations in the TCCON network. However, the data coverage has been relatively good thanks to the progress towards automation of the FTS measurement system. At Sodankylä the retrievals have been also compared with the balloon borne AirCore measurements at the site. AirCore sampling system is directly related to the World Meteorological Organization in situ trace gas measurement scales. The balloon platform allows sampling in both stratosphere and troposphere, which is a benefit, compared to the aircraft in situ measurements.
Continuously tunable optical multidimensional Fourier-transform spectrometer.
Dey, P; Paul, J; Bylsma, J; Deminico, S; Karaiskaj, D
2013-02-01
A multidimensional optical nonlinear spectrometer (MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. The MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delays between them while maintaining phase stability. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy. The present work reports on overcoming some important limitations on the original design of the MONSTR apparatus. One important advantage of the MONSTR is the fact that it is a closed platform, which provides the high stability. Once the optical alignment is performed, it is desirable to maintain the alignment over long periods of time. The previous design of the MONSTR was limited to a narrow spectral range defined by the optical coating of the beam splitters. In order to achieve tunability over a broad spectral range the internal optics needed to be changed. By using broadband coated and wedged beam splitters and compensator plates, combined with modifications of the beam paths, continuous tunability can be achieved from 520 nm to 1100 nm without changing any optics or performing alignment of the internal components of the MONSTR. Furthermore, in order to achieve continuous tunability in the spectral region between 520 nm and 720 nm, crucially important for studies on numerous biological molecules, a single longitudinal mode laser at 488.5 nm was identified and used as a metrology laser. The shorter wavelength of the metrology laser as compared to the usual HeNe laser has also increased the phase stability of the system. Finally, in order to perform experiments in the reflection geometry, a simple method to achieve active phase stabilization
SAR processing based on the exact two-dimensional transfer function
Chang, C. Y.; Jin, M. Y.; Curlander, J. C.
1992-01-01
The two-dimensional transfer functions of several synthetic aperture radar (SAR) focusing algorithms are derived considering the spaceborne SAR environments. The formulation includes the factors of the earth rotation and the antenna squint angles. The resultant transfer functions are explicitly expressed in terms of Doppler centroid frequency and Doppler frequency rate, which can be accurately estimated from the SAR data. Point target simulation results show that the algorithm based on the two-dimensional Fourier transformation outperforms the one-dimensional one for processing data acquired from high squint angles. The two-dimensional Fourier transformation approach appears to be a viable and simple solution for the processor design of future spaceborne SAR systems.
Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm
Heisler, R.
1978-01-01
A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.
Pisani, Marco; Zucco, Massimo
2009-05-11
An imaging spectrometer based on a Fabry-Perot interferometer is presented. The Fabry-Perot interferometer scans the mirror distance up to contact and the intensity modulated light signal is transformed using a Fourier Transform based algorithm, as the Michelson based Fourier Transform Spectrometers does. The resulting instrument has the advantage of a compact, high numerical aperture, high luminosity hyperspectral imaging device. Theory of operation is described along with one experimental realization and preliminary results.
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
Campbell, Joel
2008-01-01
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.
2012-01-01
By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.
Broadband Mid-Infrared Comb-Resolved Fourier Transform Spectroscopy
Lee, Kevin; Mills, Andrew; Mohr, Christian; Jiang, Jie; Fermann, Martin; Maslowski, Piotr
2014-06-01
We report on a comb-resolved, broadband, direct-comb spectroscopy system in the mid-IR and its application to the detection of trace gases and molecular line shape analysis. By coupling an optical parametric oscillator (OPO), a 100 m multipass cell, and a high-resolution Fourier transform spectrometer (FTS), sensitive, comb-resolved broadband spectroscopy of dilute gases is possible. The OPO has radiation output at 3.1-3.7 and 4.5-5.5 μm. The laser repetition rate is scanned to arbitrary values with 1 Hz accuracy around 417 MHz. The comb-resolved spectrum is produced with an absolute frequency axis depending only on the RF reference (in this case a GPS disciplined oscillator), stable to 1 part in 10^9. The minimum detectable absorption is 1.6x10-6 wn Hz-1/2. The operating range of the experimental setup enables access to strong fundamental transitions of numerous molecular species for applications based on trace gas detection such as environmental monitoring, industrial gas calibration or medical application of human breath analysis. In addition to these capabilities, we show the application for careful line shape analysis of argon-broadened CO band spectra around 4.7 μm. Fits of the obtained spectra clearly illustrate the discrepancy between the measured spectra and the Voigt profile (VP), indicating the need to include effects such as Dicke narrowing and the speed-dependence of the collisional width and shift in the line shape model, as was shown in previous cw-laser studies. In contrast to cw-laser based experiments, in this case the entire spectrum (˜ 250 wn) covering the whole P and R branches can be measured in 16 s with 417 MHz resolution, decreasing the acquisition time by orders of magnitude. The parallel acquisition allows collection of multiple lines simultaneously, removing the correlation of possible temperature and pressure drifts. While cw-systems are capable of measuring spectra with higher precision, this demonstration opens the door for fast
Fast Fourier Transform Chlorine Nuclear Quadrupole Resonance Spectroscopy.
D'Iorio, Marie
A nuclear quadrupole resonance spectrometer operating in the frequency range 1-40 MHz was updated for fast Fourier transform spectroscopy and coupled to a Nicolet 1180 computer and data acquisition system. It was used with a low temperature cryostat for studies shown down to liquid helium temperature and with a high pressure/low temperature system for studies down to liquid nitrogen temperature and up to six kilobars. The study of the ('35)Cl NQR spectrum of K(,2)OsCl(,6) at 298 K and 77 K revealed the presence of a satellite associated with the nearest neighbour chlorines to H('+) ion impurities located at vacant octahedral sties. This result is in agreement with the predictions of a point charge model calculation. A residence time for the H('+) ion was deduced and is consistent with the result obtained from dielectric measurements. A detailed study of the ('35)Cl NQR frequency in K(,2)ReCl(,6) was performed in the temperature range 85 - 130K where two structural phase transitions occur, and at pressures from 1 to 2643 bars. A number of unusual features were revealed and discussed as the possible signature of incommensurate behavior. The primary effect of the pressure was to alter the temperatures at which the phase transitions occurred. Contrary to the behavior expected, the transition temperature for the antiferrorotative transition has a negative pressure coefficient. The spin-lattice and spin-spin relaxation times for the ('35)Cl and ('37)Cl isotopes of the one dimensional XY system, PrCl(,3), were measured at 4.2K. The spin-lattice relaxation is exponential and dominated by magnetic dipole -dipole interactions. The spin-spin relaxation is non-exponential and dominated by electric quadrupolar interactions arising from the coupling of the electric dipole moment at the praseodymium site and the quadrupole moment of the chlorine ion. The temperature dependence of the spin-spin relaxation time was investigated. At 17.4 K both magnetic dipolar and electric
2014-10-16
1 Extracting micro-Doppler radar signatures from rotating targets using Fourier- Bessel Transform and Time-Frequency analysis P. Suresh1,T...kvenkataramanaiah@sssihl.edu.in Abstract In this paper, we report the efficiency of Fourier Bessel transform and time-frequency based method in conjunction with...decomposed into stationary and non-stationary components using Fourier Bessel transform in conjunction with the fractional Fourier transform. The
Fourier transforms of spherical distributions on compact symmetric spaces
Olafsson, Gestur; Schlichtkrull, Henrik
2008-01-01
In our previous articles "A local Paley-Wiener theorem for compact symmetric spaces", Adv. Math. 218 (2008), 202--215, and "Fourier series on compact symmetric spaces" (submitted) we studied Fourier series on a compact symmetric space M=U/K. In particular, we proved a Paley-Wiener type theorem for the smooth functions on M, which have sufficiently small support and are K-invariant, respectively K-finite. In this article we extend those results to K-invariant distributions on M. We show that t...
Institute of Scientific and Technical Information of China (English)
NOROUZI,Parviz; GANJALI,Mohammad Reza; SHAHTAHERI,Sayed Jamaleddin; DINARVAND,Rasoul; HAMZEHPOOR,Ali
2009-01-01
A continuous cyclic voltammetric study of methyldopa at gold micro electrode was carried out.The drug in phosphate buffer (pH 2.0) is adsorpted at 400 mV,giving rise to change in the current of well-defined oxidation peak of gold in the flow injection system.The proposed detection method has some of advantages,the greatest one of which are as follows;first,it is no more necessary to remove oxygen from the analyte solution and second,this is a very fast and appropriate technique for determination of the drug compound in a wide variety of chromatographic analysis methods.Signal-to-noise ratio has significantly increased by application of discrete Fast Fourier transform (FFT) method,background subtraction and two-dimensional integration of the electrode response over a selected potential range and time window.Also in this work some parameters such as sweep rate,eluent pH,and accumulation time and potential were optimized.The linear concentration range was of 1.0×10-7-1.0×10-11 mol·L-1 (r=0.9975) with a limit of detection and quantitation 0.004 nmol·L-1 and 0.03 nmol·L-1,respectively.The method has the requisite accuracy,sensitivity,precision and selectivity to assay methyldopa in tablets.The influences of pH of eluent,accumulation potential,sweep rate,and accumulation time on the determination of the methyldopa were considered.
Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform
Directory of Open Access Journals (Sweden)
Zohreh Moghareh Abed
2010-01-01
Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.
Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.
Perkins, W. D.
1987-01-01
This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)
Improved method of generating bit reversed numbers for calculating fast fourier transform
Digital Repository Service at National Institute of Oceanography (India)
Suresh, T.
Fast Fourier Transform (FFT) is an important tool required for signal processing in defence applications. This paper reports an improved method for generating bit reversed numbers needed in calculating FFT using radix-2. The refined algorithm takes...
D'Astous, Y.; Blanchard, M.
1982-05-01
In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)
Xi, Jiaxin; Liu, Ning
2017-09-01
Vibration characteristic of timing chain system is very important for an engine. In this study, we used a bush roller chain drive system as an example to explain how to use mulitybody dynamic techniques and short-time Fourier transform to investigate vibration characteristics of timing chain system. Multibody dynamic simulation data as chain tension force and external excitation sources curves were provided for short-time Fourier transform study. The study results of short-time Fourier transform illustrate that there are two main vibration frequency domain of timing chain system, one is the low frequency vibration caused by crankshaft sprocket velocity and camshaft sprocket torque. Another is vibration around 1000Hz lead by hydraulic tensioner. Hence, short-time Fourier transform method is useful for basic research of vibration characteristics for timing chain system.
Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.
2000-01-01
A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).
The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.
King, Roy W.; Williams, Kathryn R.
1989-01-01
Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)
Fourier transform of delayed fluorescence as an indicator of herbicide concentration.
Guo, Ya; Tan, Jinglu
2014-12-21
It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method.
Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.
2017-01-01
We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.
The Design of Lens Imaging System by Means of Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
CHEN Jiannong; XU Qiang; D.R.Selviah
2002-01-01
The relation between the 2nd fractional Fourier transform and the imaging process of an optical system is discussed. By changing the coordinate scales of the input plane in respect to the magnification of the optical imaging system, the fractional Fourier transform can be a powerful tool in designing specific imaging system. The Gaussian imaging formula of single lens is obtained by using the tool. Finally the procedures are generalized for designing a double-lens imaging system through an example.
Institute of Scientific and Technical Information of China (English)
CHEN Lin-Fei; ZHAO Dao-Mu
2006-01-01
@@ We propose a new method to add different images together by optical implementation that is realized by the multi-exposure based on fractional Fourier transform hologram. Partial image fusion is proposed and realized by this method. Multiple images encryption can also be implemented by the multi-exposure of the hologram based on fractional Fourier transform. Computer simulations prove that this method is valid.
Krovi, Hari; Russell, Alexander
2012-01-01
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups (denoted D(G), for a group G). Regarding algorithms for these invariants, we develop quantum circuits for the quantum Fourier transform over D(G); in general, we show that when one can uniformly and efficiently carry out the quantum Fourier transform over the ce...
OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation
DEFF Research Database (Denmark)
Palushani, Evarist; Richter, T.; Ludwig, R.
2012-01-01
We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information.......We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information....
Time-Domain Optical Fourier Transformation for OTDM-DWDM and DWDM-OTDM Conversion
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael
2011-01-01
Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats.......Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats....
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.
Accelerating the Non-equispaced Fast Fourier Transform on Commodity Graphics Hardware
DEFF Research Database (Denmark)
Sørensen, Thomas Sangild; Schaeffter, Tobias; Noe, Karsten Østergaard
2008-01-01
We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe the performa......We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe...
Energy Technology Data Exchange (ETDEWEB)
Zheng, Y. [Pennsylvania State Univ., University Park, PA (United States)]|[Lawrence Berkeley Lab., CA (United States); Shirley, D.A. [Pennsylvania State Univ., University Park, PA (United States)
1995-02-01
The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.
MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS
Institute of Scientific and Technical Information of China (English)
Jiachang Sun
2006-01-01
In this paper we propose the well-known Fourier method on some non-tensor product domains in Rd, including simplex and so-called super-simplex which consists of (d + 1)! simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a paralle lhexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm(FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT) and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a Laplacian-like operator over these domains is explored.
Luo, David; Kudenov, Michael W
2016-05-16
Systematic phase errors in Fourier transform spectroscopy can severely degrade the calculated spectra. Compensation of these errors is typically accomplished using post-processing techniques, such as Fourier deconvolution, linear unmixing, or iterative solvers. This results in increased computational complexity when reconstructing and calibrating many parallel interference patterns. In this paper, we describe a new method of calibrating a Fourier transform spectrometer based on the use of artificial neural networks (ANNs). In this way, it is demonstrated that a simpler and more straightforward reconstruction process can be achieved at the cost of additional calibration equipment. To this end, we provide a theoretical model for general systematic phase errors in a polarization birefringent interferometer. This is followed by a discussion of our experimental setup and a demonstration of our technique, as applied to data with and without phase error. The technique's utility is then supported by comparison to alternative reconstruction techniques using fast Fourier transforms (FFTs) and linear unmixing.
Product Summability Transform of Conjugate Series of Fourier Series
Directory of Open Access Journals (Sweden)
Vishnu Narayan Mishra
2012-01-01
Full Text Available A known theorem, Nigam (2010 dealing with the degree of approximation of conjugate of a signal belonging to Lipξ(t-class by (E,1(C,1 product summability means of conjugate series of Fourier series has been generalized for the weighted W(Lr,ξ(t, (r≥1,(t>0-class, where ξ(t is nonnegative and increasing function of t, by En1Cn1~ which is in more general form of Theorem 2 of Nigam and Sharma (2011.
Magneto-sensor circuit efficiency incremented by Fourier-transformation
Talukdar, Abdul Hafiz Ibne
2011-10-01
In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.
Computer Generation of Fourier Transform Libraries for Distributed Memory Architectures
2010-12-01
Cooley-TukeyFFT.Thefirst “fast” algorithm for theDFTwas discoveredbyCooley andTukey [Coo- ley and Tukey, 1965] 1, and is often referred to as “the...Carl Friedrich Gauss , but his work was not widely recog- nized [Heideman et al., 1985]. 2It is important to note the distinction between the terms...Applications, pages 129–136. North-Holland, 1994. 26 M. T. Heideman, D. H. Johnson, and C. S. Burrus. Gauss and the history of the fast Fourier
Digital watermarking for still image based on discrete fractional fourier transform
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Presents a digital watermarking technique based on discrete fractional Fourier transform(DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original image by the information of watermark, and concludes from experimental results that the proposed tech nique is robust to lossy compression attack.
A Graphical Presentation to Teach the Concept of the Fourier Transform
Besalu, E.
2006-01-01
A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.
Fourier and Schur-Weyl transforms applied to XXX Heisenberg magnet
Jakubczyk, P.; Lulek, T.; Jakubczyk, D.; Lulek, B.
2010-03-01
Similarities and differences between Fourier and Schur-Weyl transforms have been discussed in the context of a one-dimensional Heisenberg magnetic ring with N nodes. We demonstrate that main difference between them correspond to another partitioning of the Hilbert space of the magnet. In particular, we point out that application of the quantum Fourier transform corresponds to splitting of the Hilbert space of the model into subspaces associated with the orbits of the cyclic group, whereas, the Schur-Weyl transform corresponds to splitting into subspaces associated with orbits of the symmetric group.
Safari, M J; Afarideh, H; Jamili, S; Bayat, E
2016-01-01
A Discrete Fourier Transform Method (DFTM) for discrimination between the signal of neutrons and gamma rays in organic scintillation detectors is presented. The method is based on the transformation of signals into the frequency domain using the sine and cosine Fourier transforms in combination with the discrete Fourier transform. The method is largely benefited from considerable differences that usually is available between the zero-frequency components of sine and cosine and the norm of the amplitude of the DFT for neutrons and gamma-ray signals. Moreover, working in frequency domain naturally results in considerable suppression of the unwanted effects of various noise sources that is expected to be effective in time domain methods. The proposed method could also be assumed as a generalized nonlinear weighting method that could result in a new class of pulse shape discrimination methods, beyond definition of the DFT. A comparison to the traditional Charge Integration Method (CIM), as well as the Frequency G...
Fast Inverse Nonlinear Fourier Transforms for Fiber Bragg Grating Design and Related Problems
Wahls, Sander
2016-01-01
The problem of constructing a fiber Bragg grating profile numerically such that the reflection coefficient of the grating matches a given specification is considered. The well-known analytic solution to this problem is given by a suitable inverse nonlinear Fourier transform (also known as inverse scattering transform) of the specificed reflection coefficient. Many different algorithms have been proposed to compute this inverse nonlinear Fourier transform numerically. The most efficient ones require $\\mathcal{O}(D^{2})$ floating point operations (flops) to generate $D$ samples of the grating profile. In this paper, two new fast inverse nonlinear Fourier transform algorithms that require only $\\mathcal{O}(D\\log^{2}D)$ flops are proposed. The merits of our algorithms are demonstrated in numerical examples, in which they are compared to a conventional layer peeling method, the Toeplitz inner bordering method and integral layer peeling. One of our two algorithms also extends to the design problem for fiber-assiste...
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A new method of resolving overlapped peak, Fourier self-deconvolution (FSD) using approximation CN obtained from frequency domain wavelet transform of F(ω) yielded by Fourier transform of overlapped peak signals f(t) as the linear function, was presented in this paper.Compared with classical FSD, the new method exhibits excellent resolution for different overlapped peak signals such as HPLC signals, and have some characteristics such as an extensive applicability for any overlapped peak shape signals and a simple operation because of no selection procedure of the linear function. Its excellent resolution for those different overlapped peak signals is mainly because F(ω) obtained from Fourier transform of f(t) and CN obtained from wavelet transform of F(ω) have the similar linearity and peak width. The effect of those fake peaks can be eliminated by the algorithm proposed by authors. This method has good potential in the process of different overlapped peak signals.
Rejection of Linear FM Interference in DSSS System Based on Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
QI Lin; TAO Ran; ZHOU Si-yong
2005-01-01
A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the receiver with an interference exciser is also presented. Based on the property that the fractional Fourier transform of a signal is equivalent to rotating the signal in the time-frequency plane, the received signal is transform into a certain fractional Fourier domain, this transform will result in the least spectrum overlap between the signal and interference. Then, a narrowband filter is exploited to extract most of the interference energy. The performance analyses show that remarkable improvements in signal-to-noise ratio (SNR) and biterror-ratio (BER) are obtained.
Fourier transform profilometry based on mean envelope extraction
Zhang, Xiaoxuan; Huang, Shujun; Gao, Nan; Zhang, Zonghua
2017-02-01
Based on an image pre-processing algorithm, a three-dimensional (3D) object measurement method is proposed by combining time domain and frequency domain analysis. Firstly, extreme points of sinusoidal fringes under the disturbance of noise are accurately extracted. Secondly, mean envelope of the fringe is obtained through appropriate interpolation method and then removed. Thirdly, phase information is extracted by using specific filtering in Fourier spectrum of the pre-processed fringe pattern. Finally, simulated and experimental results show a good property of the proposed method in accuracy and measurement range. The proposed method can achieve 3D shape of objects having large slopes and/or discontinuous surfaces from one-shot acquisition by using color fringe projection technique and will have wide applications in the fields of fast measurement.
Does the Entorhinal Cortex use the Fourier Transform?
Directory of Open Access Journals (Sweden)
Jeff eOrchard
2013-12-01
Full Text Available Some neurons in the entorhinal cortex (EC fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4-12Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed "theta precession". Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011 exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labour for implementing spatial maps: position, versus map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all.
Method of local pointed function reduction of original shape in Fourier transformation
Dosch, H
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
Locke, Jonathan; White, Paul R
2011-10-01
The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species.
Juday, Richard D. (Inventor)
1992-01-01
A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.
Fourier and Hadamard transform spectrometers - A limited comparison. II
Harwit, M.; Tai, M. H.
1977-01-01
A mathematical approach was used to compare interferometric spectrometers and Hadamard transform spectrometers. The principle results are reported, noting that the simple Hadamard spectrometer encodes more efficiently than a Michelson interferometer which, in turn, encodes less efficiently than is usually acknowledged. Hirschfeld's (1977) major objections to these findings are discussed, although it is noted that none of his objections is supported by evidence.
On Analog of Fourier Transform in Interior of the Light Cone
Directory of Open Access Journals (Sweden)
Tatyana Shtepina
2014-01-01
Full Text Available We introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that Fhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.
Products of multiple Fourier series with application to the multiblade transformation
Kunz, D. L.
1981-01-01
A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.
Digital Fourier analysis advanced techniques
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to advanced digital Fourier analysis for advanced undergraduate and graduate students. Assuming knowledge of the Fast Fourier Transform, this book covers advanced topics including the Hilbert transform, cepstrum analysis, and the two-dimensional Fourier transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Advanced Techniques" includes practice problems and thorough Appendices. As a central feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. The applet source code in Visual Basic is provided online, enabling advanced students to tweak and change the programs for more sophisticated results. A complete, intuitive guide, "Digital Fourier Analysis - Advanced Techniques" is an essential reference for students in science and engineering.
Fractional Fourier transform-based optical encryption with treble random phase-encoding
Xin, Yi; Tao, Ran; Wang, Yue
2008-03-01
We propose a new architecture of optical encryption technique using the fractional Fourier transform with three statistically independent random phase masks. Compared with the existing double-phase encoding method in the fractional Fourier-domain, the proposed extra phase mask in the last fractional Fourier domain makes the architecture symmetrical, and additive processing to the encrypted image can be turned into complex stationary white noise after decryption, and enlarge the key space without any degradation of its robustness to blind decryption. This property can be utilized to improve the quality of the recover image. Simulation results have verified the validity.
Adaptive motion mapping in pancreatic SBRT patients using Fourier transforms
Jones, Bernard L; Miften, Moyed
2015-01-01
Recent studies suggest that 4DCT is unable to accurately measure respiratory-induced pancreatic tumor motion. In this work, we assessed the daily motion of pancreatic tumors treated with SBRT, and developed adaptive strategies to predict and account for this motion. The daily motion trajectory of pancreatic tumors during CBCT acquisition was calculated using a model which reconstructs the instantaneous 3D position in each 2D CBCT projection image. We developed a metric (termed "Spectral Coherence," SC) based on the Fourier frequency spectrum of motion in the SI direction, and analyzed the ability of SC to predict motion-based errors and classify patients according to motion characteristics. The amplitude of daily motion exceeded the predictions of pre-treatment 4DCT imaging by an average of 3.0 mm, 2.3 mm, and 3.5 mm in the AP, LR, and SI directions. SC was correlated with daily motion differences and tumor dose coverage. In a simulated adaptive protocol, target margins were adjusted based on SC, resulting in...
Grid-Based Fourier Transform Phase Contrast Imaging
Tahir, Sajjad
Low contrast in x-ray attenuation imaging between different materials of low electron density is a limitation of traditional x-ray radiography. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One recently developed phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a technique recently demonstrated by Bennett et al. that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 microm spot Mo source, a CCD with 22 microm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the grid in the Fourier domain. A Matlab code was written to perform the image processing. For the first time, the effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the window function type used to separate the harmonics, and the window widths, were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and new methods investigated to form improved phase contrast images.
Mesh-based phase contrast Fourier transform imaging
Tahir, Sajjad; Bashir, Sajid; MacDonald, C. A.; Petruccelli, Jonathan C.
2017-04-01
Traditional x-ray radiography is limited by low attenuation contrast in materials of low electron density. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a recently developed technique that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 μm spot Mo source, a CCD with 22 μm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the mesh in the Fourier domain. The effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the width of the window function used to separate the harmonics were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and combined to form improved phase contrast images.
Functional differential equations for the q-Fourier transform of q-Gaussians
Energy Technology Data Exchange (ETDEWEB)
Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)
2010-02-05
In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.
Inversion of Fourier Transforms by Means of Scale-Frequency Series
Directory of Open Access Journals (Sweden)
Nassar H. S. Haidar
2014-01-01
Full Text Available We report on inversion of the Fourier transform when the frequency variable can be scaled in a variety of different ways that improve the resolution of certain parts of the frequency domain. The corresponding inverse Fourier transform is shown to exist in the form of two dual scale-frequency series. Upon discretization of the continuous scale factor, this Fourier transform series inverse becomes a certain nonharmonic double series, a discretized scale-frequency (DSF series. The DSF series is also demonstrated, theoretically and practically, to be rate-optimizable with respect to its two free parameters, when it satisfies, as an entropy maximizer, a pertaining recursive nonlinear programming problem incorporating the entropy-based uncertainty principle.
Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion
Yükçü, Niyazi
2016-03-01
Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical properties of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.
Munoz, R. M. (Inventor)
1974-01-01
An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. The original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications.
Fourier-transform spectroscopy: new methods and applications: introduction by the feature editors.
Traub, W A; Winkel, R J; Goldman, A
1996-06-01
We are pleased to introduce this special issue of papers on Fourier-transform spectroscopy, which grew out of a recent topical meeting sponsored by the Optical Society of America. The topical meeting welcomed all researchers who practice the art of Fourier-transform spectroscopy in the laboratory, in the atmosphere, and in space. The power and the wide applicability of Fourier-transform spectroscopy unite these fields with a common mathematical and instrumental bond. The meeting probed each of these areas in depth, bringing out new ideas for instrumentation, analysis, and applications. There was a strong sentiment at the meeting that the quality of papers and posters was exceptionally high and that it would be important for future progress in the field to have the results of this meeting captured in print. This special issue is the fruit of that effort.
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.
q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity
Energy Technology Data Exchange (ETDEWEB)
Atakishiyeva, Mesuma K [Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, CP 62250 Cuernavaca, Morelos (Mexico); Atakishiyev, Natig M [Instituto de Matematicas, Unidad Cuernavaca Universidad Nacional Autonoma de Mexico, AP 273-3 Admon 3, Cuernavaca, Morelos 62251 (Mexico); Koornwinder, Tom H [Korteweg-de Vries Institute, University of Amsterdam, PO Box 94248, 1090 GE Amsterdam (Netherlands)], E-mail: mesuma@servm.fc.uaem.mx, E-mail: natig@matcuer.unam.mx, E-mail: T.H.Koornwinder@uva.nl
2009-10-30
It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian;
2015-01-01
We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time.......We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time....
Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and Convolution
Directory of Open Access Journals (Sweden)
Bong Jin Kim
2014-01-01
Full Text Available Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in Banach algebra S on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class F(B and in a generalized Fresnel class FA1,A2 on abstract Wiener space. We express Fourier-Feynman transform and convolution product of functionals in S as limits of Wiener integrals. Moreover we obtain change of scale formulas for Wiener integrals related to Fourier-Feynman transform and convolution product of these functionals.
Security of image encryption scheme based on multi-parameter fractional Fourier transform
Zhao, Tieyu; Ran, Qiwen; Yuan, Lin; Chi, Yingying; Ma, Jing
2016-10-01
Recently, multi-parameter fractional Fourier transform (MPFRFT) has been widely applied in the optics cryptosystem, which has attracted more and more researchers' attention. However, in further study we find a serious security problem on the MPFRFT which is the multi-choice of decryption key corresponding to an encryption key. The existence of multi-decryption-key hinders the application of this algorithm. We present a new generalized fractional Fourier transform, which can overcome the problem and enlarge the key space. The simulation results show that the proposed algorithm has higher security and key sensitivity.
The Pegg-Barnett phase operator and the discrete Fourier transform
Perez-Leija, Armando; Andrade-Morales, Luis A.; Soto-Eguibar, Francisco; Szameit, Alexander; Moya-Cessa, Héctor M.
2016-04-01
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.
Interferometric time delay correction for Fourier transform spectroscopy in the extreme ultraviolet
Meng, Yijian; Zhang, Chunmei; Marceau, Claude; Naumov, A. Yu.; Corkum, P. B.; Villeneuve, D. M.
2016-09-01
We demonstrate a Fourier transform spectrometer in the extreme ultraviolet (XUV) spectrum using a high-harmonic source, with wavelengths as short as 32 nm. The femtosecond infrared laser source is divided into two separate foci in the same gas jet to create two synchronized XUV sources. An interferometric method to determine the relative delay between the two sources is shown to improve the accuracy of the delay time, with corrections of up to 200 asec required. By correcting the time base before the Fourier transform, the frequency resolution is improved by up to an order of magnitude.
Three-dimensional radiative transfer using a Fourier-transform matrix-operator method
Martonchik, J. V.; Diner, D. J.
1985-01-01
The three-dimensional equation of transfer for a scattering medium with planar geometry is solved by using a spatial Fourier transform and extending matrix-operator techniques developed previously for the one-dimensional equation. Doubling and adding algorithms were derived by means of an interaction principle for computing the Fourier-transformed radiation field. The resulting expressions fully describe the radiative transfer process in a scattering medium, inhomogeneous in the x-, y- and z-directions, illuminated from above by an arbitrarily general intensity field and bounded from below by a surface with completely general reflection properties.
Estimation of structural modal parameters by fourier transform with an optimal window
Institute of Scientific and Technical Information of China (English)
ZHU Hong-ping; WAN Xin-hua
2005-01-01
An adaptive Fourier Transform (FT) with an optimal window has been proposed for the time-frequency analysis of nonstationary time series. The method allows for a good estimation of both frequency and amplitude of the spectrum and can be easily applied to the general case of time-varying signals. The evaluation of the proposed approach has been performed on measured time-varying signals from a suspension bridge model and a steel frame model whose data have the typical non-stationary characteristics. The numerical results show that the proposed approach can overcome some of the difficulties encountered in the classic Fourier transform technique and can achieve higher computation accuracy.
Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation
Energy Technology Data Exchange (ETDEWEB)
Aldea, N; Pintea, S; Rednic, V [National Institute for Research and Development of Isotopic and Molecular Technologies, 65-103 Donath, 400293 Cluj-Napoca (Romania); Matei, F [University of Agricultural Sciences and Veterinary Medicine, 3-5 Calea Manastur, 400372 Cluj-Napoca (Romania); Hu Tiandou; Xie Yaning, E-mail: nicolae.aldea@itim-cj.r [Beijing Synchrotron Radiation Facilities of Beijing Electron Positron Collider National Laboratory (China)
2009-08-01
The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe{sub 3}O{sub 4} core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.
DWDM-TO-OTDM Conversion by Time-Domain Optical Fourier Transformation
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Hu, Hao; Galili, Michael
2011-01-01
We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated.......We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated....
DEFF Research Database (Denmark)
Hu, Hao; Kong, Deming; Palushani, Evarist
2013-01-01
We demonstrate transmission of a 1.28-Tbaud Nyquist-OTDM signal over a record distance of 100 km with detection by time-domain optical Fourier transformation followed by FEC decoding, resulting in error-free performance for all tributaries.......We demonstrate transmission of a 1.28-Tbaud Nyquist-OTDM signal over a record distance of 100 km with detection by time-domain optical Fourier transformation followed by FEC decoding, resulting in error-free performance for all tributaries....
DEFF Research Database (Denmark)
Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads
2016-01-01
We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude......We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...
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.
The investigation on two-dimensional pilot-symbol-aided channel estimation method for OFDM system
Institute of Scientific and Technical Information of China (English)
Sun Juying; Zhang Yanhua
2008-01-01
Channel estimation for orthogonal frequency division multiplexing (OFDM) system has attracted widespread attention. In this paper, a novel efficient two-dimensional (2-D) channel estimation algorithm based on fast Fourier transform (FFT) is proposed for a time-variant, frequency-selective wideband wireless channel. Both theoretical analysis and simulation results are addressed in the paper. The simulation results prove that the proposed algorithm has simpler implementation, better performance and wider application than other traditional decision-directed algorithms.
a First Cryptosystem for Security of Two-Dimensional Data
Mishra, D. C.; Sharma, Himani; Sharma, R. K.; Kumar, Naveen
In this paper, we present a novel technique for security of two-dimensional data with the help of cryptography and steganography. The presented approach provides multilayered security of two-dimensional data. First layer security was developed by cryptography and second layer by steganography. The advantage of steganography is that the intended secret message does not attract attention to itself as an object of scrutiny. This paper proposes a novel approach for encryption and decryption of information in the form of Word Data (.doc file), PDF document (.pdf file), Text document, Gray-scale images, and RGB images, etc. by using Vigenere Cipher (VC) associated with Discrete Fourier Transform (DFT) and then hiding the data behind the RGB image (i.e. steganography). Earlier developed techniques provide security of either PDF data, doc data, text data or image data, but not for all types of two-dimensional data and existing techniques used either cryptography or steganography for security. But proposed approach is suitable for all types of data and designed for security of information by cryptography and steganography. The experimental results for Word Data, PDF document, Text document, Gray-scale images and RGB images support the robustness and appropriateness for secure transmission of these data. The security analysis shows that the presented technique is immune from cryptanalytic. This technique further provides security while decryption as a check on behind which RGB color the information is hidden.
Two-dimensional static deformation of an anisotropic medium
Indian Academy of Sciences (India)
Kuldip Singh; Dinesh Kumar Madan; Anita Goel; Nat Ram Garg
2005-08-01
The problem of two-dimensional static deformation of a monoclinic elastic medium has been studied using the eigenvalue method, following a Fourier transform. We have obtained expressions for displacements and stresses for the medium in the transformed domain. As an application of the above theory, the particular case of a normal line-load acting inside an orthotropic elastic half-space has been considered in detail and closed form expressions for the displacements and stresses are obtained. Further, the results for the displacements for a transversely isotropic as well as for an isotropic medium have also been derived in the closed form. The use of matrix notation is straightforward and avoids unwieldy mathematical expressions. To examine the effect of anisotropy, variations of dimensionless displacements for an orthotropic, transversely isotropic and isotropic elastic medium have been compared numerically and it is found that anisotropy affects the deformation signiﬁcantly.
Menke, Jan; Helms, Gunther; Larsen, Jörg
2010-01-01
The purpose of this experimental study was to evaluate whether the effective k-space coverage of MR images can in principle be viewed after multidimensional Fourier transform back to k-space. A water-soaked sponge phantom providing homogeneous k-space pattern was imaged with different standard MR sequences, utilizing elliptic acquisitions, partial-Fourier acquisitions and elliptic filtering as imaging examples. The resulting MR images were Fourier-transformed to the spatial frequency domain (the k-space) to visualize their effective k-space coverage. These frequency domain images are named "backtransformed k-space images." For a quantitative assessment, the sponge phantom was imaged with three-dimensional partial-Fourier sequences while varying the partial acquisition parameters in slice and phase direction. By linear regression analysis, the k-space coverage as expected from the sequence menu parameters was compared to the effective k-space coverage as observed in the backtransformed k-space images. The k-space coverage of elliptic and partial-Fourier acquisitions became visible in the backtransformed k-space images, as well as the effect of elliptic filtering. The expected and the observed k-space coverage showed a highly significant correlation (r=.99, PFourier-transforming MR images of a sponge phantom back to k-space. This method could be used for several purposes including sequence parameter optimization, basic imaging research, and to enhance a visual understanding of k-space, especially in three-dimensional MR imaging.
Fourier Transform Near Infrared Spectrometry: Using Interferograms To Determine Chemical Composition
Hoy, R. M.; McClure, W. Fred
1989-12-01
Previous research conducted in this laboratory has demonstrated several advantages accrued by transforming near infrared spectra from the wavelength domain to the Fourier domain. Those advantages include: [1] smoothing wavelength domain data without loss of end points, [2] correcting for particle size phenomena encountered in solid sample analyses by simply omitting the mean term Fourier coefficient from the "retransformation process", [3] minimizing the multicollinearity problem prevalent in wavelength space, [4] generating wavelength-space derivatives from Fourier space without loss of end points, [5] performing band enhancements via Fourier self-deconvolution, [6] identifying sample type using Fourier vectors, [7] estimating chemical composition using only the first few Fourier coefficients, [8] cutting of computer storage requirements by more than 96%, [9] cutting of calibration time by more than 96%, hence [10] reducing the drudgery of maintaining calibrations. That the first 12 Fourier coefficients contain sufficient information to determine chemical constituents in many products has turned out to be a major advantage leading us to understand that the chemical absorption information in the wavelength spectrum of a sample obtained with an interferometer was also present in the interferogram.
Two-dimensional optical spectroscopy
Cho, Minhaeng
2009-01-01
Discusses the principles and applications of two-dimensional vibrational and optical spectroscopy techniques. This book provides an account of basic theory required for an understanding of two-dimensional vibrational and electronic spectroscopy.
Multi-modal Color Medical Image Fusion Using Quaternion Discrete Fourier Transform
Nawaz, Qamar; Xiao, Bin; Hamid, Isma; Jiao, Du
2016-12-01
Multimodal image fusion is a process of combining multiple images, generated by identical or diverse imaging modalities, to get precise inside information about the same body organ. In recent years, various multimodal image fusion algorithms have been proposed to fuse medical image. However, most of them focus on fusing grayscale images. This paper proposes a novel algorithm for the fusion of multimodal color medical images. The proposed algorithm divides source images into blocks, converts each RGB block into quaternion representation and transforms them from special domain to frequency domain by applying quaternion discrete Fourier transform. The fused coefficients are obtained by calculating and comparing contrast values of corresponding coefficients in transformed blocks. The resultant fused image is reconstructed by merging all the blocks after applying inverse quaternion discrete Fourier transform on each block. Experimental evaluation demonstrates that the proposed algorithm qualitatively outperforms many existing state-of-the-art multimodal image fusion algorithms.
Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fiber
Wahls, Sander
2015-01-01
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\\mathcal{O}(D\\log^{2}D)$ floating point operations to compute $D$ samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with $\\log^{2}$-linear complexity. The paper also includes a many samples analysis of the generated nonlinear Fourier spectra.
Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes
Lin, Sian-Jheng
2016-09-13
In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h is the number of evaluation points. Based on the proposed Fourier-like algorithm, we then develop the encoding/ decoding algorithms for (n = 2m; k) Reed-Solomon erasure codes. The proposed encoding/erasure decoding algorithm requires O(n lg(n)), in both additive and multiplicative complexities. As the complexity leading factor is small, the proposed algorithms are advantageous in practical applications. Finally, the approaches to convert the basis between the monomial basis and the new basis are proposed.
Lu, Xiangwen; Gao, Wenpei; Zuo, Jian-Min; Yuan, Jiabin
2015-02-01
Advances in diffraction and transmission electron microscopy (TEM) have greatly improved the prospect of three-dimensional (3D) structure reconstruction from two-dimensional (2D) images or diffraction patterns recorded in a tilt series at atomic resolution. Here, we report a new graphics processing unit (GPU) accelerated iterative transformation algorithm (ITA) based on polar fast Fourier transform for reconstructing 3D structure from 2D diffraction patterns. The algorithm also applies to image tilt series by calculating diffraction patterns from the recorded images using the projection-slice theorem. A gold icosahedral nanoparticle of 309 atoms is used as the model to test the feasibility, performance and robustness of the developed algorithm using simulations. Atomic resolution in 3D is achieved for the 309 atoms Au nanoparticle using 75 diffraction patterns covering 150° rotation. The capability demonstrated here provides an opportunity to uncover the 3D structure of small objects of nanometers in size by electron diffraction.
Chan, Kenny K H; Tang, Shuo
2011-12-19
Gridding based non-uniform fast Fourier transform (NUFFT) has recently been shown as an efficient method of processing non-linearly sampled data from Fourier-domain optical coherence tomography (FD-OCT). This method requires selecting design parameters, such as kernel function type, oversampling ratio and kernel width, to balance between computational complexity and accuracy. The Kaiser-Bessel (KB) and Gaussian kernels have been used independently on the NUFFT algorithm for FD-OCT. This paper compares the reconstruction error and speed for the optimization of these design parameters and justifies particular kernel choice for FD-OCT applications. It is found that for on-the-fly computation of the kernel function, the simpler Gaussian function offers a better accuracy-speed tradeoff. The KB kernel, however, is a better choice in the pre-computed kernel mode of NUFFT, in which the processing speed is no longer dependent on the kernel function type. Finally, the algorithm is used to reconstruct in-vivo images of a human finger at a camera limited 50k A-line/s.
Directory of Open Access Journals (Sweden)
Fedotov A.
2017-02-01
Full Text Available The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.
Fedotov, A.; Fedotov, E.; Bahteev, K.
2017-02-01
The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.
Dool, T.C. van den; Hamelinck, R.F.M.M.; Kruizinga, B.; Gielesen, W.L.M.; Braam, B.C.; Nijenhuis, J.R.; Loix, N.; Luyckx, S.; Loon, D. van; Kooijman, P.P.; Swinyard, B.M.
2010-01-01
TNO, together with its partners Micromega and SRON, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. The optics of the FTS scanning mechanism (FTSM) consists of two back-to-back cat's-eyes. The optics are mounted
Subpixel translation of MEMS measured by discrete fourier transform analysis of CCD images
Yamahata, C.; Sarajlic, Edin; Stranczl, M.; Krijnen, Gijsbertus J.M.; Gijs, M.A.M.
2011-01-01
We present a straightforward method for measuring in-plane linear displacements of microelectromechanical systems (MEMS) with subnanometer resolution. The technique is based on Fourier transform analysis of a video recorded with a Charge-Coupled Device (CCD) camera attached to an optical microscope
Shifting and Variational Properties for Fourier-Feynman Transform and Convolution
Directory of Open Access Journals (Sweden)
Byoung Soo Kim
2015-01-01
Full Text Available Shifting, scaling, modulation, and variational properties for Fourier-Feynman transform of functionals in a Banach algebra S are given. Cameron and Storvick's translation theorem can be obtained as a corollary of our result. We also study shifting, scaling, and modulation properties for the convolution product of functionals in S.
Specification of the Fast Fourier Transform algorithm as a term rewriting system
Rodenburg, P.H.; Hoekzema, D.J.
2008-01-01
We specify an algorithm for multiplying polynomials with complex coefficients incorporating, the Fast Fourier Transform algorithm of Cooley and Tukey [CT]. The specification formalism we use is a variant of the formalism ASF described in. [BHK]. The difference with ASF is essentially a matter of sem
Subpixel translation of MEMS measured by discrete fourier transform analysis of CCD images
Yamahata, C.; Sarajlic, E.; Stranczl, M.; Krijnen, G.J.M.; Gijs, M.A.M.
2011-01-01
We present a straightforward method for measuring in-plane linear displacements of microelectromechanical systems (MEMS) with subnanometer resolution. The technique is based on Fourier transform analysis of a video recorded with a Charge-Coupled Device (CCD) camera attached to an optical microscope
Wiedermann, Guenter; Jennings, D. E.; Hanel, R. H.; Kunde, V. G.; Moseley, S. H.
1989-01-01
A postdispersion system for astronomical observations with Fourier transform spectrometers in the thermal infrared has been developed which improves the sensitivity of radiation noise limited observations by reducing the spectral range incident on the detector. Special attention is given to the first-generation blocked impurity band detector. Planetary, solar, and stellar observations are reported.
DEFF Research Database (Denmark)
Clausen, Sønnik; Morgenstjerne, Axel; Rathmann, Ole
1996-01-01
Surface temperatures are estimated with high precision based on a multitemperature method for Fourier-transform spectrometers. The method is based on Planck's radiation law and a nonlinear least-squares fitting algorithm applied to two or more spectra at different sample temperatures and a single...
Barbu, I.M.
2008-01-01
This thesis describes, the use of a Fourier Transform Ion Cyclotron (FTICR) mass spectrometer in the study of biological samples with, imaging mass spectrometry (MS). To achieve this goal experiments were performed on an in-house modified FTICR-MS instrument (for which special acquisition software w
VUV Fourier-transform absorption study of the Lyman and Werner bands in D-2
Lange, de A.; Dickenson, G.D.; Salumbides, E.J.; Ubachs, W.M.G.; Oliveira, de N.; Joyeux, D.; Nahon, L.
2012-01-01
An extensive survey of the D-2 absorption spectrum has been performed with the high-resolution VUV Fourier-transform spectrometer employing synchrotron radiation. The frequency range of 90 000-119 000 cm (1) covers the full depth of the potential wells of the B (1)Sigma(+)(u), B' 1 Sigma(+)(u), and
Dool, T.C. van den; Hamelinck, R.F.M.M.; Kruizinga, B.; Gielesen, W.L.M.; Braam, B.C.; Nijenhuis, J.R.; Loix, N.; Luyckx, S.; Loon, D. van; Kooijman, P.P.; Swinyard, B.M.
2010-01-01
TNO, together with its partners Micromega and SRON, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. The optics of the FTS scanning mechanism (FTSM) consists of two back-to-back cat's-eyes. The optics are mounted o
Fourier Transform Moire Deflectometry for Measuring the 3-D Temperature Field
Institute of Scientific and Technical Information of China (English)
MA Li; WANG Ming; LIU Song; QI Xiaopin
2000-01-01
Fourier transform evaluation of fringe phase is applied to Moire deflectometry. 3-D gas temperature distribution for a given layer is reconstructed by optical tomography. The results show that the high-precise and automatic measurement for the 3-D gas temperature field can be realized by this technique.
Fourier transform spectroscopy around 3 microns with a broad difference frequency comb
Meek, Samuel A; Guelachvili, Guy; Hänsch, Theodor W; Picqué, Nathalie
2013-01-01
We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.2 microns. High power per comb mode (>10-7 W/mode) is obtained over a broad spectral span (>700 nm). The source is used for direct absorption spectroscopy with a Michelson-based Fourier transform interferometer.
DEFF Research Database (Denmark)
Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads
2016-01-01
We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...
The Fourier transform solution for the Green's function of monoenergetic neutron transport theory
Ganapol, Barry D.
2014-01-01
Nearly 45 years ago, Ken Case published his seminal paper on the singular eigenfunction solution for the Green's function of the monoenergetic neutron transport equation with isotropic scattering. Previously, the solution had been obtained by Fourier transform. While it is apparent the two had to be equivalent, a convincing equivalence proof for general anisotropic scattering remained a challenge until now.
The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.
Suslick, Kenneth S.; And Others
1987-01-01
Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)
Directory of Open Access Journals (Sweden)
Percival Almoro
1998-12-01
Full Text Available Microscopic deformations on the surface of a circular diaphragm were measured using double exposure holographic interferometry and Fourier transform method (FTM. The three-dimensional surface deformations were successfully visualized by applying FTM to holographic interferogram analysis. The minimum surface displacement measured was 0.317 µm. This was calibrated via the Michelson interferometry technique.
Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.
Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing
2016-10-01
The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.
Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...
Soil science research is increasingly applying Fourier transform infrared (FTIR) spectroscopy for analysis of soil organic matter (SOM). However, the compositional complexity of soils and the dominance of the mineral component can limit spectroscopic resolution of SOM and other minor components. The...
Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform
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…
DEFF Research Database (Denmark)
Uceda Otero, E. P.; Eliel, G. S. N.; Fonseca, E. J. S.
2013-01-01
In this work we have used Fourier transform infrared (FTIR) / vibrational absorption (VA) spectroscopy to study two cancer cell lines: the Henrietta Lacks (HeLa) human cervix carcinoma and 5637 human bladder carcinoma cell lines. Our goal is to experimentally investigate biochemical changes and d...
The Relationship between Tsallis Statistics, the Fourier Transform, and Nonlinear Coupling
Nelson, Kenric P
2008-01-01
Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \\to q$ . The essence of this translation is to improve the mathematical symmetry of the q-algebra and make q directly proportional to the nonlinear coupling. A conjugate transformation is defined $\\hat q \\equiv \\frac{{- 2q}}{{2 + q}}$ which provides a dual mapping between the heavy-tail q-Gaussian distributions, whose translated q parameter is between $ - 2 < q < 0$, and the compact-support q-Gaussians, between $0 < q < \\infty $ . This conjugate transformation is used to extend the definition of the q-Fourier transform to the domain of compact support. A conjugate q-Fourier transform is proposed which transforms a q-Gaussian into a conjugate $\\hat q$ -Gaussian, which has the same exponential decay as the Fourier transform of a power-law function. The nonlinear statistical coupling is defined such that the conjugate ...
Wuttke, Joachim
2009-01-01
An algorithm is described for computing the Laplace transform (one-sided Fourier sine and cosine transform) of the stretched (or compressed) exponential function exp(-t^beta) (also known as Kohlrausch-Williams-Watts function, as characteristic function of a Levy stable distribution, or as complementary cumulative Weibull distribution) for exponents beta between 0.1 and 2. For low and high frequencies, the well-known series expansions are used; for intermediate frequencies, the explicit integration is strongly accelerated by the Ooura-Mori double exponential transformation. The algorithm is implemented in C as library libkww. The source code is available at http://www.messen-und-deuten.de/kww
Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin
2015-03-01
The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.
A New LFM-Signal Detector Based on Fractional Fourier Transform
Directory of Open Access Journals (Sweden)
Yin Zhiping
2010-01-01
Full Text Available A new LFM-signal detector formulated by the integration of the 4th-power modulus of the fractional Fourier transform is proposed. It has similar performance to the modulus square detector of Radon-ambiguity transform because of the equivalence relationship between them. But the new detector has much lower computational complexity in the case that the number of the searching angles is far less than the length of the signal. Moreover, it is proved that the new detector can be generalized to the integration of the nth-power ( modulus of the fractional Fourier transform via mathematical derivation. Computer simulation results have confirmed the effectiveness of the proposed detector in LFM-signal detection.
A New LFM-Signal Detector Based on Fractional Fourier Transform
Directory of Open Access Journals (Sweden)
Zhiping Yin
2010-01-01
Full Text Available A new LFM-signal detector formulated by the integration of the 4th-power modulus of the fractional Fourier transform is proposed. It has similar performance to the modulus square detector of Radon-ambiguity transform because of the equivalence relationship between them. But the new detector has much lower computational complexity in the case that the number of the searching angles is far less than the length of the signal. Moreover, it is proved that the new detector can be generalized to the integration of the nth-power (2
The Fractional Fourier Transform and Its Application to Energy Localization Problems
Directory of Open Access Journals (Sweden)
ter Morsche Hennie G
2003-01-01
Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.
Perspective: The first ten years of broadband chirped pulse Fourier transform microwave spectroscopy
Park, G. Barratt; Field, Robert W.
2016-05-01
Since its invention in 2006, the broadband chirped pulse Fourier transform spectrometer has transformed the field of microwave spectroscopy. The technique enables the collection of a ≥10 GHz bandwidth spectrum in a single shot of the spectrometer, which allows broadband, high-resolution microwave spectra to be acquired several orders of magnitude faster than what was previously possible. We discuss the advantages and challenges associated with the technique and look back on the first ten years of chirped pulse Fourier transform spectroscopy. In addition to enabling faster-than-ever structure determination of increasingly complex species, the technique has given rise to an assortment of entirely new classes of experiments, ranging from chiral sensing by three-wave mixing to microwave detection of multichannel reaction kinetics. However, this is only the beginning. Future generations of microwave experiments will make increasingly creative use of frequency-agile pulse sequences for the coherent manipulation and interrogation of molecular dynamics.
Fractional Fourier transform for partially coherent beam in spatial-frequency domain
Institute of Scientific and Technical Information of China (English)
Cai Yang-Jian; Lin Qiang
2004-01-01
By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatialfrequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian-Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatialfrequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain.
Park, G Barratt; Field, Robert W
2016-05-28
Since its invention in 2006, the broadband chirped pulse Fourier transform spectrometer has transformed the field of microwave spectroscopy. The technique enables the collection of a ≥10 GHz bandwidth spectrum in a single shot of the spectrometer, which allows broadband, high-resolution microwave spectra to be acquired several orders of magnitude faster than what was previously possible. We discuss the advantages and challenges associated with the technique and look back on the first ten years of chirped pulse Fourier transform spectroscopy. In addition to enabling faster-than-ever structure determination of increasingly complex species, the technique has given rise to an assortment of entirely new classes of experiments, ranging from chiral sensing by three-wave mixing to microwave detection of multichannel reaction kinetics. However, this is only the beginning. Future generations of microwave experiments will make increasingly creative use of frequency-agile pulse sequences for the coherent manipulation and interrogation of molecular dynamics.
Fourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves
García-Prada, Oscar; Hernández Ruipérez, Daniel; Pioli, Fabio; Tejero Prieto, Carlos
2005-12-01
We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases, the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic equations on a triple—vortices—and explore some of its basic properties. Our approach combines direct methods with dimensional reduction techniques, relating triples over a curve with vector bundles over the product of the curve with the complex projective line.
Sadabadi, Mahdiye Sadat; Shafiee, Masoud; Karrari, Mehdi
2008-07-01
In this paper, parameter identification of two-dimensional continuous-time systems via two-dimensional modulating functions is proposed. In the proposed method, trigonometric functions and sine-cosine wavelets are used as modulating functions. By this, a partial differential equation on the finite-time intervals is converted into an algebraic equation linear in parameters. The parameters of the system can then be estimated using the least square algorithms. The underlying computations utilize a two-dimensional fast Fourier transform algorithm, without the need for estimating the unknown initial or boundary conditions, at the beginning of each finite-time interval. Numerical simulations are presented to show the effectiveness of the proposed algorithm.
DEFF Research Database (Denmark)
Clausen, Anders; Guan, Pengyu; Mulvad, Hans Christian Hansen
2014-01-01
All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented.......All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented....
Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.
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.
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.
Directory of Open Access Journals (Sweden)
Vahid Bagheri
2014-11-01
Full Text Available This paper introduce a new data SONAR classification method based on Short-Time Fractional Fourier Transform (STFrFT analysis. The passive SONAR system receives the acoustic signals radiated by vessels and attempts to categorize them as a function of the similarities between vessels of the same class.Here, a time-frequency processing and feature extraction method is developed in order to improve the performance of a feedforwardneural network, which is used to classify five classes of vessels.Processing of time-varying signals in fractional fourier domain allows us to estimate the signal with higher concentration than conventional fourier domain, making the technique robust against additive noise, maintaining same computational complexity. With the purpose of dimension reduction and classification improvement, we use Linear Discriminant Analysis (LDA technique. The feasibility of the proposed technique (STFrFTLDA has been tested experimentally using a real database. The experimental results show the superiority of the proposed method
Program for the analysis of time series. [by means of fast Fourier transform algorithm
Brown, T. J.; Brown, C. G.; Hardin, J. C.
1974-01-01
A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.
Institute of Scientific and Technical Information of China (English)
QI Lin; TAO Ran; ZHOU Siyong; WANG Yue
2004-01-01
This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method.
Maccone, Claudio
2007-04-01
The present article describes that the range of any radiotelescope (and radar in general) may be increased by virtue of software, if one replaces the fast Fourier transform by the Karhunen Loève transform. The range increases with the inverse of the fourth root of the signal-to-noise ratio when this ratio decreases. Thus, the range on any radiotelescope (and radar) may be increased without changing the hardware at all, but by changing the software only. This improvement in the range of the radiotelescope is currently implemented at the 32-m antenna located at Medicina, near Bologna, in Italy, for both SETI and general radioastronomy.
Tropical Forest Biomass Estimation from Vertical Fourier Transforms of Lidar and InSAR Profiles
Treuhaft, R. N.; Goncalves, F.; Drake, J.; Hensley, S.; Chapman, B. D.; Michel, T.; Dos Santos, J. R.; Dutra, L.; Graca, P. A.
2010-12-01
Structural forest biomass estimation from lidar or interferometric SAR (InSAR) has demonstrated better performance than radar-power-based approaches for the higher biomasses (>150 Mg/ha) found in tropical forests. Structural biomass estimation frequently regresses field biomass to some function of forest height. With airborne, 25-m footprint lidar data and fixed-baseline C-band InSAR data over tropical wet forests of La Selva Biological Station, Costa Rica, we compare the use of Fourier transforms of vertical profiles at a few frequencies to the intrinsically low-frequency “average height”. RMS scatters of Fourier-estimated biomass about field-measured biomass improved by 40% and 20% over estimates base on average height from lidar and fixed-baseline InSAR, respectively. Vertical wavelengths between 14 and 100 m were found to best estimate biomass. The same airborne data acquisition over La Selva was used to generate many 10’s of repeat-track L-band InSAR baselines with time delays of 1-72 hours, and vertical wavelengths of 5-100 m. We will estimate biomass from the Fourier transforms of L-band radar power profiles (InSAR complex coherence). The effects of temporal decorrelation will be modeled in the Fourier domain to try to model and reduce their impact. Using L-band polarimetric interferometry, average heights will be estimated as well and biomass regression performance compared to the Fourier transform approach. The more traditional approach of using L-band radar polarimetry will also be compared to structural biomass estimation.
Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms
Schmittfull, Marcel; Vlah, Zvonimir; McDonald, Patrick
2016-05-01
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. The method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.
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
Dong, Bing; Qin, Shun; Hu, Xinqi
2013-09-01
Large-aperture segmented primary mirror will be widely used in next-generation space-based and ground-based telescopes. The effects of intersegment gaps, obstructions, position and figure errors of segments, which are all involved in the pupil plane, on the image quality metric should be analyzed using diffractive imaging theory. Traditional Fast Fourier Transform (FFT) method is very time-consuming and costs a lot of memory especially in dealing with large pupil-sampling matrix. A Partial Fourier Transform (PFT) method is first proposed to substantially speed up the computation and reduce memory usage for diffractive imaging analysis. Diffraction effects of a 6-meter segmented mirror including 18 hexagonal segments are simulated and analyzed using PFT method. The influence of intersegment gaps and position errors of segments on Strehl ratio is quantitatively analyzed by computing the Point Spread Function (PSF). By comparing simulation results with theoretical results, the correctness and feasibility of PFT method is confirmed.
The X1Σ +g ground state of Mg2 studied by Fourier-transform spectroscopy
Knöckel, H.; Rühmann, S.; Tiemann, E.
2013-03-01
The A^1Σ u^+ - X^1Σ g^+ UV spectrum of Mg2 has been investigated with high resolution Fourier-transform spectroscopy. Mg2 vapor was created in a heat pipe. Various spectroscopic methods have been employed, such as conventional absorption spectroscopy with light from a broad band lamp and laser-induced fluorescence. The high resolution of the Fourier-transform spectrometer, together with computer aided evaluation methods of the spectra, yields precise transition frequencies. The new data and data available from earlier investigations are applied in direct potential fits of lower and upper electronic states. Various representations of potential energy curves for the ground state X^1Σ g^+ have been employed and their benefits in terms of smallest number of parameters are discussed. Scattering lengths are derived for the homonuclear isotopologues and compared with previous results.
Foliage Plant Retrieval using Polar Fourier Transform, Color Moments and Vein Features
Kadir, Abdul; Susanto, Adhi; Santosa, Paulus Insap
2011-01-01
This paper proposed a method that combines Polar Fourier Transform, color moments, and vein features to retrieve leaf images based on a leaf image. The method is very useful to help people in recognizing foliage plants. Foliage plants are plants that have various colors and unique patterns in the leaf. Therefore, the colors and its patterns are information that should be counted on in the processing of plant identification. To compare the performance of retrieving system to other result, the experiments used Flavia dataset, which is very popular in recognizing plants. The result shows that the method gave better performance than PNN, SVM, and Fourier Transform. The method was also tested using foliage plants with various colors. The accuracy was 90.80% for 50 kinds of plants.
Kaneko, Tak
2008-01-01
Context: Fourier transform (or lag) correlators in radio interferometers can serve as an efficient means of synthesising spectral channels. However aliasing corrupts the edge channels so they usually have to be excluded from the data set. In systems with around 10 channels, the loss in sensitivity can be significant. In addition, the low level of residual aliasing in the remaining channels may cause systematic errors. Moreover, delay errors have been widely reported in implementations of broadband analogue correlators and simulations have shown that delay errors exasperate the effects of aliasing. Aims: We describe a software-based approach that suppresses aliasing by oversampling the cross-correlation function. This method can be applied to interferometers with individually-tracking antennas equipped with a discrete path compensator system. It is based on the well-known property of interferometers where the drift scan response is the Fourier transform of the source's band-limited spectrum. Methods: In this p...
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.
Sharpening the response of an FIR filter using Fractional Fourier Transform
Directory of Open Access Journals (Sweden)
Somesh Chaturvedi
2012-03-01
Full Text Available In this paper we have implemented FIR filter with the help of Kaiser Window and Fractional Fourier Transform (FRFT. The window shape parameter is tuned for the transition band by considering linear phase FRFT Finite Impulse Response (FIR filter. Here FRFT of Kaiser Window is taken and convolved with the response function for tuning purposes of the transition band which makes effective transition band. This proposed method includes the change of parameters of Kaiser window by which other windows like Rectangle, Bartlett, Hamming Blackman and Hanning windows are generated by using FRFT. The efficiencies of this method in terms of main lobe and side ripples are better than the above mentioned windows under Fourier transform.
Melchert, O; Roth, B
2016-01-01
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to applications in computational biophotonics. In our survey of the numerical procedure we account for the circumstance that the objective function might result from a more complex measurement process and is, in the worst case, known on a finite sequence of coordinate values, only. We contrast the performance of the resulting algorithms with a procedure based on a straight forward numerical quadrature of the underlying integral transform and asses its efficienty for two benchmark Fourier-Bessel pairs. An application to the problem of finite-size beam-shape convolution in polar coordinates, relevant in the context of tissue optics and optoacoustics, is used to illustrate the versatility and computational efficiency of the numerical procedure.
The data processing pipeline for the Herschel SPIRE Fourier Transform Spectrometer
Fulton, T; Polehampton, E T; Valtchanov, I; Hopwood, R; Lu, N; Baluteau, J -P; Mainetti, G; Pearson, C; Papageorgiou, A; Guest, S; Zhang, L; Imhof, P; Swinyard, B M; Griffin, M J; Lim, T L
2016-01-01
We present the data processing pipeline to generate calibrated data products from the Spectral and Photometric Imaging Receiver (SPIRE) imaging Fourier Transform Spectrometer on the Herschel Space Observatory. The pipeline processes telemetry from SPIRE observations and produces calibrated spectra for all resolution modes. The spectrometer pipeline shares some elements with the SPIRE photometer pipeline, including the conversion of telemetry packets into data timelines and calculation of bolometer voltages. We present the following fundamental processing steps unique to the spectrometer: temporal and spatial interpolation of the scan mechanism and detector data to create interferograms; Fourier transformation; apodization; and creation of a data cube. We also describe the corrections for various instrumental effects including first- and second-level glitch identification and removal, correction of the effects due to emission from the Herschel telescope and from within the spectrometer instrument, interferogra...
Suppression law of quantum states in a 3D photonic fast Fourier transform chip
Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio
2016-01-01
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135