Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.
Fast algorithm of adaptive Fourier series
Gao, You; Ku, Min; Qian, Tao
2018-05-01
Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was originated for the goal of positive frequency representations of signals. It achieved the goal and at the same time offered fast decompositions of signals. There then arose several types of AFDs. AFD merged with the greedy algorithm idea, and in particular, motivated the so-called pre-orthogonal greedy algorithm (Pre-OGA) that was proven to be the most efficient greedy algorithm. The cost of the advantages of the AFD type decompositions is, however, the high computational complexity due to the involvement of maximal selections of the dictionary parameters. The present paper offers one formulation of the 1-D AFD algorithm by building the FFT algorithm into it. Accordingly, the algorithm complexity is reduced, from the original $\\mathcal{O}(M N^2)$ to $\\mathcal{O}(M N\\log_2 N)$, where $N$ denotes the number of the discretization points on the unit circle and $M$ denotes the number of points in $[0,1)$. This greatly enhances the applicability of AFD. Experiments are carried out to show the high efficiency of the proposed algorithm.
Fourier transform wavefront control with adaptive prediction of the atmosphere.
Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre
2007-09-01
Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.
Using Fourier transform IR spectroscopy to analyze biological materials
Baker, Matthew J; Trevisan, Júlio; Bassan, Paul; Bhargava, Rohit; Butler, Holly J; Dorling, Konrad M; Fielden, Peter R; Fogarty, Simon W; Fullwood, Nigel J; Heys, Kelly A; Hughes, Caryn; Lasch, Peter; Martin-Hirsch, Pierre L; Obinaju, Blessing; Sockalingum, Ganesh D; Sulé-Suso, Josep; Strong, Rebecca J; Walsh, Michael J; Wood, Bayden R; Gardner, Peter; Martin, Francis L
2015-01-01
IR spectroscopy is an excellent method for biological analyses. It enables the nonperturbative, label-free extraction of biochemical information and images toward diagnosis and the assessment of cell functionality. Although not strictly microscopy in the conventional sense, it allows the construction of images of tissue or cell architecture by the passing of spectral data through a variety of computational algorithms. Because such images are constructed from fingerprint spectra, the notion is that they can be an objective reflection of the underlying health status of the analyzed sample. One of the major difficulties in the field has been determining a consensus on spectral pre-processing and data analysis. This manuscript brings together as coauthors some of the leaders in this field to allow the standardization of methods and procedures for adapting a multistage approach to a methodology that can be applied to a variety of cell biological questions or used within a clinical setting for disease screening or diagnosis. We describe a protocol for collecting IR spectra and images from biological samples (e.g., fixed cytology and tissue sections, live cells or biofluids) that assesses the instrumental options available, appropriate sample preparation, different sampling modes as well as important advances in spectral data acquisition. After acquisition, data processing consists of a sequence of steps including quality control, spectral pre-processing, feature extraction and classification of the supervised or unsupervised type. A typical experiment can be completed and analyzed within hours. Example results are presented on the use of IR spectra combined with multivariate data processing. PMID:24992094
Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging
International Nuclear Information System (INIS)
Soloviev, Vadim Y.
2006-01-01
A novel adaptive mesh technique in the Fourier domain is introduced for problems in fluorescence lifetime imaging. A dynamical adaptation of the three-dimensional scheme based on the finite volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. Light propagation in the medium is modeled by the telegraph equation, while the lifetime reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the method are demonstrated by image reconstruction of two spherical fluorescent objects embedded in a tissue phantom
Fourier transform digital holographic adaptive optics imaging system
Liu, Changgeng; Yu, Xiao; Kim, Myung K.
2013-01-01
A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541
A portable Fourier transform infrared gas analyzer with a photoacoustic detector performed reliably during pollution prevention research at two industrial facilities. It exhibited good agreement (within approximately 6%) with other analytical instruments (dispersive infrared and ...
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Yuntao Liang
2015-01-01
Full Text Available Aimed at monitoring emission of organic gases such as CH4, C2H6, C3H8, iso-C4H10, n-C4H10, C2H4, C3H6, C2H2, CO, and CO2, from coal mines, petroleum refineries, and other plants, a Fourier Transform Infrared (FT-IR spectrometer was used to develop a portable gas analyzer for patrolling and examining gas exhaust. Firstly, structure of the instrument was introduced. Then, a spectral analysis approach was presented. Finally, instrument was tested with standard gases and with actual gases emitted from a petroleum refinery. For the latter test, a gas chromatograph (GC was used as a reference instrument. The test results showed that the detection limit of every component of analyte was less than 10 × 10−6. The maximum test error of every analyte was less than 15 × 10−6 when its practical concentration was no more than 500 × 10−6. A final comparison showed that the result curves of analytes obtained with FT-IR spectrometer almost overlapped with those obtained with GC, and their resulting noise was less than 6.4% when the practical gas concentration was above 100 × 10−6. As a result, our instrument was suitable to be used as a portable instrument for monitoring exhaust gases.
Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.
2017-05-01
The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.
Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data
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Darian M. Onchiș
2011-09-01
Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.
Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.
Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong
2018-02-13
Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.
Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian
2015-03-01
Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Olivier, Scot S.; Werner, John S.; Zawadzki, Robert J.; Laut, Sophie P.; Jones, Steven M.
2010-09-07
This invention permits retinal images to be acquired at high speed and with unprecedented resolution in three dimensions (4.times.4.times.6 .mu.m). The instrument achieves high lateral resolution by using adaptive optics to correct optical aberrations of the human eye in real time. High axial resolution and high speed are made possible by the use of Fourier-domain optical coherence tomography. Using this system, we have demonstrated the ability to image microscopic blood vessels and the cone photoreceptor mosaic.
Fourier-space TEM reconstructions with symmetry adapted functions for all rotational point groups.
Trapani, Stefano; Navaza, Jorge
2013-05-01
A general-purpose and simple expression for the coefficients of symmetry adapted functions referred to conveniently oriented symmetry axes is given for all rotational point groups. The expression involves the computation of reduced Wigner-matrix elements corresponding to an angle specific to each group and has the computational advantage of leading to Fourier-space TEM (transmission electron microscopy) reconstruction procedures involving only real valued unknowns. Using this expression, a protocol for ab initio view and center assignment and reconstruction so far used for icosahedral particles has been tested with experimental data in other point groups. Copyright © 2013 Elsevier Inc. All rights reserved.
Night myopia studied with an adaptive optics visual analyzer.
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Pablo Artal
Full Text Available PURPOSE: Eyes with distant objects in focus in daylight are thought to become myopic in dim light. This phenomenon, often called "night myopia" has been studied extensively for several decades. However, despite its general acceptance, its magnitude and causes are still controversial. A series of experiments were performed to understand night myopia in greater detail. METHODS: We used an adaptive optics instrument operating in invisible infrared light to elucidate the actual magnitude of night myopia and its main causes. The experimental setup allowed the manipulation of the eye's aberrations (and particularly spherical aberration as well as the use of monochromatic and polychromatic stimuli. Eight subjects with normal vision monocularly determined their best focus position subjectively for a Maltese cross stimulus at different levels of luminance, from the baseline condition of 20 cd/m(2 to the lowest luminance of 22 × 10(-6 cd/m(2. While subjects performed the focusing tasks, their eye's defocus and aberrations were continuously measured with the 1050-nm Hartmann-Shack sensor incorporated in the adaptive optics instrument. The experiment was repeated for a variety of controlled conditions incorporating specific aberrations of the eye and chromatic content of the stimuli. RESULTS: We found large inter-subject variability and an average of -0.8 D myopic shift for low light conditions. The main cause responsible for night myopia was the accommodation shift occurring at low light levels. Other factors, traditionally suggested to explain night myopia, such as chromatic and spherical aberrations, have a much smaller effect in this mechanism. CONCLUSIONS: An adaptive optics visual analyzer was applied to study the phenomenon of night myopia. We found that the defocus shift occurring in dim light is mainly due to accommodation errors.
Bertilsson, Simon; Larsson, Fredrik; Furlani, Maurizio; Albinsson, Ingvar; Mellander, Bengt-Erik
2017-10-01
In the last few years the use of Li-ion batteries has increased rapidly, powering small as well as large applications, from electronic devices to power storage facilities. The Li-ion battery has, however, several safety issues regarding occasional overheating and subsequent thermal runaway. During such episodes, gas emissions from the electrolyte are of special concern because of their toxicity, flammability and the risk for gas explosion. In this work, the emissions from heated typical electrolyte components as well as from commonly used electrolytes are characterized using FT-IR spectroscopy and FT-IR coupled with thermogravimetric (TG) analysis, when heating up to 650 °C. The study includes the solvents EC, PC, DEC, DMC and EA in various single, binary and ternary mixtures with and without the LiPF6 salt, a commercially available electrolyte, (LP71), containing EC, DEC, DMC and LiPF6 as well as extracted electrolyte from a commercial 6.8 Ah Li-ion cell. Upon thermal heating, emissions of organic compounds and of the toxic decomposition products hydrogen fluoride (HF) and phosphoryl fluoride (POF3) were detected. The electrolyte and its components have also been extensively analyzed by means of infrared spectroscopy for identification purposes.
Adaptive synchrosqueezing based on a quilted short-time Fourier transform
Berrian, Alexander; Saito, Naoki
2017-08-01
In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST, based on the short-time Fourier transform (STFT), enables the sharpening of instantaneous frequency (IF) information derived from the STFT, as well as the separation of amplitude-phase components corresponding to distinct IF curves. However, this SST is limited by the time-frequency resolution of the underlying window function, and may not resolve signals exhibiting diverse time-frequency behaviors with sufficient accuracy. In this work, we develop a framework for an SST based on a "quilted" short-time Fourier transform (SST-QSTFT), which allows adaptation to signal behavior in separate time-frequency regions through the use of multiple windows. This motivates us to introduce a discrete reassignment frequency formula based on a finite difference of the phase spectrum, ensuring computational accuracy for a wider variety of windows. We develop a theoretical framework for the SST-QSTFT in both the continuous and the discrete settings, and describe an algorithm for the automatic selection of optimal windows depending on the region of interest. Using synthetic data, we demonstrate the superior numerical performance of SST-QSTFT relative to other SST methods in a noisy context. Finally, we apply SST-QSTFT to audio recordings of animal calls to demonstrate the potential of our method for the analysis of real bioacoustic signals.
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I. C. Ramos
2015-10-01
Full Text Available We present the adaptation to non-free boundary conditions of a pseudospectral method based on the (complex Fourier transform. The method is applied to the numerical integration of the Oberbeck-Boussinesq equations in a Rayleigh-Bénard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number (. These results are the basis for the later study, by the same method, of wet convection in a solar still. Received: 20 Novembre 2014, Accepted: 15 September 2015; Edited by: C. A. Condat, G. J. Sibona; DOI:http://dx.doi.org/10.4279/PIP.070015 Cite as: I C Ramos, C B Briozzo, Papers in Physics 7, 070015 (2015
A novel ECG data compression method based on adaptive Fourier decomposition
Tan, Chunyu; Zhang, Liming
2017-12-01
This paper presents a novel electrocardiogram (ECG) compression method based on adaptive Fourier decomposition (AFD). AFD is a newly developed signal decomposition approach, which can decompose a signal with fast convergence, and hence reconstruct ECG signals with high fidelity. Unlike most of the high performance algorithms, our method does not make use of any preprocessing operation before compression. Huffman coding is employed for further compression. Validated with 48 ECG recordings of MIT-BIH arrhythmia database, the proposed method achieves the compression ratio (CR) of 35.53 and the percentage root mean square difference (PRD) of 1.47% on average with N = 8 decomposition times and a robust PRD-CR relationship. The results demonstrate that the proposed method has a good performance compared with the state-of-the-art ECG compressors.
Adaptive Fourier decomposition based R-peak detection for noisy ECG Signals.
Ze Wang; Chi Man Wong; Feng Wan
2017-07-01
An adaptive Fourier decomposition (AFD) based R-peak detection method is proposed for noisy ECG signals. Although lots of QRS detection methods have been proposed in literature, most detection methods require high signal quality. The proposed method extracts the R waves from the energy domain using the AFD and determines the R-peak locations based on the key decomposition parameters, achieving the denoising and the R-peak detection at the same time. Validated by clinical ECG signals in the MIT-BIH Arrhythmia Database, the proposed method shows better performance than the Pan-Tompkin (PT) algorithm in both situations of a native PT and the PT with a denoising process.
International Nuclear Information System (INIS)
Roger Lew; Brian P. Dyre; Steffen Werner; Jeffrey C. Joe; Brian Wotring; Tuan Tran
2008-01-01
The development of real-time predictors of mental workload is critical for the practical application of augmented cognition to human-machine systems. This paper explores a novel method based on a short-time Fourier transform (STFT) for analyzing galvanic skin conductance (SC) and pupillometry time-series data to extract estimates of mental workload with temporal bandwidth high-enough to be useful for augmented cognition applications. We tested the method in the context of a process control task based on the DURESS simulation developed by Vincente and Pawlak (1994; ported to Java by Cosentino, and Ross, 1999). SC, pupil dilation, blink rate, and visual scanning patterns were measured for four participants actively engaged in controlling the simulation. Fault events were introduced that required participants to diagnose errors and make control adjustments to keep the simulator operating within a target range. We were interested in whether the STFT of these measures would produce visible effects of the increase in mental workload and stress associated with these events. Graphical exploratory data analysis of the STFT showed visible increases in the power spectrum across a range of frequencies directly following fault events. We believe this approach shows potential as a relatively unobtrusive, low-cost, high bandwidth measure of mental workload that could be particularly useful for the application of augmented cognition to human-machine systems
Energy Technology Data Exchange (ETDEWEB)
Roger Lew; Brian P. Dyre; Steffen Werner; Jeffrey C. Joe; Brian Wotring; Tuan Tran
2008-09-01
The development of real-time predictors of mental workload is critical for the practical application of augmented cognition to human-machine systems. This paper explores a novel method based on a short-time Fourier transform (STFT) for analyzing galvanic skin conductance (SC) and pupillometry time-series data to extract estimates of mental workload with temporal bandwidth high-enough to be useful for augmented cognition applications. We tested the method in the context of a process control task based on the DURESS simulation developed by Vincente and Pawlak (1994; ported to Java by Cosentino,& Ross, 1999). SC, pupil dilation, blink rate, and visual scanning patterns were measured for four participants actively engaged in controlling the simulation. Fault events were introduced that required participants to diagnose errors and make control adjustments to keep the simulator operating within a target range. We were interested in whether the STFT of these measures would produce visible effects of the increase in mental workload and stress associated with these events. Graphical exploratory data analysis of the STFT showed visible increases in the power spectrum across a range of frequencies directly following fault events. We believe this approach shows potential as a relatively unobtrusive, low-cost, high bandwidth measure of mental workload that could be particularly useful for the application of augmented cognition to human-machine systems.
Adaptive ISAR Imaging of Maneuvering Targets Based on a Modified Fourier Transform.
Wang, Binbin; Xu, Shiyou; Wu, Wenzhen; Hu, Pengjiang; Chen, Zengping
2018-04-27
Focusing on the inverse synthetic aperture radar (ISAR) imaging of maneuvering targets, this paper presents a new imaging method which works well when the target's maneuvering is not too severe. After translational motion compensation, we describe the equivalent rotation of maneuvering targets by two variables-the relative chirp rate of the linear frequency modulated (LFM) signal and the Doppler focus shift. The first variable indicates the target's motion status, and the second one represents the possible residual error of the translational motion compensation. With them, a modified Fourier transform matrix is constructed and then used for cross-range compression. Consequently, the imaging of maneuvering is converted into a two-dimensional parameter optimization problem in which a stable and clear ISAR image is guaranteed. A gradient descent optimization scheme is employed to obtain the accurate relative chirp rate and Doppler focus shift. Moreover, we designed an efficient and robust initialization process for the gradient descent method, thus, the well-focused ISAR images of maneuvering targets can be achieved adaptively. Human intervention is not needed, and it is quite convenient for practical ISAR imaging systems. Compared to precedent imaging methods, the new method achieves better imaging quality under reasonable computational cost. Simulation results are provided to validate the effectiveness and advantages of the proposed method.
Athale, R.; Lee, S. H.
1976-01-01
Various defects in mass-produced pictures transmitted to earth from a satellite are investigated. It is found that the following defects are readily detectable via Fourier spectrum analysis: (1) bit slip, (2) breakup causing loss of image, and (3) disabled track at the top of the imagery. The scratches made on the film during mass production, which are difficult to detect by visual observation, also show themselves readily in Fourier spectrum analysis. A relation is established between the number of scratches, their width and depth and the intensity of their Fourier spectra. Other defects that are found to be equally suitable for Fourier spectrum analysis or visual (image analysis) detection are synchronous loss without blurring of image, and density variation in gray scale. However, the Fourier spectrum analysis is found to be unsuitable for detection of such defects as pin holes, annotation error, synchronous loss with blurring of images, and missing image in the beginning of the work order. The design of an automated, real time system, which will reject defective films, is treated.
Vogel, Curtis R; Yang, Qiang
2006-08-21
We present two different implementations of the Fourier domain preconditioned conjugate gradient algorithm (FD-PCG) to efficiently solve the large structured linear systems that arise in optimal volume turbulence estimation, or tomography, for multi-conjugate adaptive optics (MCAO). We describe how to deal with several critical technical issues, including the cone coordinate transformation problem and sensor subaperture grid spacing. We also extend the FD-PCG approach to handle the deformable mirror fitting problem for MCAO.
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Gilberto Herrera-Ruíz
2013-03-01
Full Text Available A New Adaptive Self-Tuning Fourier Coefficients Algorithm for Periodic Torque Ripple Minimization in Permanent Magnet Synchronous Motors (PMSM Torque ripple occurs in Permanent Magnet Synchronous Motors (PMSMs due to the non-sinusoidal flux density distribution around the air-gap and variable magnetic reluctance of the air-gap due to the stator slots distribution. These torque ripples change periodically with rotor position and are apparent as speed variations, which degrade the PMSM drive performance, particularly at low speeds, because of low inertial filtering. In this paper, a new self-tuning algorithm is developed for determining the Fourier Series Controller coefficients with the aim of reducing the torque ripple in a PMSM, thus allowing for a smoother operation. This algorithm adjusts the controller parameters based on the component’s harmonic distortion in time domain of the compensation signal. Experimental evaluation is performed on a DSP-controlled PMSM evaluation platform. Test results obtained validate the effectiveness of the proposed self-tuning algorithm, with the Fourier series expansion scheme, in reducing the torque ripple.
Gómez-Espinosa, Alfonso; Hernández-Guzmán, Víctor M; Bandala-Sánchez, Manuel; Jiménez-Hernández, Hugo; Rivas-Araiza, Edgar A; Rodríguez-Reséndiz, Juvenal; Herrera-Ruíz, Gilberto
2013-03-19
A New Adaptive Self-Tuning Fourier Coefficients Algorithm for Periodic Torque Ripple Minimization in Permanent Magnet Synchronous Motors (PMSM) Torque ripple occurs in Permanent Magnet Synchronous Motors (PMSMs) due to the non-sinusoidal flux density distribution around the air-gap and variable magnetic reluctance of the air-gap due to the stator slots distribution. These torque ripples change periodically with rotor position and are apparent as speed variations, which degrade the PMSM drive performance, particularly at low speeds, because of low inertial filtering. In this paper, a new self-tuning algorithm is developed for determining the Fourier Series Controller coefficients with the aim of reducing the torque ripple in a PMSM, thus allowing for a smoother operation. This algorithm adjusts the controller parameters based on the component's harmonic distortion in time domain of the compensation signal. Experimental evaluation is performed on a DSP-controlled PMSM evaluation platform. Test results obtained validate the effectiveness of the proposed self-tuning algorithm, with the Fourier series expansion scheme, in reducing the torque ripple.
Ma, JiaLi; Zhang, TanTan; Dong, MingChui
2015-05-01
This paper presents a novel electrocardiogram (ECG) compression method for e-health applications by adapting an adaptive Fourier decomposition (AFD) algorithm hybridized with a symbol substitution (SS) technique. The compression consists of two stages: first stage AFD executes efficient lossy compression with high fidelity; second stage SS performs lossless compression enhancement and built-in data encryption, which is pivotal for e-health. Validated with 48 ECG records from MIT-BIH arrhythmia benchmark database, the proposed method achieves averaged compression ratio (CR) of 17.6-44.5 and percentage root mean square difference (PRD) of 0.8-2.0% with a highly linear and robust PRD-CR relationship, pushing forward the compression performance to an unexploited region. As such, this paper provides an attractive candidate of ECG compression method for pervasive e-health applications.
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Shengxin Wang
2016-06-01
Full Text Available Pathological tremor is an approximately rhythmic movement and considerably affects patients’ daily living activities. Biomechanical loading and functional electrical stimulation are proposed as potential alternatives for canceling the pathological tremor. However, the performance of suppression methods is associated with the separation of tremor from the recorded signals. In this literature, an algorithm incorporating a fast Fourier transform augmented with a sliding convolution window, an interpolation procedure, and a damping module of the frequency is presented to isolate tremulous components from the measured signals and estimate the instantaneous tremor frequency. Meanwhile, a mechanism platform is designed to provide the simulation tremor signals with different degrees of voluntary movements. The performance of the proposed algorithm and existing procedures is compared with simulated signals and experimental signals collected from patients. The results demonstrate that the proposed solution could detect the unknown dominant frequency and distinguish the tremor components with higher accuracy. Therefore, this algorithm is useful for actively compensating tremor by functional electrical stimulation without affecting the voluntary movement.
Introduction to n-adaptive fuzzy models to analyze public opinion on AIDS
Kandasamy, D W B V; Kandasamy, Dr.W.B.Vasantha; Smarandache, Dr.Florentin
2006-01-01
There are many fuzzy models like Fuzzy matrices, Fuzzy Cognitive Maps, Fuzzy relational Maps, Fuzzy Associative Memories, Bidirectional Associative memories and so on. But almost all these models can give only one sided solution like hidden pattern or a resultant output vector dependent on the input vector depending in the problem at hand. So for the first time we have defined a n-adaptive fuzzy model which can view or analyze the problem in n ways (n >=2) Though we have defined these n- adaptive fuzzy models theorectically we are not in a position to get a n-adaptive fuzzy model for n > 2 for practical real world problems. The highlight of this model is its capacity to analyze the same problem in different ways thereby arriving at various solutions that mirror multiple perspectives. We have used the 2-adaptive fuzzy model having the two fuzzy models, fuzzy matrices model and BAMs viz. model to analyze the views of public about HIV/ AIDS disease, patient and the awareness program. This book has five chapters ...
Higgins, James D; Wright, Kevin M; Bomblies, Kirsten; Franklin, F Chris H
2014-01-01
Arabidopsis arenosa is a close relative of the model plant A. thaliana, and exists in nature as stable diploid and autotetraploid populations. Natural tetraploids have adapted to whole genome duplication and do not commonly show meiotic errors such as multivalent and univalent formation, which can lead to chromosome non-disjunction and reduced fertility. A genome scan for genes strongly differentiated between diploid and autotetraploid A. arenosa identified a subset of meiotic genes that may be responsible for adaptation to polyploid meiosis. To investigate the mechanisms by which A. arenosa adapted to its polyploid state, and the functionality of the identified potentially adaptive polymorphisms, a thorough cytological analysis is required. Therefore, in this chapter we describe methods and techniques to analyze male meiosis in A. arenosa, including optimum plant growth conditions, and immunocytological and cytological approaches developed with the specific purpose of understanding meiotic adaptation in an autotetraploid. In addition we present a meiotic cytological atlas to be used as a reference for particular stages and discuss observations arising from a comparison of meiosis between diploid and autotetraploid A. arenosa.
Higgins, James D.; Wright, Kevin M.; Bomblies, Kirsten; Franklin, F. Chris H.
2014-01-01
Arabidopsis arenosa is a close relative of the model plant A. thaliana, and exists in nature as stable diploid and autotetraploid populations. Natural tetraploids have adapted to whole genome duplication and do not commonly show meiotic errors such as multivalent and univalent formation, which can lead to chromosome non-disjunction and reduced fertility. A genome scan for genes strongly differentiated between diploid and autotetraploid A. arenosa identified a subset of meiotic genes that may be responsible for adaptation to polyploid meiosis. To investigate the mechanisms by which A. arenosa adapted to its polyploid state, and the functionality of the identified potentially adaptive polymorphisms, a thorough cytological analysis is required. Therefore, in this chapter we describe methods and techniques to analyze male meiosis in A. arenosa, including optimum plant growth conditions, and immunocytological and cytological approaches developed with the specific purpose of understanding meiotic adaptation in an autotetraploid. In addition we present a meiotic cytological atlas to be used as a reference for particular stages and discuss observations arising from a comparison of meiosis between diploid and autotetraploid A. arenosa. PMID:24427164
Directory of Open Access Journals (Sweden)
James D Higgins
2014-01-01
Full Text Available Arabidopsis arenosa is a close relative of the model plant Arabidopsis thaliana, and exists in nature as stable diploid and autotetraploid populations. Natural tetraploids have adapted to whole genome duplication and do not commonly show meiotic errors such as multivalent and univalent formation, which can lead to chromosome non-disjunction and reduced fertility. A genome scan for genes strongly differentiated between diploid and autotetraploid A. arenosa identified a subset of meiotic genes that may be responsible for adaptation to polyploid meiosis. To investigate the mechanisms by which A. arenosa adapted to its polyploid state, and the functionality of the identified potentially adaptive polymorphisms, a thorough cytological analysis is required. Therefore, in this chapter we describe methods and techniques to analyze male meiosis in A. arenosa, including optimum plant growth conditions, and immunocytological and cytological approaches developed with the specific purpose of understanding meiotic adaptation in an autotetraploid. In addition we present a meiotic cytological atlas to be used as a reference for particular stages and discuss observations arising from a comparison of meiosis between diploid and autotetraploid A. arenosa.
Analyzing extreme sea levels for broad-scale impact and adaptation studies
Wahl, T.; Haigh, I. D.; Nicholls, R. J.; Arns, A.; Dangendorf, S.; Hinkel, J.; Slangen, A.
2017-12-01
Coastal impact and adaptation assessments require detailed knowledge on extreme sea levels (ESL), because increasing damage due to extreme events is one of the major consequences of sea-level rise (SLR) and climate change. Over the last few decades, substantial research efforts have been directed towards improved understanding of past and future SLR; different scenarios were developed with process-based or semi-empirical models and used for coastal impact studies at various temporal and spatial scales to guide coastal management and adaptation efforts. Uncertainties in future SLR are typically accounted for by analyzing the impacts associated with a range of scenarios and model ensembles. ESL distributions are then displaced vertically according to the SLR scenarios under the inherent assumption that we have perfect knowledge on the statistics of extremes. However, there is still a limited understanding of present-day ESL which is largely ignored in most impact and adaptation analyses. The two key uncertainties stem from: (1) numerical models that are used to generate long time series of storm surge water levels, and (2) statistical models used for determining present-day ESL exceedance probabilities. There is no universally accepted approach to obtain such values for broad-scale flood risk assessments and while substantial research has explored SLR uncertainties, we quantify, for the first time globally, key uncertainties in ESL estimates. We find that contemporary ESL uncertainties exceed those from SLR projections and, assuming that we meet the Paris agreement, the projected SLR itself by the end of the century. Our results highlight the necessity to further improve our understanding of uncertainties in ESL estimates through (1) continued improvement of numerical and statistical models to simulate and analyze coastal water levels and (2) exploit the rich observational database and continue data archeology to obtain longer time series and remove model bias
Open-path Fourier transform infrared (OP/FTIR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric gases at an integrated swine production facility. The concentration-pathlength products of the target gases at this site often exceeded th...
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Learn, R; Feigenbaum, E
2016-06-01
Two algorithms that enhance the utility of the absorbing boundary layer are presented, mainly in the framework of the Fourier beam-propagation method. One is an automated boundary layer width selector that chooses a near-optimal boundary size based on the initial beam shape. The second algorithm adjusts the propagation step sizes based on the beam shape at the beginning of each step in order to reduce aliasing artifacts.
Hoch, Jeffrey C.
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.
Hoch, Jeffrey C
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.
Bramness, Jørgen G; Walby, Fredrik A; Morken, Gunnar; Røislien, Jo
2015-08-01
Seasonal variation in the number of suicides has long been acknowledged. It has been suggested that this seasonality has declined in recent years, but studies have generally used statistical methods incapable of confirming this. We examined all suicides occurring in Norway during 1969-2007 (more than 20,000 suicides in total) to establish whether seasonality decreased over time. Fitting of additive Fourier Poisson time-series regression models allowed for formal testing of a possible linear decrease in seasonality, or a reduction at a specific point in time, while adjusting for a possible smooth nonlinear long-term change without having to categorize time into discrete yearly units. The models were compared using Akaike's Information Criterion and analysis of variance. A model with a seasonal pattern was significantly superior to a model without one. There was a reduction in seasonality during the period. Both the model assuming a linear decrease in seasonality and the model assuming a change at a specific point in time were both superior to a model assuming constant seasonality, thus confirming by formal statistical testing that the magnitude of the seasonality in suicides has diminished. The additive Fourier Poisson time-series regression model would also be useful for studying other temporal phenomena with seasonal components. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Directory of Open Access Journals (Sweden)
Amparo Gómez-Artiga
2013-05-01
Full Text Available This study presents a personality evaluation instrument adapted to the vocational setting: the Adaptive Vocational Personality Questionnaire (AVPQ. The questionnaire was developed and tested in a sample of 2160 university students in the final years of their degree programs. The purpose of the study is to validate the questionnaire, providing evidence about its internal structure and its usefulness for predicting scores on a criterion scale. A confirmatory factor analysis combined with a cross-validation design was used: the exploratory sample (n = 879 helped to identify the model with the factorial structure that best fit the relations among the items. As expected, this model had two related but clearly separate factors: Adaptive Personality Characteristics (AC with 9 items and Non-Adaptive Personality Characteristics (NAC with 11 items. The validation sample (n =932 was used to test the generalization capacity of this model, which was satisfactory and showed a good reliability index. Regarding its usefulness in predicting proactive job-search behaviors, the results were also satisfactory. The questionnaire and keys are provided, as well as the criteria for calculating the scores on each scale and on the entire questionnaire.
Karemere, Hermès; Ribesse, Nathalie; Marchal, Bruno; Macq, Jean
2015-01-01
This study deals with the adaptation of Katana referral hospital in Eastern Democratic Republic of Congo in a changing environment that is affected for more than a decade by intermittent armed conflicts. His objective is to generate theoretical proposals for addressing differently the analysis of hospitals governance in the aims to assess their performance and how to improve that performance. The methodology applied approach uses a case study using mixed methods ( qualitative and quantitative) for data collection. It uses (1) hospital data to measure the output of hospitals, (2) literature review to identify among others, events and interventions recorded in the history of hospital during the study period and (3) information from individual interviews to validate the interpretation of the results of the previous two sources of data and understand the responsiveness of management team referral hospital during times of change. The study brings four theoretical propositions: (1) Interaction between key agents is a positive force driving adaptation if the actors share a same vision, (2) The strength of the interaction between agents is largely based on the nature of institutional arrangements, which in turn are shaped by the actors themselves, (3) The owner and the management team play a decisive role in the implementation of effective institutional arrangements and establishment of positive interactions between agents, (4) The analysis of recipient population's perception of health services provided allow to better tailor and adapt the health services offer to the population's needs and expectations. Research shows that it isn't enough just to provide support (financial and technical), to manage a hospital for operate and adapt to a changing environment but must still animate, considering that it is a complex adaptive system and that this animation is nothing other than the induction of a positive interaction between agents.
Fourier Transform Mass Spectrometry
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-01-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802
Vargas-Caraveo, Alejandra; Castillo-Michel, Hiram; Mejia-Carmona, Gloria Erika; Pérez-Ishiwara, David Guillermo; Cotte, Marine; Martínez-Martínez, Alejandro
2014-07-01
Psychological stress is a condition that not only generates behavioral disorders but also disrupts homeostasis and immune activity that can exacerbate or lead to inflammatory diseases. The aim of this work was to study biochemical changes in circulating immune cells from rats under psychological stress by using vibrational spectroscopy. A stress model was used, where exposure to a stressor was repeated for 5 days. Subsequently, circulating lymphocytes were examined for their biomolecular vibrational fingerprints with synchrotron radiation based-Fourier transform infrared microspectroscopy. The results showed an increased absorption at the ester lipid region (1720-1755 cm-1) in lymphocytes from stressed rats, suggesting lipid peroxidation. Statistical significant changes in wavenumber peak position and absorbance in the nucleic acid region were also observed (915-950 cm-1 Z-DNA, 1090-1150 cm-1 symmetric stretching of Psbnd Osbnd C, 1200-1260 cm-1 asymmetric PO2 and 1570-1510 cm-1 methylated nucleotides) which suggest a reduction of transcriptional activity in lymphocytes from stressed rat. These results unravel part of the mechanisms by which psychological stress may affect the immune system leading to systemic consequences.
Urquhart, N; Godolphin, W; Campbell, D J
1979-05-01
We report a clinical evaluation of the enzyme immunoassay (EMIT) performed with the GEMSAEC centrifugal analyzer as compared to gas-liquid and liquid chromatography for anticonvulsant drugs and theophylline, respectively. A good correlation was obtained for all drugs, although some difficulties were experienced with one lot of reagent for ethosuximide. The analyzer has an economic advantage if many samples are being analyzed for few drugs in each sample.
Directory of Open Access Journals (Sweden)
Jennifer S. Arnold
2012-03-01
Full Text Available Adaptive collaborative management emphasizes stakeholder engagement as a crucial component of resilient social-ecological systems. Collaboration among diverse stakeholders is expected to enhance learning, build social legitimacy for decision making, and establish relationships that support learning and adaptation in the long term. However, simply bringing together diverse stakeholders does not guarantee productive engagement. Using critical discourse analysis, we examined how diverse stakeholders negotiated knowledge and power in a workshop designed to inform adaptive management of riparian livestock grazing on a National Forest in the southwestern USA. Publicly recognized as a successful component of a larger collaborative effort, we found that the workshop effectively brought together diverse participants, yet still restricted dialogue in important ways. Notably, workshop facilitators took on the additional roles of riparian experts and instructors. As they guided workshop participants toward a consensus view of riparian conditions and management recommendations, they used their status as riparian experts to emphasize commonalities with stakeholders supportive of riparian grazing and accentuate differences with stakeholders skeptical of riparian grazing, including some Forest Service staff with power to influence management decisions. Ultimately, the management plan published one year later did not fully adopt the consensus view from the workshop, but rather included and acknowledged a broader diversity of stakeholder perspectives. Our findings suggest that leaders and facilitators of adaptive collaborative management can more effectively manage for productive stakeholder engagement and, thus, social-ecological resilience if they are more tentative in their convictions, more critical of the role of expert knowledge, and more attentive to the knowledge, interests, and power of diverse stakeholders.
Directory of Open Access Journals (Sweden)
Nguyen, GTH.
2016-01-01
Full Text Available To understand drought adaptation practices, we compared two groups of sugarcane growers in Thanh Cong commune, Thach Thanh district, Thanh Hoa province in Vietnam. Results of this study point out that farmers, depending on their preferred type of market channels, reacted differently to the impacts of drought. Contractual farmers paid more attention to the impact on sugarcane tillering and sugar content, while market-oriented farmers paid more attention to sugarcane colour, as this trait directly determined the market price on the cane that is either consumed as cane or as juice. In responding to water stress in the growing season, the open market-oriented farmers showed more flexibility in changing their cropping calendar. They were also more willing to invest in enhancing the water management system and in providing organic fertilizer than the contractual farmers. On the other hand, the low cane price and the harvesting date set in contract by the processing company lessened the contractual farmers' flexibility in investing in water management technologies; thus, hampering their adaptation to drought.
Indian Academy of Sciences (India)
polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.
Indian Academy of Sciences (India)
The theory of Fourier series deals with periodic functions. By a periodic ..... including Dirichlet, Riemann and Cantor occupied themselves with the problem of ... to converge only on a set which is negligible in a certain sense (Le. of measure ...
An Adaptive S-Method to Analyze Micro-Doppler Signals for Human Activity Classification.
Li, Fangmin; Yang, Chao; Xia, Yuqing; Ma, Xiaolin; Zhang, Tao; Zhou, Zhou
2017-11-29
In this paper, we propose the multiwindow Adaptive S-method (AS-method) distribution approach used in the time-frequency analysis for radar signals. Based on the results of orthogonal Hermite functions that have good time-frequency resolution, we vary the length of window to suppress the oscillating component caused by cross-terms. This method can bring a better compromise in the auto-terms concentration and cross-terms suppressing, which contributes to the multi-component signal separation. Finally, the effective micro signal is extracted by threshold segmentation and envelope extraction. To verify the proposed method, six states of motion are separated by a classifier of a support vector machine (SVM) trained to the extracted features. The trained SVM can detect a human subject with an accuracy of 95.4% for two cases without interference.
An Adaptive S-Method to Analyze Micro-Doppler Signals for Human Activity Classification
Directory of Open Access Journals (Sweden)
Fangmin Li
2017-11-01
Full Text Available In this paper, we propose the multiwindow Adaptive S-method (AS-method distribution approach used in the time-frequency analysis for radar signals. Based on the results of orthogonal Hermite functions that have good time-frequency resolution, we vary the length of window to suppress the oscillating component caused by cross-terms. This method can bring a better compromise in the auto-terms concentration and cross-terms suppressing, which contributes to the multi-component signal separation. Finally, the effective micro signal is extracted by threshold segmentation and envelope extraction. To verify the proposed method, six states of motion are separated by a classifier of a support vector machine (SVM trained to the extracted features. The trained SVM can detect a human subject with an accuracy of 95.4% for two cases without interference.
Directory of Open Access Journals (Sweden)
Baptiste Nettier
2017-12-01
Full Text Available Social-ecological resilience is defined by Brian Walker and colleagues as "the capacity of a social-ecological system (SES to absorb disturbances and reorganize while undergoing change so as to continue to retain essentially the same function, structure, feedbacks, and therefore identity." It is an increasingly widespread concept whose success depends, among other things, on the promise of its rapid transfer from science into practice and its operational character for the sustainable management of SESs. However, tangible examples of management methods based on resilience remain limited in the scientific literature. Here, we test the resilience management framework proposed by Brian Walker and David Salt by applying it to the case of mountain summer pastures in the French Alps, which are complex SESs in which human and ecological dimensions are closely linked and subject to substantial perturbations due to climate change. Three steps were implemented: (1 building a conceptual model based on expert knowledge of the functioning of summer pastures; (2 building, from the model, a template for summer pasture resilience analysis; and (3 testing the operational character of the model and the template for two pairs of contrasting cases. This heuristic tool enables understanding the ways in which farmers and herders manage the resilience of their system but does not aim to quantify resilience. The method developed, together with the resilience concept, provide insights into the functioning of summer pastures from both biophysical and management perspectives. The modeling process constitutes a learning process, which will support the implementation of adaptive management. We identified three critical points for making the method truly operational: basing modeling on an equal consideration of social and ecological dimensions, defining the boundaries of the modeled system based on the social dimension, and selecting a scale of analysis coherent with the type
App. 1. Fourier series and Fourier transform
International Nuclear Information System (INIS)
Anon.
1977-01-01
Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr
A new BP Fourier algorithm and its application in English teaching evaluation
Pei, Xuehui; Pei, Guixin
2017-08-01
BP neural network algorithm has wide adaptability and accuracy when used in complicated system evaluation, but its calculation defects such as slow convergence have limited its practical application. The paper tries to speed up the calculation convergence of BP neural network algorithm with Fourier basis functions and presents a new BP Fourier algorithm for complicated system evaluation. First, shortages and working principle of BP algorithm are analyzed for subsequent targeted improvement; Second, the presented BP Fourier algorithm adopts Fourier basis functions to simplify calculation structure, designs new calculation transfer function between input and output layers, and conducts theoretical analysis to prove the efficiency of the presented algorithm; Finally, the presented algorithm is used in evaluating university English teaching and the application results shows that the presented BP Fourier algorithm has better performance in calculation efficiency and evaluation accuracy and can be used in evaluating complicated system practically.
Bargatze, L. F.
2015-12-01
files, or the addition of new or the deletion of old data products. Next, ADAPT routines analyzed the query results and issued updates to the metadata stored in the UCLA CDAWEB and SPDF metadata registries. In this way, the SPASE metadata registries generated by ADAPT can be relied on to provide up to date and complete access to Heliophysics CDF data resources on a daily basis.
Meijerink, S.; Stiller, S.J.
2013-01-01
This paper explores the relevance of various leadership concepts for climate change adaptation. After defi ning four main leadership challenges which are derived from the key characteristics of climate adaptation issues, a review of modern leadership theories addressing these challenges is
NIEMELÄ, EERO
2008-01-01
Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...
Reiding, Karli R.; Ruhaak, L. Renee; Uh, Hae-Won; el Bouhaddani, Said; van den Akker, Erik B.; Plomp, Rosina; McDonnell, Liam A.; Houwing-Duistermaat, Jeanine J.; Slagboom, P. Eline; Beekman, Marian; Wuhrer, Manfred
2017-01-01
Glycosylation is an abundant co- and post-translational protein modification of importance to protein processing and activity. Although not template-defined, glycosylation does reflect the biological state of an organism and is a high-potential biomarker for disease and patient stratification. However, to interpret a complex but informative sample like the total plasma N-glycome, it is important to establish its baseline association with plasma protein levels and systemic processes. Thus far, large-scale studies (n >200) of the total plasma N-glycome have been performed with methods of chromatographic and electrophoretic separation, which, although being informative, are limited in resolving the structural complexity of plasma N-glycans. MS has the opportunity to contribute additional information on, among others, antennarity, sialylation, and the identity of high-mannose type species. Here, we have used matrix-assisted laser desorption/ionization (MALDI)-Fourier transform ion cyclotron resonance (FTICR)-MS to study the total plasma N-glycome of 2144 healthy middle-aged individuals from the Leiden Longevity Study, to allow association analysis with markers of metabolic health and inflammation. To achieve this, N-glycans were enzymatically released from their protein backbones, labeled at the reducing end with 2-aminobenzoic acid, and following purification analyzed by negative ion mode intermediate pressure MALDI-FTICR-MS. In doing so, we achieved the relative quantification of 61 glycan compositions, ranging from Hex4HexNAc2 to Hex7HexNAc6dHex1Neu5Ac4, as well as that of 39 glycosylation traits derived thereof. Next to confirming known associations of glycosylation with age and sex by MALDI-FTICR-MS, we report novel associations with C-reactive protein (CRP), interleukin 6 (IL-6), body mass index (BMI), leptin, adiponectin, HDL cholesterol, triglycerides (TG), insulin, gamma-glutamyl transferase (GGT), alanine aminotransferase (ALT), and smoking. Overall, the
Reiding, Karli R; Ruhaak, L Renee; Uh, Hae-Won; El Bouhaddani, Said; van den Akker, Erik B; Plomp, Rosina; McDonnell, Liam A; Houwing-Duistermaat, Jeanine J; Slagboom, P Eline; Beekman, Marian; Wuhrer, Manfred
2017-02-01
Glycosylation is an abundant co- and post-translational protein modification of importance to protein processing and activity. Although not template-defined, glycosylation does reflect the biological state of an organism and is a high-potential biomarker for disease and patient stratification. However, to interpret a complex but informative sample like the total plasma N-glycome, it is important to establish its baseline association with plasma protein levels and systemic processes. Thus far, large-scale studies (n >200) of the total plasma N-glycome have been performed with methods of chromatographic and electrophoretic separation, which, although being informative, are limited in resolving the structural complexity of plasma N-glycans. MS has the opportunity to contribute additional information on, among others, antennarity, sialylation, and the identity of high-mannose type species.Here, we have used matrix-assisted laser desorption/ionization (MALDI)-Fourier transform ion cyclotron resonance (FTICR)-MS to study the total plasma N-glycome of 2144 healthy middle-aged individuals from the Leiden Longevity Study, to allow association analysis with markers of metabolic health and inflammation. To achieve this, N-glycans were enzymatically released from their protein backbones, labeled at the reducing end with 2-aminobenzoic acid, and following purification analyzed by negative ion mode intermediate pressure MALDI-FTICR-MS. In doing so, we achieved the relative quantification of 61 glycan compositions, ranging from Hex 4 HexNAc 2 to Hex 7 HexNAc 6 dHex 1 Neu5Ac 4 , as well as that of 39 glycosylation traits derived thereof. Next to confirming known associations of glycosylation with age and sex by MALDI-FTICR-MS, we report novel associations with C-reactive protein (CRP), interleukin 6 (IL-6), body mass index (BMI), leptin, adiponectin, HDL cholesterol, triglycerides (TG), insulin, gamma-glutamyl transferase (GGT), alanine aminotransferase (ALT), and smoking. Overall
International Nuclear Information System (INIS)
Hallenga, K.
1991-01-01
This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
Ratliff, Eric A; Kaduri, Pamela; Masao, Frank; Mbwambo, Jessie K K; McCurdy, Sheryl A
2016-04-01
Contrary to popular belief, policies on drug use are not always based on scientific evidence or composed in a rational manner. Rather, decisions concerning drug policies reflect the negotiation of actors' ambitions, values, and facts as they organize in different ways around the perceived problems associated with illicit drug use. Drug policy is thus best represented as a complex adaptive system (CAS) that is dynamic, self-organizing, and coevolving. In this analysis, we use a CAS framework to examine how harm reduction emerged around heroin trafficking and use in Tanzania over the past thirty years (1985-present). This account is an organizational ethnography based on of the observant participation of the authors as actors within this system. We review the dynamic history and self-organizing nature of harm reduction, noting how interactions among system actors and components have coevolved with patterns of heroin us, policing, and treatment activities over time. Using a CAS framework, we describe harm reduction as a complex process where ambitions, values, facts, and technologies interact in the Tanzanian sociopolitical environment. We review the dynamic history and self-organizing nature of heroin policies, noting how the interactions within and between competing prohibitionist and harm reduction policies have changed with patterns of heroin use, policing, and treatment activities over time. Actors learn from their experiences to organize with other actors, align their values and facts, and implement new policies. Using a CAS approach provides researchers and policy actors a better understanding of patterns and intricacies in drug policy. This knowledge of how the system works can help improve the policy process through adaptive action to introduce new actors, different ideas, and avenues for communication into the system. Copyright © 2015 Elsevier B.V. All rights reserved.
Fractional finite Fourier transform.
Khare, Kedar; George, Nicholas
2004-07-01
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.
Santos, José; Monteagudo, Ángel
2017-03-27
The canonical code, although prevailing in complex genomes, is not universal. It was shown the canonical genetic code superior robustness compared to random codes, but it is not clearly determined how it evolved towards its current form. The error minimization theory considers the minimization of point mutation adverse effect as the main selection factor in the evolution of the code. We have used simulated evolution in a computer to search for optimized codes, which helps to obtain information about the optimization level of the canonical code in its evolution. A genetic algorithm searches for efficient codes in a fitness landscape that corresponds with the adaptability of possible hypothetical genetic codes. The lower the effects of errors or mutations in the codon bases of a hypothetical code, the more efficient or optimal is that code. The inclusion of the fitness sharing technique in the evolutionary algorithm allows the extent to which the canonical genetic code is in an area corresponding to a deep local minimum to be easily determined, even in the high dimensional spaces considered. The analyses show that the canonical code is not in a deep local minimum and that the fitness landscape is not a multimodal fitness landscape with deep and separated peaks. Moreover, the canonical code is clearly far away from the areas of higher fitness in the landscape. Given the non-presence of deep local minima in the landscape, although the code could evolve and different forces could shape its structure, the fitness landscape nature considered in the error minimization theory does not explain why the canonical code ended its evolution in a location which is not an area of a localized deep minimum of the huge fitness landscape.
The derivative-free Fourier shell identity for photoacoustics.
Baddour, Natalie
2016-01-01
In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.
Broom, Donald M
2006-01-01
The term adaptation is used in biology in three different ways. It may refer to changes which occur at the cell and organ level, or at the individual level, or at the level of gene action and evolutionary processes. Adaptation by cells, especially nerve cells helps in: communication within the body, the distinguishing of stimuli, the avoidance of overload and the conservation of energy. The time course and complexity of these mechanisms varies. Adaptive characters of organisms, including adaptive behaviours, increase fitness so this adaptation is evolutionary. The major part of this paper concerns adaptation by individuals and its relationships to welfare. In complex animals, feed forward control is widely used. Individuals predict problems and adapt by acting before the environmental effect is substantial. Much of adaptation involves brain control and animals have a set of needs, located in the brain and acting largely via motivational mechanisms, to regulate life. Needs may be for resources but are also for actions and stimuli which are part of the mechanism which has evolved to obtain the resources. Hence pigs do not just need food but need to be able to carry out actions like rooting in earth or manipulating materials which are part of foraging behaviour. The welfare of an individual is its state as regards its attempts to cope with its environment. This state includes various adaptive mechanisms including feelings and those which cope with disease. The part of welfare which is concerned with coping with pathology is health. Disease, which implies some significant effect of pathology, always results in poor welfare. Welfare varies over a range from very good, when adaptation is effective and there are feelings of pleasure or contentment, to very poor. A key point concerning the concept of individual adaptation in relation to welfare is that welfare may be good or poor while adaptation is occurring. Some adaptation is very easy and energetically cheap and
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
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...
The fractional Fourier transform and applications
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
International Development Research Centre (IDRC) Digital Library (Canada)
building skills, knowledge or networks on adaptation, ... the African partners leading the AfricaAdapt network, together with the UK-based Institute of Development Studies; and ... UNCCD Secretariat, Regional Coordination Unit for Africa, Tunis, Tunisia .... 26 Rural–urban Cooperation on Water Management in the Context of.
Fourier analysis an introduction
Stein, Elias M
2003-01-01
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th
Nonlinear single-spin spectrum analyzer.
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2013-03-15
Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.
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…
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special 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. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
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 foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
Fourier transformation for engineering and natural science
International Nuclear Information System (INIS)
Klingen, B.
2001-01-01
The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)
X-ray interferometric Fourier holography
International Nuclear Information System (INIS)
Balyan, M.K.
2016-01-01
The X-ray interferometric Fourier holography is proposed and theoretically investigated. Fourier The X-ray interferometric Young fringes and object image reconstruction are investigated. It is shown that the interference pattern of two slits formed on the exit surface of the crystal-analyzer (the third plate of the interferometer) is the X-ray interferometric Young fringes. An expression for X-ray interferometric Young fringes period is obtained. The subsequent reconstruction of the slit image as an object is performed by means of Fourier transform of the intensity distribution on the hologram. Three methods of reconstruction of the amplitude transmission complex function of the object are presented: analytical - approximate method, method of iteration and step by step method. As an example the X-ray Fourier interferometric hologram recording and the complex amplitude transmission function reconstruction for a beryllium circular wire are considered
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
Fourier plane imaging microscopy
Energy Technology Data Exchange (ETDEWEB)
Dominguez, Daniel, E-mail: daniel.dominguez@ttu.edu; Peralta, Luis Grave de [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Alharbi, Nouf; Alhusain, Mdhaoui [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Bernussi, Ayrton A. [Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)
2014-09-14
We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonic crystals.
Fourier duality as a quantization principle
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs
Fourier Transform Mass Spectrometry.
Gross, Michael L.; Rempel, Don L.
1984-01-01
Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)
Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
Axelrod, Jeremy
2015-01-01
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
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.
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
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
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
Applied Fourier analysis from signal processing to medical imaging
Olson, Tim
2017-01-01
The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medical i maging, and heat and wave equations. Fo...
Fast Fourier transform telescope
International Nuclear Information System (INIS)
Tegmark, Max; Zaldarriaga, Matias
2009-01-01
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 Nlog 2 N rather than N 2 ) 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.
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).
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Fourier-Hermite communications; where Fourier meets Hermite
Korevaar, C.W.; Kokkeler, Andre B.J.; de Boer, Pieter-Tjerk; Smit, Gerardus Johannes Maria
A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency
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.
On fractional Fourier transform moments
Alieva, T.; Bastiaans, M.J.
2000-01-01
Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their
Grafakos, Loukas
2014-01-01
This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews fr...
Fourier convergence analysis applied to neutron diffusion Eigenvalue problem
International Nuclear Information System (INIS)
Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook
2004-01-01
Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge
International Nuclear Information System (INIS)
Muir, M.D.
1975-01-01
The design and design philosophy of a high performance, extremely versatile transient analyzer is described. This sub-system was designed to be controlled through the data acquisition computer system which allows hands off operation. Thus it may be placed on the experiment side of the high voltage safety break between the experimental device and the control room. This analyzer provides control features which are extremely useful for data acquisition from PPPL diagnostics. These include dynamic sample rate changing, which may be intermixed with multiple post trigger operations with variable length blocks using normal, peak to peak or integrate modes. Included in the discussion are general remarks on the advantages of adding intelligence to transient analyzers, a detailed description of the characteristics of the PPPL transient analyzer, a description of the hardware, firmware, control language and operation of the PPPL transient analyzer, and general remarks on future trends in this type of instrumentation both at PPPL and in general
Iterative wave-front reconstruction in the Fourier domain.
Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry
2017-05-15
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.
Fourier phase in Fourier-domain optical coherence tomography
Uttam, Shikhar; Liu, Yang
2015-01-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
Fourier transform of momentum distribution in vanadium
International Nuclear Information System (INIS)
Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.
1985-01-01
Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Quadrature formulas for Fourier coefficients
Bojanov, Borislav; Petrova, Guergana
2009-01-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Fourier transform nuclear magnetic resonance
International Nuclear Information System (INIS)
Geick, R.
1981-01-01
This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)
Centrifugal analyzer development
International Nuclear Information System (INIS)
Burtis, C.A.; Bauer, M.L.; Bostick, W.D.
1976-01-01
The development of the centrifuge fast analyzer (CFA) is reviewed. The development of a miniature CFA with computer data analysis is reported and applications for automated diagnostic chemical and hematological assays are discussed. A portable CFA system with microprocessor was adapted for field assays of air and water samples for environmental pollutants, including ammonia, nitrates, nitrites, phosphates, sulfates, and silica. 83 references
International Nuclear Information System (INIS)
Arima, S.; Oda, M.; Miyashita, K.; Takada, M.
1977-01-01
A radiometric analyzer for measuring the characteristic values of a sample by radiation includes a humer of radiation measuring subsystems having different ratios of sensitivities to the elements of the sample and linearizing circuits having inverse function characteristics of calibration functions which correspond to the radiation measuring subsystems. A weighing adder operates a desirable linear combination of the outputs of the linearizing circuits. Operators for operating between two or more different linear combinations are included
Overcoming Spurious Regression Using time-Varying Fourier ...
African Journals Online (AJOL)
Non-stationary time series data have been traditionally analyzed in the frequency domain by assuming constant amplitudes regardless of the timelag. A new approach called time-varying amplitude method (TVAM) is presented here. Oscillations are analyzed for changes in the magnitude of Fourier Coefficients which are ...
1994-01-01
Measurement of the total organic carbon content in water is important in assessing contamination levels in high purity water for power generation, pharmaceutical production and electronics manufacture. Even trace levels of organic compounds can cause defects in manufactured products. The Sievers Model 800 Total Organic Carbon (TOC) Analyzer, based on technology developed for the Space Station, uses a strong chemical oxidizing agent and ultraviolet light to convert organic compounds in water to carbon dioxide. After ionizing the carbon dioxide, the amount of ions is determined by measuring the conductivity of the deionized water. The new technique is highly sensitive, does not require compressed gas, and maintenance is minimal.
Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems
Leuschner, Matthias; Fritzen, Felix
2017-11-01
Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...
Fourier series, Fourier transform and their applications to mathematical physics
Serov, Valery
2017-01-01
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...
Fourier series and orthogonal polynomials
Jackson, Dunham
2004-01-01
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe
Fourier rebinning algorithm for inverse geometry CT.
Mazin, Samuel R; Pele, Norbert J
2008-11-01
Inverse geometry computed tomography (IGCT) is a new type of volumetric CT geometry that employs a large array of x-ray sources opposite a smaller detector array. Volumetric coverage and high isotropic resolution produce very large data sets and therefore require a computationally efficient three-dimensional reconstruction algorithm. The purpose of this work was to adapt and evaluate a fast algorithm based on Defrise's Fourier rebinning (FORE), originally developed for positron emission tomography. The results were compared with the average of FDK reconstructions from each source row. The FORE algorithm is an order of magnitude faster than the FDK-type method for the case of 11 source rows. In the center of the field-of-view both algorithms exhibited the same resolution and noise performance. FORE exhibited some resolution loss (and less noise) in the periphery of the field-of-view. FORE appears to be a fast and reasonably accurate reconstruction method for IGCT.
FOURIER SERIES MODELS THROUGH TRANSFORMATION
African Journals Online (AJOL)
DEPT
monthly temperature data (1996 – 2005) collected from the National Root ... KEY WORDS: Fourier series, square transformation, multiplicative model, ... fluctuations or movements are often periodic(Ekpeyong,2005). .... significant trend or not, if the trend is not significant, the grand mean may be used as an estimate of trend.
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Uncertainty Principles and Fourier Analysis
Indian Academy of Sciences (India)
analysis on the part of the reader. Those who are not fa- miliar with Fourier analysis are encouraged to look up Box. 1 along with [3]. (A) Heisenberg's inequality: Let us measure concentration in terms of standard deviation i.e. for a square integrable func-. 00 tion defined on 1R and normalized so that J If(x)12d,x = 1,. -00. 00.
An introduction to Fourier series and integrals
Seeley, Robert T
2006-01-01
This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Properties of the distributional finite Fourier transform
Carmichael, Richard D.
2016-01-01
The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.
Fourier techniques in X-ray timing
van der Klis, M.
1988-01-01
Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum
Advantage of Fast Fourier Interpolation for laser modeling
International Nuclear Information System (INIS)
Epatko, I.V.; Serov, R.V.
2006-01-01
The abilities of a new algorithm: the 2-dimensional Fast Fourier Interpolation (FFI) with magnification factor (zoom) 2 n whose purpose is to improve the spatial resolution when necessary, are analyzed in details. FFI procedure is useful when diaphragm/aperture size is less than half of the current simulation scale. The computation noise due to FFI procedure is less than 10 -6 . The additional time for FFI is approximately equal to one Fast Fourier Transform execution time. For some applications using FFI procedure, the execution time decreases by a 10 4 factor compared with other laser simulation codes. (authors)
Fourier analysis of the aerodynamic behavior of cup anemometers
International Nuclear Information System (INIS)
Pindado, Santiago; Pérez, Imanol; Aguado, Maite
2013-01-01
The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force. (paper)
Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis
LoPresto, Michael C.
2013-01-01
What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.
Rotational Fourier tracking of diffusing polygons.
Mayoral, Kenny; Kennair, Terry P; Zhu, Xiaoming; Milazzo, James; Ngo, Kathy; Fryd, Michael M; Mason, Thomas G
2011-11-01
We use optical microscopy to measure the rotational Brownian motion of polygonal platelets that are dispersed in a liquid and confined by depletion attractions near a wall. The depletion attraction inhibits out-of-plane translational and rotational Brownian fluctuations, thereby facilitating in-plane imaging and video analysis. By taking fast Fourier transforms (FFTs) of the images and analyzing the angular position of rays in the FFTs, we determine an isolated particle's rotational trajectory, independent of its position. The measured in-plane rotational diffusion coefficients are significantly smaller than estimates for the bulk; this difference is likely due to the close proximity of the particles to the wall arising from the depletion attraction.
Comparative analysis of imaging configurations and objectives for Fourier microscopy.
Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid
2015-11-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.
Improved Fourier-transform profilometry
International Nuclear Information System (INIS)
Mao Xianfu; Chen Wenjing; Su Xianyu
2007-01-01
An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object
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.
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
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..
Fourier Spectroscopy: A Bayesian Way
Directory of Open Access Journals (Sweden)
Stefan Schmuck
2017-01-01
Full Text Available The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.
Pointwise convergence of Fourier series
Arias de Reyna, Juan
2002-01-01
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
International Nuclear Information System (INIS)
Li Shun; Zhang Sijiong
2014-01-01
A numerical model is presented to simulate the influence function of deformable mirror actuators. The numerical model is formed by Bessel Fourier orthogonal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems. (research papers)
Imaging through scattering media by Fourier filtering and single-pixel detection
Jauregui-Sánchez, Y.; Clemente, P.; Lancis, J.; Tajahuerce, E.
2018-02-01
We present a novel imaging system that combines the principles of Fourier spatial filtering and single-pixel imaging in order to recover images of an object hidden behind a turbid medium by transillumination. We compare the performance of our single-pixel imaging setup with that of a conventional system. We conclude that the introduction of Fourier gating improves the contrast of images in both cases. Furthermore, we show that the combination of single-pixel imaging and Fourier spatial filtering techniques is particularly well adapted to provide images of objects transmitted through scattering media.
Applications of Fourier transforms to generalized functions
Rahman, M
2011-01-01
This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...
Hourani, Nadim; Andersson, Jan T.; Mö ller, Isabelle; Amad, Maan H.; Witt, Matthí as; Sarathy, Mani
2013-01-01
oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Fourier transform n.m.r. spectroscopy
International Nuclear Information System (INIS)
Shaw, D.
1976-01-01
This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques
A simple approach to Fourier aliasing
International Nuclear Information System (INIS)
Foadi, James
2007-01-01
In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and structured, introductions to the topic, commonly met in advanced, specialized books
Tunable fractional-order Fourier transformer
International Nuclear Information System (INIS)
Malyutin, A A
2006-01-01
A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)
Fourier transform n. m. r. spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Shaw, D [Varian Ltd., Walton (UK)
1976-01-01
This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques.
Metasurface Enabled Wide-Angle Fourier Lens.
Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo
2018-06-01
Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Digital dynamic amplitude-frequency spectra analyzer
International Nuclear Information System (INIS)
Kalinnikov, V.A.; )
2006-01-01
The spectra analyzer is intended for the dynamic spectral analysis of signals physical installations and noise filtering. The recurrence Fourier transformation algorithm is used in the digital dynamic analyzer. It is realized on the basis of the fast logic FPGA matrix and the special signal ADSP microprocessor. The discretization frequency is 2 kHz-10 MHz. The number of calculated spectral coefficients is not less 512. The functional fast-action is 20 ns [ru
Spectrums Transform Operators in Bases of Fourier and Walsh Functions
Directory of Open Access Journals (Sweden)
V. V. Syuzev
2017-01-01
Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel
International Nuclear Information System (INIS)
Westphal, G.P.; Lemmel, H.; Grass, F.; De Regge, P.P.; Burns, K.; Markowicz, A.
2005-01-01
Dubbed 'Analyzer' because of its simplicity, a neutron activation analysis facility for short-lived isomeric transitions is based on a low-cost rabbit system and an adaptive digital filter which are controlled by a software performing irradiation control, loss-free gamma-spectrometry, spectra evaluation, nuclide identification and calculation of concentrations in a fully automatic flow of operations. Designed for TRIGA reactors and constructed from inexpensive plastic tubing and an aluminum in-core part, the rabbit system features samples of 5 ml and 10 ml with sample separation at 150 ms and 200 ms transport time or 25 ml samples without separation at a transport time of 300 ms. By automatically adapting shaping times to pulse intervals the preloaded digital filter gives best throughput at best resolution up to input counting rates of 10 6 cps. Loss-free counting enables quantitative correction of counting losses of up to 99%. As a test of system reproducibility in sample separation geometry, K, Cl, Mn, Mg, Ca, Sc, and V have been determined in various reference materials at excellent agreement with consensus values. (author)
Quantum arithmetic with the Quantum Fourier Transform
Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos
2014-01-01
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.
On the inverse windowed Fourier transform
Rebollo Neira, Laura; Fernández Rubio, Juan Antonio
1999-01-01
The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.; Boashash, B.
2003-01-01
We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept
Teaching Fourier optics through ray matrices
International Nuclear Information System (INIS)
Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F
2005-01-01
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics
International Nuclear Information System (INIS)
Akins, E.W.; Scott, E.A.; Williams, C.M.
1987-01-01
Twenty-seven patients with 33 chronic myocaridal infarctions underwent MR imaging and radionuclide ventriculography at rest. The radionuclide ventriculographs, in left anterior oblique (LAO) and left posterior oblique (LPO) projections, were analyzed by two independent observers by visual inspection and combined Fourier-transformed amplitude and phase imaging. Only 15 (45%) of the 33 infarctions were detected by visual inspection, but 21 (64%) were detected on the LAO Fourier-transformed images along. Thirty (91%) were detected by using both LAO and LPO Fourier-transformed images. On MR imaging, 28 (85%) of the myocardial infarctions appeared as areas of focal wall thinning. Combined Fourier-transformed amplitude and phase imaging in both LAO and LPO views discloses more myocardial infarctions than visual inspection or LAO Fourier-transformed images alone because inferior infarctions, which are frequently missed in the LAO view, are easily seen in the LPO view
Periodic transonic flow simulation using fourier-based algorithm
International Nuclear Information System (INIS)
Mohaghegh, Mohammad Reza; Malekjafarian, Majid
2014-01-01
The present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady Euler and Navier-Stokes equations, using time spectral method (TSM) and compares it with the traditional methods like BDF and explicit structured adaptive grid method. The TSM uses a Fourier representation in time and hence solves for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. The TSM has been validated with 2D external aerodynamics test cases. These test cases are NACA 64A010 (CT6) and NACA 0012 (CT1 and CT5) pitching airfoils. Because of turbulent nature of flow, Baldwin-Lomax turbulence model has been used in viscous flow analysis with large oscillation amplitude (CT5 type). The results presented by the TSM are compared with experimental data and the two other methods. By enforcing periodicity and using Fourier representation in time that has a spectral accuracy, tremendous reduction of computational cost has been obtained compared to the conventional time-accurate methods. Results verify the small number of time intervals per pitching cycle (just four time intervals) required to capture the flow physics with small oscillation amplitude (CT6) and large oscillation amplitude (CT5) as compared to the other two methods.
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.
Realization of quantum Fourier transform over ZN
International Nuclear Information System (INIS)
Fu Xiang-Qun; Bao Wan-Su; Li Fa-Da; Zhang Yu-Chao
2014-01-01
Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z N . According to probability amplitude, we prove that the transform can be used to realize QFT over Z N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z N . (general)
Replica Fourier Transform: Properties and applications
International Nuclear Information System (INIS)
Crisanti, A.; De Dominicis, C.
2015-01-01
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
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
Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation.
Li, Xin; Zhong, Yongmin; Smith, Julian; Gu, Chengfan
2017-01-02
Prediction of tissue damage under thermal loads plays important role for thermal ablation planning. A new methodology is presented in this paper by combing non-Fourier bio-heat transfer, constitutive elastic mechanics as well as non-rigid motion of dynamics to predict and analyze thermal distribution, thermal-induced mechanical deformation and thermal-mechanical damage of soft tissues under thermal loads. Simulations and comparison analysis demonstrate that the proposed methodology based on the non-Fourier bio-heat transfer can account for the thermal-induced mechanical behaviors of soft tissues and predict tissue thermal damage more accurately than classical Fourier bio-heat transfer based model.
Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem
International Nuclear Information System (INIS)
Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook
2005-01-01
Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique
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. Copyright © 2014 Elsevier Ltd. All rights reserved.
Scheibler, Robin; Hurley, Paul
2012-03-01
We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.
New focus on Fourier optics techniques
Calvo, M.L.; Alieva, T.; Bastiaans, M.J.; Rodrigo Martín-Romo, J.A.; Rodríguez Merlo, D.; Vlad, V.I.
2004-01-01
We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.
The finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
On the Scaled Fractional Fourier Transformation Operator
International Nuclear Information System (INIS)
Hong-Yi, Fan; Li-Yun, Hu
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
Mountain Wave Analysis Using Fourier Methods
National Research Council Canada - National Science Library
Roadcap, John R
2007-01-01
...) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms...
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
Is Fourier analysis performed by the visual system or by the visual investigator.
Ochs, A L
1979-01-01
A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.
Marengo, J. A.; Muller-Karger, F. E.; Pelling, M.; Reynolds, C. J.; Merril, S. B.; Nunes, L. H.; Paterson, S.; Gray, A.; Lockman, J. T.; Kartez, J.; Moreira, F.; Greco, R.; Harari, J.; Souza, C. G.; Alves, L. M.; Hosokawa, E.; Tabuchi, E.
2016-12-01
One of the clear signals of present climate change is sea level rise (SLR). There is mounting evidence of other changes, including warmer temperatures in many localities, and changes in the intensity and frequency of extreme meteorological events, including wind, rain, and waves. A rising sea level combined with these factors and tides is expected to affect coastal communities through a number of processes, including increased risk of flooding and contamination of water sources. An international collaboration between Brazil, the United Kingdom, and the United States was designed to evaluate local decision making processes and to open convening space for local urban managers to reflect on possible actions toward adaption to SLR and the constraints imposed by framing administrative and institutional structures. The overall goal of the project is to help coastal communities better understand factors that facilitate or hinder their intrinsic, local decision-making processes related to planning for adaptation to risk. The project carried out these tests in 2014 and 2015 in one coastal city in each partnering nation. The framework was designed by an interdisciplinary team that incorporated social and natural scientists from these three nations, and which included local government officials. To support the overall goal, this paper 1) discusses some aspects of adaptive capacity and participant survey research conducted through the project, 2) presents technical modelling results for adaptation options that may reduce the potential damages of SLR and storm surge in each location, and 3) identifies project design considerations for similar transnational adaptation projects.
Mapped Fourier Methods for stiff problems in toroidal geometry
Guillard , Herve
2014-01-01
Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the compositio...
Information decomposition method to analyze symbolical sequences
International Nuclear Information System (INIS)
Korotkov, E.V.; Korotkova, M.A.; Kudryashov, N.A.
2003-01-01
The information decomposition (ID) method to analyze symbolical sequences is presented. This method allows us to reveal a latent periodicity of any symbolical sequence. The ID method is shown to have advantages in comparison with application of the Fourier transformation, the wavelet transform and the dynamic programming method to look for latent periodicity. Examples of the latent periods for poetic texts, DNA sequences and amino acids are presented. Possible origin of a latent periodicity for different symbolical sequences is discussed
Menenti, M.; Azzali, S.; Verhoef, W.; Van Swol, R.
1993-01-01
Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.
Analyzing Visibility Configurations.
Dachsbacher, C
2011-04-01
Many algorithms, such as level of detail rendering and occlusion culling methods, make decisions based on the degree of visibility of an object, but do not analyze the distribution, or structure, of the visible and occluded regions across surfaces. We present an efficient method to classify different visibility configurations and show how this can be used on top of existing methods based on visibility determination. We adapt co-occurrence matrices for visibility analysis and generalize them to operate on clusters of triangular surfaces instead of pixels. We employ machine learning techniques to reliably classify the thus extracted feature vectors. Our method allows perceptually motivated level of detail methods for real-time rendering applications by detecting configurations with expected visual masking. We exemplify the versatility of our method with an analysis of area light visibility configurations in ray tracing and an area-to-area visibility analysis suitable for hierarchical radiosity refinement. Initial results demonstrate the robustness, simplicity, and performance of our method in synthetic scenes, as well as real applications.
The Fourier decomposition method for nonlinear and non-stationary time series analysis.
Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik
2017-03-01
for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
Non-Fourier heat conduction and phase transition in laser ablation of polytetrafluoroethylene (PTFE)
Zhang, Yu; Zhang, Daixian; Wu, Jianjun; Li, Jian; He, Zhaofu
2017-11-01
The phase transition in heat conduction of polytetrafluoroethylene-like polymers was investigated and applied in many fields of science and engineering. Considering more details including internal absorption of laser radiation, reflectivity of material and non-Fourier effect etc., the combined heat conduction and phase transition in laser ablation of polytetrafluoroethylene were modeled and investigated numerically. The thermal and mechanic issues in laser ablation were illustrated and analyzed. Especially, the phenomenon of temperature discontinuity formed in the combined phase transition and non-Fourier heat conduction was discussed. Comparisons of target temperature profiles between Fourier and non-Fourier heat conduction in melting process were implemented. It was indicated that the effect of non-Fourier plays an important role in the temperature evolvement. The effect of laser fluence was proven to be significant and the thermal wave propagation was independent on the laser intensity for the non-Fourier heat conduction. Besides, the effect of absorption coefficients on temperature evolvements was studied. For different ranges of absorption coefficients, different temperature evolvements can be achieved. The above numerical simulation provided insight into physical processes of combined non-Fourier heat conduction and phase transition in laser ablation.
Fourier analysis of conductive heat transfer for glazed roofing materials
Energy Technology Data Exchange (ETDEWEB)
Roslan, Nurhana Lyana; Bahaman, Nurfaradila; Almanan, Raja Noorliyana Raja; Ismail, Razidah [Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia); Zakaria, Nor Zaini [Faculty of Applied Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia)
2014-07-10
For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heat transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate.
Error Analysis for Fourier Methods for Option Pricing
Häppölä, Juho
2016-01-06
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.
Fourier phasing with phase-uncertain mask
International Nuclear Information System (INIS)
Fannjiang, Albert; Liao, Wenjing
2013-01-01
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)
Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.
Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun
2009-05-01
Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.
Direct fourier method reconstruction based on unequally spaced fast fourier transform
International Nuclear Information System (INIS)
Wu Xiaofeng; Zhao Ming; Liu Li
2003-01-01
First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)
International Nuclear Information System (INIS)
Tam, K.C.; Perez-Mendez, V.
1981-01-01
The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been analyzed in detail. it was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect which tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time
Limited-angle 3-D reconstructions using Fourier transform iterations and Radon transform iterations
International Nuclear Information System (INIS)
Tam, K.C.; Perez-Mendez, V.
1979-12-01
The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero was calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms was analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect that tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time. 8 figures, 2 tables
Magneto-sensor circuit efficiency incremented by Fourier-transformation
Talukdar, Abdul Hafiz Ibne; Useinov, Arthur; Hussain, Muhammad Mustafa
2011-01-01
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.
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.
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 optical cryptosystem using complex spatial modulation
International Nuclear Information System (INIS)
Sarkadi, T; Koppa, P
2014-01-01
Our goal is to enhance the security level of a Fourier optical encryption system. Therefore we propose a Mach–Zehnder interferometer based encryption setup. The input data is organized in a binary array, and it is encoded in the two wave fronts propagated in the arms of the interferometer. Both input wave fronts are independently encrypted by Fourier systems, hence the proposed method has two encryption keys. During decryption, the encrypted wave fronts are propagated through the interferometer setup. The interference pattern of the output shows the reconstructed data in cases where the correct decryption Fourier keys are used. We propose a novel input image modulation method with a user defined phase parameter. We show that the security level of the proposed cryptosystem can be enhanced by an optimally chosen phase parameter. (paper)
Harmonic analysis from Fourier to wavelets
Pereyra, Maria Cristina
2012-01-01
In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...
Projective Fourier duality and Weyl quantization
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Group-invariant finite Fourier transforms
International Nuclear Information System (INIS)
Shenefelt, M.H.
1988-01-01
The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible
Analyzing Fourier Transforms for NASA DFRC's Fiber Optic Strain Sensing System
Fiechtner, Kaitlyn Leann
2010-01-01
This document provides a basic overview of the fiber optic technology used for sensing stress, strain, and temperature. Also, the document summarizes the research concerning speed and accuracy of the possible mathematical algorithms that can be used for NASA DFRC's Fiber Optic Strain Sensing (FOSS) system.
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
2016-01-01
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. PMID:27006089
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.
An optical Fourier transform coprocessor with direct phase determination.
Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D
2017-10-20
The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.
Fourier analysis in several complex variables
Ehrenpreis, Leon
2006-01-01
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations.The three-part treatment begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis. Topics include the geometric structure of ideals and modules, quantitative estimates, and examples in which the theory can be applied. The second part focuses on applications to partial differential equations and covers the solution of homogeneous and inh
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
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.
Progress report of a static Fourier transform spectrometer breadboard
Rosak, A.; Tintó, F.
2017-11-01
MOLI instrument -for MOtionLess Interferometer- takes advantage of the new concept of static Fourier transform spectrometer. It is a high-resolution spectrometer working over a narrow bandwidth, which is adapted to a wide range of atmospheric sounding missions and compatible with micro-satellite platform. The core of this instrument is an echelette cube. Mirrors on the classical design are replaced by stepped mirrors -integrated into that interference cube- thus suppressing any moving part. The steps' directions being set over a perpendicular axis, the overlap of both stepped mirrors creates a cluster of so-called "echelettes", each one corresponding to a different optical path difference (OPD). Hence the Fourier transform of the incoming radiance is directly imaged on a CCD array in a single acquisition. The frequency domain of the measurements is selected by an interferential filter disposed on the incoming optical path. A rotating wheel equipped with several filters allows the successive measurement of spectra around some bands of interest, i.e. O2, CO2 and CO absorption bands.
Maayouf, R M A
2002-01-01
The present work introduces a new design to replace the (Finnish make) reverse time of flight (RTOF) analyzer used for the Fourier diffractometer facilities. The new design applies a data acquisition system, a special interface card and software program installed in a PC computer, to perform the cross-correlation functions between signals received from the chopper-decoder and detector. It has been found from test measurements performed with the Cairo Fourier diffractometer facility (CFDF) and the similar high resolution one at JINR (Dubna-Russia) that the new design can successfully replace the Finnish make RTOF analyzer.
High-resolution magnetic-domain imaging by Fourier transform holography at 21 nm wavelength
International Nuclear Information System (INIS)
Schaffert, Stefan; Pfau, Bastian; Günther, Christian M; Schneider, Michael; Korff Schmising, Clemens von; Eisebitt, Stefan; Geilhufe, Jan
2013-01-01
Exploiting x-ray magnetic circular dichroism at the L-edges of 3d transition metals, Fourier transform holography has become a standard technique to investigate magnetic samples with sub-100 nm spatial resolution. Here, magnetic imaging in the 21 nm wavelength regime using M-edge circular dichroism is demonstrated. Ultrafast pulses in this wavelength regime are increasingly available from both laser- and accelerator-driven soft x-ray sources. We explain the adaptations concerning sample preparation and data evaluation compared to conventional holography in the 1 nm wavelength range. We find the correction of the Fourier transform hologram to in-plane Fourier components to be critical for high-quality reconstruction and demonstrate 70 nm spatial resolution in magnetization imaging with this approach. (paper)
The periodogram at the Fourier frequencies
Kokoszka, P; Mikosch, T
In the time series literature one can often find the claim that the periodogram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,
Pi, Fourier Transform and Ludolph van Ceulen
Vajta, Miklos
2000-01-01
The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of p (first by hand and then from the mid-20th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as
Fourier transform infrared spectrometery: an undergraduate experiment
International Nuclear Information System (INIS)
Lerner, L
2016-01-01
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. (paper)
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.
2001-01-01
The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution
The Fourier transform of tubular densities
Prior, C B; Goriely, A
2012-01-01
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
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Fourier analysis in combinatorial number theory
International Nuclear Information System (INIS)
Shkredov, Il'ya D
2010-01-01
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Fourier analysis in combinatorial number theory
Energy Technology Data Exchange (ETDEWEB)
Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-09-16
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
A Fourier analysis of extremal events
DEFF Research Database (Denmark)
Zhao, Yuwei
is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
The Fourier modal method for aperiodic structures
Pisarenco, M.; Maubach, J.M.L.; Setija, I.D.; Mattheij, R.M.M.
2010-01-01
This paper extends the area of application of the Fourier modal method from periodic structures to non-periodic ones illuminated under arbitrary angles. This is achieved by placing perfectly matched layers at the lateral boundaries and reformulating the problem in terms of a contrast field.
Discrete Fourier analysis of multigrid algorithms
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2011-01-01
The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Fourier inversion on a reductive symmetric space
Ban, E.P. van den
1999-01-01
Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we
Fractional-Fourier-domain weighted Wigner distribution
Stankovic, L.; Alieva, T.; Bastiaans, M.J.
2001-01-01
A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the
Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Schlichtkrull, H.
1994-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Carmona, J.; Delorme, P.
1997-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
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.
Compression of fiber supercontinuum pulses to the Fourier-limit in a high-numerical-aperture focus
DEFF Research Database (Denmark)
Tu, Haohua; Liu, Yuan; Turchinovich, Dmitry
2011-01-01
A multiphoton intrapulse interference phase scan (MIIPS) adaptively and automatically compensates the combined phase distortion from a fiber supercontinuum source, a spatial light modulator pulse shaper, and a high-NA microscope objective, allowing Fourier-transform-limited compression of the sup......A multiphoton intrapulse interference phase scan (MIIPS) adaptively and automatically compensates the combined phase distortion from a fiber supercontinuum source, a spatial light modulator pulse shaper, and a high-NA microscope objective, allowing Fourier-transform-limited compression...... power of 18–70mW, and a repetition rate of 76MHz, permitting the application of this source to nonlinear optical microscopy and coherently controlled microspectroscopy....
New significance test methods for Fourier analysis of geophysical time series
Directory of Open Access Journals (Sweden)
Z. Zhang
2011-09-01
Full Text Available When one applies the discrete Fourier transform to analyze finite-length time series, discontinuities at the data boundaries will distort its Fourier power spectrum. In this paper, based on a rigid statistics framework, we present a new significance test method which can extract the intrinsic feature of a geophysical time series very well. We show the difference in significance level compared with traditional Fourier tests by analyzing the Arctic Oscillation (AO and the Nino3.4 time series. In the AO, we find significant peaks at about 2.8, 4.3, and 5.7 yr periods and in Nino3.4 at about 12 yr period in tests against red noise. These peaks are not significant in traditional tests.
Automatic Fourier transform and self-Fourier beams due to parabolic potential
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2015-12-15
We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2007-01-01
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found
Deploying Fourier Coefficients to Unravel Soybean Canopy Diversity.
Jubery, Talukder Z; Shook, Johnathon; Parmley, Kyle; Zhang, Jiaoping; Naik, Hsiang S; Higgins, Race; Sarkar, Soumik; Singh, Arti; Singh, Asheesh K; Ganapathysubramanian, Baskar
2016-01-01
Soybean canopy outline is an important trait used to understand light interception ability, canopy closure rates, row spacing response, which in turn affects crop growth and yield, and directly impacts weed species germination and emergence. In this manuscript, we utilize a methodology that constructs geometric measures of the soybean canopy outline from digital images of canopies, allowing visualization of the genetic diversity as well as a rigorous quantification of shape parameters. Our choice of data analysis approach is partially dictated by the need to efficiently store and analyze large datasets, especially in the context of planned high-throughput phenotyping experiments to capture time evolution of canopy outline which will produce very large datasets. Using the Elliptical Fourier Transformation (EFT) and Fourier Descriptors (EFD), canopy outlines of 446 soybean plant introduction (PI) lines from 25 different countries exhibiting a wide variety of maturity, seed weight, and stem termination were investigated in a field experiment planted as a randomized complete block design with up to four replications. Canopy outlines were extracted from digital images, and subsequently chain coded, and expanded into a shape spectrum by obtaining the Fourier coefficients/descriptors. These coefficients successfully reconstruct the canopy outline, and were used to measure traditional morphometric traits. Highest phenotypic diversity was observed for roundness, while solidity showed the lowest diversity across all countries. Some PI lines had extraordinary shape diversity in solidity. For interpretation and visualization of the complexity in shape, Principal Component Analysis (PCA) was performed on the EFD. PI lines were grouped in terms of origins, maturity index, seed weight, and stem termination index. No significant pattern or similarity was observed among the groups; although interestingly when genetic marker data was used for the PCA, patterns similar to canopy
Fourier analysis: from cloaking to imaging
Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping
2016-04-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.
Fourier analysis: from cloaking to imaging
International Nuclear Information System (INIS)
Wu, Kedi; Ping Wang, Guo; Cheng, Qiluan
2016-01-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers. (review)
Multichannel Dynamic Fourier-Transform IR Spectrometer
Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.
2017-09-01
A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.
Discrete Fourier transform in nanostructures using scattering
International Nuclear Information System (INIS)
Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.
2004-01-01
In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed
The PROSAIC Laplace and Fourier Transform
International Nuclear Information System (INIS)
Smith, G.A.
1994-01-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting
Correcting sample drift using Fourier harmonics.
Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L
2018-07-01
During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-01-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-09-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples covering the case of amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Quantum Fourier Transform Over Galois Rings
Zhang, Yong
2009-01-01
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...
Fourier Transform Spectrometer Controller for Partitioned Architectures
DEFF Research Database (Denmark)
Tamas-Selicean, Domitian; Keymeulen, D.; Berisford, D.
2013-01-01
The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Resear......, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture....
A Fourier analysis of extreme events
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
Fourier transform resampling: Theory and application
International Nuclear Information System (INIS)
Hawkins, W.G.
1996-01-01
One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)
Sets of Fourier coefficients using numerical quadrature
International Nuclear Information System (INIS)
Lyness, J. N.
2001-01-01
One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r)=(line i ntegral)(sub 0)(sup 1) f(x)e(sup -2(pi)irx)dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x)= h(sub p-1)(x)+ g(sub p)(x), where h(sub -1)(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g(sub p)(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h(sub p-1)(x) and numerical quadrature to approximately those of g(sub p)(x)
Social-psychological specific of individual adaptation
Ovsyanik, Olga
2012-01-01
There is analyzing of specific of social-psychological adaptation person by model of adaptation. Structure model of adaptation of women of our age group, which was named “adaptation complex” was made by theoretic analyzes of problem of adaptation adult.
International Nuclear Information System (INIS)
Wunschel, David S.; Pasa Tolic, Ljiljana; Feng, Bingbing; Smith, Richard D.
2000-01-01
We have attempted to expand the size range of PCR products that can be analyzed by electroscopy ionization (ESI) Fourier transformion cyclotron resonance (FTICR) mass spectrometry. The mass measurement accuracy obtained illustrates that a signel base substitution could be identified at the size of PCR product with a 7 tesla ESI-FTICR
DEFF Research Database (Denmark)
Lassen, Jan; Løvendahl, Peter; Madsen, Jørgen
2012-01-01
Individual methane (CH4) production was recorded repeatedly on 93 dairy cows during milking in an automatic milking system (AMS), with the aim of estimating individual cow differences in CH4 production. Methane and CO2 were measured with a portable air sampler and analyzer unit based on Fourier...
Mižišin, Michal
2013-01-01
Web server attack analyzer - Abstract The goal of this work was to create prototype of analyzer of injection flaws attacks on web server. Proposed solution combines capabilities of web application firewall and web server log analyzer. Analysis is based on configurable signatures defined by regular expressions. This paper begins with summary of web attacks, followed by detection techniques analysis on web servers, description and justification of selected implementation. In the end are charact...
International Nuclear Information System (INIS)
Popp, P.; Grosse, H.J.; Leonhardt, J.; Mothes, S.; Oppermann, G.
1984-01-01
The invention concerns an electron attachment analyzer for detecting traces of electroaffine substances in electronegative gases, especially in air. The analyzer can be used for monitoring working places, e. g., in operating theatres. The analyzer consists of two electrodes inserted in a base frame of insulating material (quartz or ceramics) and a high-temperature resistant radiation source ( 85 Kr, 3 H, or 63 Ni)
Ultrafast and versatile spectroscopy by temporal Fourier transform
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.
2014-06-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.
Fourier spectral simulations for wake fields in conducting cavities
International Nuclear Information System (INIS)
Min, M.; Chin, Y.-H.; Fischer, P.F.; Chae, Y.-Chul; Kim, K.-J.
2007-01-01
We investigate Fourier spectral time-domain simulations applied to wake field calculations in two-dimensional cylindrical structures. The scheme involves second-order explicit leap-frogging in time and Fourier spectral approximation in space, which is obtained from simply replacing the spatial differentiation operator of the YEE scheme by the Fourier differentiation operator on nonstaggered grids. This is a first step toward investigating high-order computational techniques with the Fourier spectral method, which is relatively simple to implement.
A Note on Fourier and the Greenhouse Effect
Postma, Joseph E.
2015-01-01
Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...
Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
Zhang, Zhihua
2014-01-01
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842
A computerised EEG-analyzing system for small laboratory animals
Kropveld, D.; Chamuleau, R. A.; Popken, R. J.; Smith, J.
1983-01-01
The experimental setup, including instrumentation and software packaging, is described for the use of a minicomputer as an on-line analyzing system of the EEG in rats. Complete fast Fourier transformation of the EEG sampled in 15 episodes of 10 s each is plotted out within 7 min after the start of
Some Applications of Fourier's Great Discovery for Beginners
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…
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",…
International Nuclear Information System (INIS)
Stritar, A.
1986-01-01
The development of Nuclear Power Plant Analyzers in USA is described. There are two different types of Analyzers under development in USA, the forst in Idaho and Los Alamos national Lab, the second in brookhaven National lab. That one is described in detail. The computer hardware and the mathematical models of the reactor vessel thermalhydraulics are described. (author)
Haavelsrud, Magnus; Stenberg, Oddbjorn
2012-01-01
Eleven articles on peace education published in the first volume of the Journal of Peace Education are analyzed. This selection comprises peace education programs that have been planned or carried out in different contexts. In analyzing peace pedagogies as proposed in the 11 contributions, we have chosen network analysis as our method--enabling…
DEFF Research Database (Denmark)
Revsbæk, Line; Tanggaard, Lene
2015-01-01
The article presents a notion of “analyzing in the present” as a source of inspiration in analyzing qualitative research materials. The term emerged from extensive listening to interview recordings during everyday commuting to university campus. Paying attention to the way different parts of vari...
Gearbox vibration diagnostic analyzer
1992-01-01
This report describes the Gearbox Vibration Diagnostic Analyzer installed in the NASA Lewis Research Center's 500 HP Helicopter Transmission Test Stand to monitor gearbox testing. The vibration of the gearbox is analyzed using diagnostic algorithms to calculate a parameter indicating damaged components.
Partial Fourier analysis of time-harmonic Maxwell's equations in axisymmetric domains
International Nuclear Information System (INIS)
Nkemzi, Boniface
2003-01-01
We analyze the Fourier method for treating time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with non-axisymmetric data. The Fourier method reduces the three-dimensional boundary value problem to a system of decoupled two-dimensional boundary value problems on the plane meridian domain of the axisymmetric domain. The reduction process is fully described and suitable weighted spaces are introduced on the meridian domain to characterize the two-dimensional solutions. In particular, existence and uniqueness of solutions of the two-dimensional problems is proved and a priori estimates for the solutions are given. (author)
Alternating multivariate trigonometric functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2008-01-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel
Investigations of new cardiac functional imaging using Fourier analysis of gated blood-pool study
International Nuclear Information System (INIS)
Maeda, H.; Takeda, K.; Nakagawa, T.; Yamaguchi, N.; Taguchi, M.; Konishi, T.; Hamada, M.
1982-01-01
A new cardiac functional imaging, using temporal Fourier analysis of 28-frame gated cardiac blood-pool studies, was developed. A time-activity curve of each pixel was approximated by its Fourier series. Approximation by the sum for terms to the 3rd frequency of its Fourier series was considered to be most reasonable because of having the least aberration due to statistical fluctuation and close agreement between the global left ventricular curve and the regional fitted curves in normal subjects. To evaluate the ventricular systolic and diastolic performances, 9 parameters were analyzed from thus fitted curves on a pixel-by-pixel basis and displayed on a colour CRT in 64x64 matrix form. In patients with hypertrophic obstructive cardiomyopathy and other cardiac lesions, detailed information on the regional ventricular systolic and diastolic performances was clearly visualized by this method, which was difficult to obtain from the usual functional images of phase and amplitude at the fundamental frequency alone
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.
Instantaneous lineshape analysis of Fourier domain mode-locked lasers.
Todor, Sebastian; Biedermann, Benjamin; Wieser, Wolfgang; Huber, Robert; Jirauschek, Christian
2011-04-25
We present a theoretical and experimental analysis of the instantaneous lineshape of Fourier domain mode-locked (FDML) lasers, yielding good agreement. The simulations are performed employing a recently introduced model for FDML operation. Linewidths around 10 GHz are found, which is significantly below the sweep filter bandwidth. The effect of detuning between the sweep filter drive frequency and cavity roundtrip time is studied revealing features that cannot be resolved in the experiment, and shifting of the instantaneous power spectrum against the sweep filter center frequency is analyzed. We show that, in contrast to most other semiconductor based lasers, the instantaneous linewidth is governed neither by external noise sources nor by amplified spontaneous emission, but it is directly determined by the complex FDML dynamics.
Topography description of thin films by optical Fourier Transform
International Nuclear Information System (INIS)
Jaglarz, Janusz
2008-01-01
In this work, the main problems concerning the scattering of light by real surfaces and films are presented in view of results obtained with the bidirectional reflection distribution function (BRDF) method and optical profilometry (OP). The BRDF and OP studies, being complementary to the atomic force microscopy (AFM), allow one to get information about surface topography. From the optical data, the surface power spectral density (PSD) functions for absorbing and transparent rough films have been found. Both functions have been evaluated from the Fourier transform (FT) of the surface profiles. The usefulness of BRDF-and OP methods in characterization of real surfaces is demonstrated when analyzing the optical data obtained for metallic TiN-and organic PVK thin films deposited on various substrates
Topography description of thin films by optical Fourier Transform
Energy Technology Data Exchange (ETDEWEB)
Jaglarz, Janusz [Institute of Physics, Cracow University of Technology, ul. Podchoraz.ych 1, 30-084 Krakow (Poland)], E-mail: pujaglar@cyfronet.krakow.pl
2008-09-30
In this work, the main problems concerning the scattering of light by real surfaces and films are presented in view of results obtained with the bidirectional reflection distribution function (BRDF) method and optical profilometry (OP). The BRDF and OP studies, being complementary to the atomic force microscopy (AFM), allow one to get information about surface topography. From the optical data, the surface power spectral density (PSD) functions for absorbing and transparent rough films have been found. Both functions have been evaluated from the Fourier transform (FT) of the surface profiles. The usefulness of BRDF-and OP methods in characterization of real surfaces is demonstrated when analyzing the optical data obtained for metallic TiN-and organic PVK thin films deposited on various substrates.
Cuna, C; Lupsa, N; Cuna, S; Tuzson, B
2003-01-01
The paper presents the concept of different mass analyzers that were specifically designed as small dimension instruments able to detect with great sensitivity and accuracy the main environmental pollutants. The mass spectrometers are very suited instrument for chemical and isotopic analysis, needed in environmental surveillance. Usually, this is done by sampling the soil, air or water followed by laboratory analysis. To avoid drawbacks caused by sample alteration during the sampling process and transport, the 'in situ' analysis is preferred. Theoretically, any type of mass analyzer can be miniaturized, but some are more appropriate than others. Quadrupole mass filter and trap, magnetic sector, time-of-flight and ion cyclotron mass analyzers can be successfully shrunk, for each of them some performances being sacrificed but we must know which parameters are necessary to be kept unchanged. To satisfy the miniaturization criteria of the analyzer, it is necessary to use asymmetrical geometries, with ion beam obl...
Validation of Fourier analysis of videokeratographic data.
Sideroudi, Haris; Labiris, Georgios; Ditzel, Fienke; Tsaragli, Efi; Georgatzoglou, Kimonas; Siganos, Haralampos; Kozobolis, Vassilios
2017-06-15
The aim was to assess the repeatability of Fourier transfom analysis of videokeratographic data using Pentacam in normal (CG), keratoconic (KC) and post-CXL (CXL) corneas. This was a prospective, clinic-based, observational study. One randomly selected eye from all study participants was included in the analysis: 62 normal eyes (CG group), 33 keratoconus eyes (KC group), while 34 eyes, which had already received CXL treatment, formed the CXL group. Fourier analysis of keratometric data were obtained using Pentacam, by two different operators within each of two sessions. Precision, repeatability and Intraclass Correlation Coefficient (ICC), were calculated for evaluating intrassesion and intersession repeatability for the following parameters: Spherical Component (SphRmin, SphEcc), Maximum Decentration (Max Dec), Regular Astigmatism, and Irregularitiy (Irr). Bland-Altman analysis was used for assessing interobserver repeatability. All parameters were presented to be repeatable, reliable and reproductible in all groups. Best intrasession and intersession repeatability and reliability were detected for parameters SphRmin, SphEcc and Max Dec parameters for both operators using ICC (intrasession: ICC > 98%, intersession: ICC > 94.7%) and within subject standard deviation. Best precision and lowest range of agreement was found for the SphRmin parameter (CG: 0.05, KC: 0.16, and CXL: 0.2) in all groups, while the lowest repeatability, reliability and reproducibility was detected for the Irr parameter. The Pentacam system provides accurate measurements of Fourier tranform keratometric data. A single Pentacam scan will be sufficient for most clinical applications.
Fourier optics treatment of classical relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2006-08-15
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)
International Nuclear Information System (INIS)
Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet; Torres, Yezid
2014-01-01
We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations. (paper)
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,
Analog fourier transform channelizer and OFDM receiver
2007-01-01
An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...
Bruzzo, Ugo; Maciocia, Antony
2017-12-01
This special issue celebrates the 34 years since the discovery of the Fourier-Mukai Transform by Shigeru Mukai. It mostly contains papers presented at the conference held in the Mathematics Research Centre of the University of Warwick, 15th to 19th June 2015 as part of a year long Warwick symposium on Derived categories and applications. The conference was also the annual conference of the Vector Bundles on Algebraic Curves series led by Peter Newstead. The symposium was principally supported by the Engineering and Physical Sciences Research Council of the UK and there was further funding from the London Mathematical Society and the Foundation Compositio.
Noise figure of amplified dispersive Fourier transformation
International Nuclear Information System (INIS)
Goda, Keisuke; Jalali, Bahram
2010-01-01
Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.
Fourier transform infrared spectroscopy of peptides.
Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell
2014-01-01
Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data.
Complex nonlinear Fourier transform and its inverse
International Nuclear Information System (INIS)
Saksida, Pavle
2015-01-01
We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)
Functional Fourier transforms and the loop equation
International Nuclear Information System (INIS)
Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.
1986-01-01
The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables
Fourier transform spectroscopy of six stars
Energy Technology Data Exchange (ETDEWEB)
Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia
1981-01-01
This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.
Generalized Fourier transforms Fk,a
DEFF Research Database (Denmark)
Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent
2009-01-01
We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....
Fourier-transforming with quantum annealers
Directory of Open Access Journals (Sweden)
Itay eHen
2014-07-01
Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.
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.
Fourier transform ion cyclotron resonance mass spectrometry
Marshall, Alan G.
1998-06-01
As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.
Approximate modal analysis using Fourier decomposition
International Nuclear Information System (INIS)
Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana
2010-01-01
The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.
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.
The Fourier transform of tubular densities
International Nuclear Information System (INIS)
Prior, C B; Goriely, A
2012-01-01
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. (paper)
Fourier transform zero field NMR and NQR
International Nuclear Information System (INIS)
Zax, D.B.
1985-01-01
In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI
Resolution optimization with irregularly sampled Fourier data
International Nuclear Information System (INIS)
Ferrara, Matthew; Parker, Jason T; Cheney, Margaret
2013-01-01
Image acquisition systems such as synthetic aperture radar (SAR) and magnetic resonance imaging often measure irregularly spaced Fourier samples of the desired image. In this paper we show the relationship between sample locations, their associated backprojection weights, and image resolution as characterized by the resulting point spread function (PSF). Two new methods for computing data weights, based on different optimization criteria, are proposed. The first method, which solves a maximal-eigenvector problem, optimizes a PSF-derived resolution metric which is shown to be equivalent to the volume of the Cramer–Rao (positional) error ellipsoid in the uniform-weight case. The second approach utilizes as its performance metric the Frobenius error between the PSF operator and the ideal delta function, and is an extension of a previously reported algorithm. Our proposed extension appropriately regularizes the weight estimates in the presence of noisy data and eliminates the superfluous issue of image discretization in the choice of data weights. The Frobenius-error approach results in a Tikhonov-regularized inverse problem whose Tikhonov weights are dependent on the locations of the Fourier data as well as the noise variance. The two new methods are compared against several state-of-the-art weighting strategies for synthetic multistatic point-scatterer data, as well as an ‘interrupted SAR’ dataset representative of in-band interference commonly encountered in very high frequency radar applications. (paper)
Fourier transform spectra of quantum dots
Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.
2010-05-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
On localization for double Fourier series
Goffman, Casper; Waterman, Daniel
1978-01-01
The localization theorems for Fourier series of functions of a single variable are classical and easy to prove. The situation is different for Fourier series of functions of several variables, even if one restricts consideration to rectangular, in particular square, partial sums. We show that the answer to the problem can be obtained by considering the notion of generalized bounded variation, which we introduced. Given a nondecreasing sequence {λn} of positive numbers such that Σ 1/λn diverges, a function g defined on an interval I of R1 is said to be of Λ-bounded variation (ΛBV) if Σ|g(an) — g(bn)|/λn converges for every sequence of nonoverlapping intervals (an, bn) [unk]I. If λn = n, we say that g is of harmonic bounded variation (HBV). The definition suitably modified can be extended to functions of several variables. We show that in the case of two variables the localization principle holds for rectangular partial sums if ΛBV = HBV, and that if ΛBV is not contained in HBV, then the localization principle does not hold for ΛBV even in the case of square partial sums. PMID:16592492
The prosaic Laplace and Fourier transform
International Nuclear Information System (INIS)
Smith, G.A.
1995-01-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics
Digital Fourier microscopy for soft matter dynamics
International Nuclear Information System (INIS)
Giavazzi, Fabio; Cerbino, Roberto
2014-01-01
Soft matter is studied with a large portfolio of methods. Light scattering and video microscopy are the most employed at optical wavelengths. Light scattering provides ensemble-averaged information on soft matter in the reciprocal space. The wave-vectors probed correspond to length scales ranging from a few nanometers to fractions of millimetre. Microscopy probes the sample directly in the real space, by offering a unique access to the local properties. However, optical resolution issues limit the access to length scales smaller than approximately 200 nm. We describe recent work that bridges the gap between scattering and microscopy. Several apparently unrelated techniques are found to share a simple basic idea: the correlation properties of the sample can be characterized in the reciprocal space via spatial Fourier analysis of images collected in the real space. We describe the main features of such digital Fourier microscopy (DFM), by providing examples of several possible experimental implementations of it, some of which not yet realized in practice. We also provide an overview of experimental results obtained with DFM for the study of the dynamics of soft materials. Finally, we outline possible future developments of DFM that would ease its adoption as a standard laboratory method. (topical review)
Extraction spectrophotometric analyzer
International Nuclear Information System (INIS)
Batik, J.; Vitha, F.
1985-01-01
Automation is discussed of extraction spectrophotometric determination of uranium in a solution. Uranium is extracted from accompanying elements in an HCl medium with a solution of tributyl phosphate in benzene. The determination is performed by measuring absorbance at 655 nm in a single-phase ethanol-water-benzene-tributyl phosphate medium. The design is described of an analyzer consisting of an analytical unit and a control unit. The analyzer performance promises increased productivity of labour, improved operating and hygiene conditions, and mainly more accurate results of analyses. (J.C.)
Kuijpers, A.H.W.M.; Verbeek, G.; Verheij, J.W.
1997-01-01
Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be
Americal options analyzed differently
Nieuwenhuis, J.W.
2003-01-01
In this note we analyze in a discrete-time context and with a finite outcome space American options starting with the idea that every tradable should be a martingale under a certain measure. We believe that in this way American options become more understandable to people with a good working
Analyzing Political Television Advertisements.
Burson, George
1992-01-01
Presents a lesson plan to help students understand that political advertisements often mislead, lie, or appeal to emotion. Suggests that the lesson will enable students to examine political advertisements analytically. Includes a worksheet to be used by students to analyze individual political advertisements. (DK)
A new method to cluster genomes based on cumulative Fourier power spectrum.
Dong, Rui; Zhu, Ziyue; Yin, Changchuan; He, Rong L; Yau, Stephen S-T
2018-06-20
Analyzing phylogenetic relationships using mathematical methods has always been of importance in bioinformatics. Quantitative research may interpret the raw biological data in a precise way. Multiple Sequence Alignment (MSA) is used frequently to analyze biological evolutions, but is very time-consuming. When the scale of data is large, alignment methods cannot finish calculation in reasonable time. Therefore, we present a new method using moments of cumulative Fourier power spectrum in clustering the DNA sequences. Each sequence is translated into a vector in Euclidean space. Distances between the vectors can reflect the relationships between sequences. The mapping between the spectra and moment vector is one-to-one, which means that no information is lost in the power spectra during the calculation. We cluster and classify several datasets including Influenza A, primates, and human rhinovirus (HRV) datasets to build up the phylogenetic trees. Results show that the new proposed cumulative Fourier power spectrum is much faster and more accurately than MSA and another alignment-free method known as k-mer. The research provides us new insights in the study of phylogeny, evolution, and efficient DNA comparison algorithms for large genomes. The computer programs of the cumulative Fourier power spectrum are available at GitHub (https://github.com/YaulabTsinghua/cumulative-Fourier-power-spectrum). Copyright © 2018. Published by Elsevier B.V.
Lansdowne, Chatwin; Steele, Glen; Zucha, Joan; Schlesinger, Adam
2013-01-01
We describe the benefit of using closed-loop measurements for a radio receiver paired with a counterpart transmitter. We show that real-time analysis of the soft decision output of a receiver can provide rich and relevant insight far beyond the traditional hard-decision bit error rate (BER) test statistic. We describe a Soft Decision Analyzer (SDA) implementation for closed-loop measurements on single- or dual- (orthogonal) channel serial data communication links. The analyzer has been used to identify, quantify, and prioritize contributors to implementation loss in live-time during the development of software defined radios. This test technique gains importance as modern receivers are providing soft decision symbol synchronization as radio links are challenged to push more data and more protocol overhead through noisier channels, and software-defined radios (SDRs) use error-correction codes that approach Shannon's theoretical limit of performance.
International Nuclear Information System (INIS)
Bennewitz, F.; Hummel, R.; Oelmann, K.
1986-01-01
The KWU Nuclear Plant Analyzer is a real time engineering simulator based on the KWU computer programs used in plant transient analysis and licensing. The primary goal is to promote the understanding of the technical and physical processes of a nuclear power plant at an on-site training facility. Thus the KWU Nuclear Plant Analyzer is available with comparable low costs right at the time when technical questions or training needs arise. This has been achieved by (1) application of the transient code NLOOP; (2) unrestricted operator interaction including all simulator functions; (3) using the mainframe computer Control Data Cyber 176 in the KWU computing center; (4) four color graphic displays controlled by a dedicated graphic computer, no control room equipment; and (5) coupling of computers by telecommunication via telephone
Analyzed Using Statistical Moments
International Nuclear Information System (INIS)
Oltulu, O.
2004-01-01
Diffraction enhanced imaging (DEl) technique is a new x-ray imaging method derived from radiography. The method uses a monorheumetten x-ray beam and introduces an analyzer crystal between an object and a detector Narrow angular acceptance of the analyzer crystal generates an improved contrast over the evaluation radiography. While standart radiography can produce an 'absorption image', DEl produces 'apparent absorption' and 'apparent refraction' images with superior quality. Objects with similar absorption properties may not be distinguished with conventional techniques due to close absorption coefficients. This problem becomes more dominant when an object has scattering properties. A simple approach is introduced to utilize scattered radiation to obtain 'pure absorption' and 'pure refraction' images
Emission spectrometric isotope analyzer
International Nuclear Information System (INIS)
Mauersberger, K.; Meier, G.; Nitschke, W.; Rose, W.; Schmidt, G.; Rahm, N.; Andrae, G.; Krieg, D.; Kuefner, W.; Tamme, G.; Wichlacz, D.
1982-01-01
An emission spectrometric isotope analyzer has been designed for determining relative abundances of stable isotopes in gaseous samples in discharge tubes, in liquid samples, and in flowing gaseous samples. It consists of a high-frequency generator, a device for defined positioning of discharge tubes, a grating monochromator with oscillating slit and signal converter, signal generator, window discriminator, AND connection, read-out display, oscillograph, gas dosing device and chemical conversion system with carrier gas source and vacuum pump
Fourier transform and its application to 1D and 2D NMR
International Nuclear Information System (INIS)
Canet, D.
1988-01-01
In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr
Multicomplementary operators via finite Fourier transform
International Nuclear Information System (INIS)
Klimov, Andrei B; Sanchez-Soto, Luis L; Guise, Hubert de
2005-01-01
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
Fractional Fourier transform for confluent hypergeometric beams
International Nuclear Information System (INIS)
Tang, Bin; Jiang, Chun; Zhu, Haibin
2012-01-01
Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.
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.
DEFF Research Database (Denmark)
Bennetzen, Martin V; Cox, Jürgen; Mann, Matthias
2012-01-01
an algorithm to retrieve kinase predictions from the public NetworKIN webpage in a semiautomated way and applies hereafter advanced statistics to facilitate a user-tailored in-depth analysis of the phosphoproteomic data sets. The interface of the software provides a high degree of analytical flexibility......Phosphoproteomic experiments are routinely conducted in laboratories worldwide, and because of the fast development of mass spectrometric techniques and efficient phosphopeptide enrichment methods, researchers frequently end up having lists with tens of thousands of phosphorylation sites...... and is designed to be intuitive for most users. PhosphoSiteAnalyzer is a freeware program available at http://phosphosite.sourceforge.net ....
Electrodynamic thermogravimetric analyzer
International Nuclear Information System (INIS)
Spjut, R.E.; Bar-Ziv, E.; Sarofim, A.F.; Longwell, J.P.
1986-01-01
The design and operation of a new device for studying single-aerosol-particle kinetics at elevated temperatures, the electrodynamic thermogravimetric analyzer (EDTGA), was examined theoretically and experimentally. The completed device consists of an electrodynamic balance modified to permit particle heating by a CO 2 laser, temperature measurement by a three-color infrared-pyrometry system, and continuous weighing by a position-control system. In this paper, the position-control, particle-weight-measurement, heating, and temperature-measurement systems are described and their limitations examined
Analyzing Chinese Financial Reporting
Institute of Scientific and Technical Information of China (English)
SABRINA; ZHANG
2008-01-01
If the world’s capital markets could use a harmonized accounting framework it would not be necessary for a comparison between two or more sets of accounting standards. However,there is much to do before this becomes reality.This article aims to pres- ent a general overview of China’s General Accepted Accounting Principles(GAAP), U.S.General Accepted Accounting Principles and International Financial Reporting Standards(IFRS),and to analyze the differ- ences among IFRS,U.S.GAAP and China GAAP using fixed assets as an example.
International Nuclear Information System (INIS)
Agranovich, Daniel; Popov, Ivan; Ben Ishai, Paul; Feldman, Yuri; Polygalov, Eugene
2017-01-01
One of the approaches to bypass the problem of electrode polarization in dielectric measurements is the free electrode method. The advantage of this technique is that, the probing electric field in the material is not supplied by contact electrodes, but rather by electromagnetic induction. We have designed an inductive dielectric analyzer based on a sensor comprising two concentric toroidal coils. In this work, we present an analytic derivation of the relationship between the impedance measured by the sensor and the complex dielectric permittivity of the sample. The obtained relationship was successfully employed to measure the dielectric permittivity and conductivity of various alcohols and aqueous salt solutions. (paper)
On a General Class of Trigonometric Functions and Fourier Series
Pavao, H. Germano; Capelas de Oliveira, E.
2008-01-01
We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)
Reducing Approximation Error in the Fourier Flexible Functional Form
Directory of Open Access Journals (Sweden)
Tristan D. Skolrud
2017-12-01
Full Text Available The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
FFT-BM, Code Accuracy Evaluations with the 1D Fast Fourier Transform (FFT) Methodology
International Nuclear Information System (INIS)
D'Auria, F.
2004-01-01
1 - Description of program or function: FFT-BM is an integrated version of the programs package performing code accuracy evaluations with the 1D Fast Fourier Transform (FFT) methodology. It contains two programs: - CASEM: Takes care of the complete manipulation of data in order to evaluate the quantities through which the FFT method quantifies the code accuracy. - AAWFTO completes the evaluation of the average accuracy (AA) and related weighted frequency (WF) values in order to obtain the AAtot and WFtot values characterising the global calculation performance. 2 - Methods: The Fast Fourier Transform, or FFT, which is based on the Fourier analysis method is an optimised method for calculating the amplitude Vs frequency, of functions or experimental or computed data. In order to apply this methodology, after selecting the parameters to be analyzed, it is necessary to choose the following parameters: - number of curves (exp + calc) to be analyzed; - number of time windows to be analyzed; - sampling frequency; - cut frequency; - time begin and time end of each time window. 3 - Restrictions on the complexity of the problem: Up to 30 curves (exp + calc) and 5 time windows may be analyzed
Adaptive Matrices for Color Texture Classification
Bunte, Kerstin; Giotis, Ioannis; Petkov, Nicolai; Biehl, Michael; Real, P; DiazPernil, D; MolinaAbril, H; Berciano, A; Kropatsch, W
2011-01-01
In this paper we introduce an integrative approach towards color texture classification learned by a supervised framework. Our approach is based on the Generalized Learning Vector Quantization (GLVQ), extended by an adaptive distance measure which is defined in the Fourier domain and 2D Gabor
International Nuclear Information System (INIS)
Burns, D.A.
1994-09-01
A fully automated analyzer has been developed for plutonium solutions. It was assembled from several commercially available modules, is based upon segmented flow analysis, and exhibits precision about an order of magnitude better than commercial units (0.5%-O.05% RSD). The system was designed to accept unmeasured, untreated liquid samples in the concentration range 40-240 g/L and produce a report with sample identification, sample concentrations, and an abundance of statistics. Optional hydraulics can accommodate samples in the concentration range 0.4-4.0 g/L. Operating at a typical rate of 30 to 40 samples per hour, it consumes only 0.074 mL of each sample and standard, and generates waste at the rate of about 1.5 mL per minute. No radioactive material passes through its multichannel peristaltic pump (which remains outside the glovebox, uncontaminated) but rather is handled by a 6-port, 2-position chromatography-type loop valve. An accompanying computer is programmed in QuickBASIC 4.5 to provide both instrument control and data reduction. The program is truly user-friendly and communication between operator and instrument is via computer screen displays and keyboard. Two important issues which have been addressed are waste minimization and operator safety (the analyzer can run in the absence of an operator, once its autosampler has been loaded)
Multiple capillary biochemical analyzer
Dovichi, N.J.; Zhang, J.Z.
1995-08-08
A multiple capillary analyzer allows detection of light from multiple capillaries with a reduced number of interfaces through which light must pass in detecting light emitted from a sample being analyzed, using a modified sheath flow cuvette. A linear or rectangular array of capillaries is introduced into a rectangular flow chamber. Sheath fluid draws individual sample streams through the cuvette. The capillaries are closely and evenly spaced and held by a transparent retainer in a fixed position in relation to an optical detection system. Collimated sample excitation radiation is applied simultaneously across the ends of the capillaries in the retainer. Light emitted from the excited sample is detected by the optical detection system. The retainer is provided by a transparent chamber having inward slanting end walls. The capillaries are wedged into the chamber. One sideways dimension of the chamber is equal to the diameter of the capillaries and one end to end dimension varies from, at the top of the chamber, slightly greater than the sum of the diameters of the capillaries to, at the bottom of the chamber, slightly smaller than the sum of the diameters of the capillaries. The optical system utilizes optic fibers to deliver light to individual photodetectors, one for each capillary tube. A filter or wavelength division demultiplexer may be used for isolating fluorescence at particular bands. 21 figs.
Energy Technology Data Exchange (ETDEWEB)
Burns, D.A.
1994-09-01
A fully automated analyzer has been developed for plutonium solutions. It was assembled from several commercially available modules, is based upon segmented flow analysis, and exhibits precision about an order of magnitude better than commercial units (0.5%-O.05% RSD). The system was designed to accept unmeasured, untreated liquid samples in the concentration range 40-240 g/L and produce a report with sample identification, sample concentrations, and an abundance of statistics. Optional hydraulics can accommodate samples in the concentration range 0.4-4.0 g/L. Operating at a typical rate of 30 to 40 samples per hour, it consumes only 0.074 mL of each sample and standard, and generates waste at the rate of about 1.5 mL per minute. No radioactive material passes through its multichannel peristaltic pump (which remains outside the glovebox, uncontaminated) but rather is handled by a 6-port, 2-position chromatography-type loop valve. An accompanying computer is programmed in QuickBASIC 4.5 to provide both instrument control and data reduction. The program is truly user-friendly and communication between operator and instrument is via computer screen displays and keyboard. Two important issues which have been addressed are waste minimization and operator safety (the analyzer can run in the absence of an operator, once its autosampler has been loaded).
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.
Research studies performed using the Cairo Fourier Diffractometer Facility
International Nuclear Information System (INIS)
Maayouf, R.M.A.; Ridikas, D.
2009-12-01
This report represents the results of the research studies performed using the Cairo Fourier Diffractometer Facility (CFDF), within 10 years after it was installed and put into operation at the beginning of 1996. The main components of the CFDF were supplied by the IAEA according to the technical assistance project EGY/1/022 'Upgrading of Research Reactor Utilization'. The present report is the second published INDC report, while the first one, published at the beginning of 1997, was about the performance of the CFDF and its main characteristic parameters. Plenty of measurements were performed since then, yielding several publications both in local and international scientific periodicals and resulting in 8 M.Sc. and Ph.D. degrees from Egyptian Universities. In addition, a new approach for the analysis of the neutron spectra was implemented using the CFDF. Specially designed interface card with proper software program was applied instead of the reverse time of flight (RTOF) and Finnish made analyzer originally attached to the facility. It has been verified that the new approach can successfully replace the RTOF analyzer, significantly decreasing the time of measurement and saving the reactor's operation time. Besides, a special fault diagnostic system program was developed and tested for caring and handling the possible failures of the CFDF. Moreover, measurements were carried out for the diffraction spectra emitted at different points of one of the samples. The latter was scanned across the neutron beam of the CFDF, for studying the stress after welding; used in industrial applications. (author)
Buccal microbiology analyzed by infrared spectroscopy
de Abreu, Geraldo Magno Alves; da Silva, Gislene Rodrigues; Khouri, Sônia; Favero, Priscila Pereira; Raniero, Leandro; Martin, Airton Abrahão
2012-01-01
Rapid microbiological identification and characterization are very important in dentistry and medicine. In addition to dental diseases, pathogens are directly linked to cases of endocarditis, premature delivery, low birth weight, and loss of organ transplants. Fourier Transform Infrared Spectroscopy (FTIR) was used to analyze oral pathogens Aggregatibacter actinomycetemcomitans ATCC 29523, Aggregatibacter actinomycetemcomitans-JP2, and Aggregatibacter actinomycetemcomitans which was clinically isolated from the human blood-CI. Significant spectra differences were found among each organism allowing the identification and characterization of each bacterial species. Vibrational modes in the regions of 3500-2800 cm-1, the 1484-1420 cm-1, and 1000-750 cm-1 were used in this differentiation. The identification and classification of each strain were performed by cluster analysis achieving 100% separation of strains. This study demonstrated that FTIR can be used to decrease the identification time, compared to the traditional methods, of fastidious buccal microorganisms associated with the etiology of the manifestation of periodontitis.
Fourier Transform Infrared and Resonance Raman Spectroscopic Studies of Bacteriorhodopsin.
Earnest, Thomas Nixon
Fourier transform infrared and resonance Raman spectroscopy were used to investigate the structure and function of the light-activated, transmembrane proton pump, bacteriorhodopsin, from the purple membrane of Halobacterium halobium. Bacteriorhodopsin (bR) is a 27,000 dalton integral membrane protein consisting of 248 amino acids with a retinylidene chromophore. Absorption of a photon leads to the translocation of one or two protons from the inside of the cell to the outside. Resonance Raman spectroscopy allows for the study of the configuration of retinal in bR and its photointermediates by the selective enhancement of vibrational modes of the chromophore. This technique was used to determine that the chromophore is attached to lysine-216 in both the bR _{570} and the M _{412} intermediates. In bR with tyrosine-64 selectively nitrated or aminated, the chromophore appears to have the same configuration in that bR _{570} (all- trans) and M _{412} (13- cis) states as it does in unmodified bR. Polarized Fourier transform infrared spectroscopy (FTIR) permits the study of the direction of transition dipole moments arising from molecular vibrations of the protein and the retinal chromophore. The orientation of alpha helical and beta sheet components was determined for bR with the average helical tilt found to lie mostly parallel to the membrane normal. The beta sheet structures also exhibit an IR linear dichroism for the amide I and amide II bands which suggest that the peptide backbone is mostly perpendicular to the membrane plane although it is difficult to determine whether the bands originate from sheet or turn components. The orientation of secondary structure components of the C-1 (residues 72-248) and C-2 (residues 1-71) fragments were also investigated to determine the structure of these putative membrane protein folding intermediates. Polarized, low temperature FTIR -difference spectroscopy was then used to investigate the structure of bR as it undergoes
International Nuclear Information System (INIS)
Schneider, W.J.; Edwards, D. Jr.
1979-01-01
The desirability for long-term reliability of large scale helium refrigerator systems used on superconducting accelerator magnets has necessitated detection of impurities to levels of a few ppM. An analyzer that measures trace impurity levels of condensable contaminants in concentrations of less than a ppM in 15 atm of He is described. The instrument makes use of the desorption temperature at an indicated pressure of the various impurities to determine the type of contaminant. The pressure rise at that temperature yields a measure of the contaminant level of the impurity. A LN 2 cryogenic charcoal trap is also employed to measure air impurities (nitrogen and oxygen) to obtain the full range of contaminant possibilities. The results of this detector which will be in use on the research and development helium refrigerator of the ISABELLE First-Cell is described
Analyzing Water's Optical Absorption
2002-01-01
A cooperative agreement between World Precision Instruments (WPI), Inc., and Stennis Space Center has led the UltraPath(TM) device, which provides a more efficient method for analyzing the optical absorption of water samples at sea. UltraPath is a unique, high-performance absorbance spectrophotometer with user-selectable light path lengths. It is an ideal tool for any study requiring precise and highly sensitive spectroscopic determination of analytes, either in the laboratory or the field. As a low-cost, rugged, and portable system capable of high- sensitivity measurements in widely divergent waters, UltraPath will help scientists examine the role that coastal ocean environments play in the global carbon cycle. UltraPath(TM) is a trademark of World Precision Instruments, Inc. LWCC(TM) is a trademark of World Precision Instruments, Inc.
Directory of Open Access Journals (Sweden)
Lin Chin-Yu
2006-04-01
Full Text Available Abstract Background Association mapping using abundant single nucleotide polymorphisms is a powerful tool for identifying disease susceptibility genes for complex traits and exploring possible genetic diversity. Genotyping large numbers of SNPs individually is performed routinely but is cost prohibitive for large-scale genetic studies. DNA pooling is a reliable and cost-saving alternative genotyping method. However, no software has been developed for complete pooled-DNA analyses, including data standardization, allele frequency estimation, and single/multipoint DNA pooling association tests. This motivated the development of the software, 'PDA' (Pooled DNA Analyzer, to analyze pooled DNA data. Results We develop the software, PDA, for the analysis of pooled-DNA data. PDA is originally implemented with the MATLAB® language, but it can also be executed on a Windows system without installing the MATLAB®. PDA provides estimates of the coefficient of preferential amplification and allele frequency. PDA considers an extended single-point association test, which can compare allele frequencies between two DNA pools constructed under different experimental conditions. Moreover, PDA also provides novel chromosome-wide multipoint association tests based on p-value combinations and a sliding-window concept. This new multipoint testing procedure overcomes a computational bottleneck of conventional haplotype-oriented multipoint methods in DNA pooling analyses and can handle data sets having a large pool size and/or large numbers of polymorphic markers. All of the PDA functions are illustrated in the four bona fide examples. Conclusion PDA is simple to operate and does not require that users have a strong statistical background. The software is available at http://www.ibms.sinica.edu.tw/%7Ecsjfann/first%20flow/pda.htm.
A New approach for the data acquisition system of the cairo fourier diffractometer
International Nuclear Information System (INIS)
Maayouf, R.M.A.; Khalil, M.I.
2000-01-01
The present work deals with a new approach for the reverse time of flight (RTOF) analysis of the diffraction spectra. The approach is based on the same RTOF concept used for the design of a separate RTOF analyzer and applies, for data acquisition, a special interface card and software program installed in a PC computer, to perform the cross-correlation functions between the three signals received from the chopper decoder, detector and the pulsed neutron source respectively. The new approach have been realized for use with a Fourier diffractometer facility based on the RTOF concept. It has been found from test measurements performed with the high resolution Fourier diffractometer (HRFD) at the IBR-2 reactor (JINR, Dubna) that the new approach can successfully replace the RTOF analyzer
Pei, Soo-Chang; Ding, Jian-Jiun
2005-03-01
Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.
Regularized spherical polar fourier diffusion MRI with optimal dictionary learning.
Cheng, Jian; Jiang, Tianzi; Deriche, Rachid; Shen, Dinggang; Yap, Pew-Thian
2013-01-01
Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods proposed for reconstruction of diffusion-weighted signal and the Ensemble Average Propagator (EAP) utilize two kinds of Dictionary Learning (DL) methods: 1) Discrete Representation DL (DR-DL), and 2) Continuous Representation DL (CR-DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding errors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI) for effective compressed-sensing reconstruction of the q-space diffusion-weighted signal and the EAP. In DL-SPFI, a dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. Compared with the start-of-the-art CR-DL and DR-DL methods proposed by Merlet et al. and Bilgic et al., respectively, our work offers the following advantages. First, the learned dictionary is proved to be optimal for Gaussian diffusion signals. Second, to our knowledge, this is the first work to learn a voxel-adaptive dictionary. The importance of the adaptive dictionary in EAP reconstruction will be demonstrated theoretically and empirically. Third, optimization in DL-SPFI is only performed in a small subspace resided by the SPF coefficients, as opposed to the q-space approach utilized by Merlet et al. We experimentally evaluated DL-SPFI with respect to L1-norm regularized SPFI (L1-SPFI), which uses the original SPF basis, and the DR-DL method proposed by Bilgic et al. The experiment results on synthetic and real data indicate that the learned dictionary produces
Fourier Hull Fatigue Assessment Method’s Proposing and Software Development
Directory of Open Access Journals (Sweden)
Jing Chen
2014-05-01
Full Text Available In this paper, based on the spectral analysis and the strain energy theory, the systematic errors of Rain-flow Counting Method have been quantitatively analyzed, from which a Fourier Counting Method is put forward. And according to this new method, software has been developed combined with sampling data of the real container ship via rigorous theoretical derivation and compact modular design, which has certain theoretical innovation significance and practical value.
Henry, Christine; Criner, Amanda Keck; Imel, Megan; King, Derek
2018-04-01
Data collected with a handheld Fourier Transform Infrared (FTIR) device is analyzed and considered as a useful method for detecting and quantifying oxidation on the surface of ceramic matrix composite (CMC) materials. Experiments examine silicon carbide (SiC) coupons, looking for changes in chemical composition before and after thermal exposure. Using mathematical, physical and statistical models for FTIR reflectance data, this research seeks to quantify any detected spectral changes as an indicator of surface oxidation on the CMC coupon.
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).
Response of Autonomic Nervous System to Body Positions: Fourier and Wavelet Analysis
Xu, Aiguo; Gonnella, G.; Federici, A.; Stramaglia, S.; Simone, F.; Zenzola, A.; Santostasi, R.
2003-01-01
Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1), and the second parts (HD2) of $90^{\\circ}$ head down tilt and during recovery (REC). The wavelet transform was performed using the Haar function of period $T=2^j$ ($% j=1$,2,$... $,6) to obtain wavelet coefficients. ...
Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy*
Liu, Yan-de; Ying, Yi-bin; Fu, Xia-ping
2005-01-01
To develop nondestructive acidity prediction for intact Fuji apples, the potential of Fourier transform near infrared (FT-NIR) method with fiber optics in interactance mode was investigated. Interactance in the 800 nm to 2619 nm region was measured for intact apples, harvested from early to late maturity stages. Spectral data were analyzed by two multivariate calibration techniques including partial least squares (PLS) and principal component regression (PCR) methods. A total of 120 Fuji appl...
Experimental and clinical analyses of optimum Fourier filtering in ECG-gated blood pool scintigraphy
International Nuclear Information System (INIS)
Shimabukuro, Kunisada
1988-01-01
A phantom study was undertaken to determine the optimum order harmonics in Fourier analysis for volume curves obtained by ECG-gated blood pool scintigraphy. The volume curve obtained by Tc-99m scintigraphy was computed by the 1st through 10th order harmonics of Fourier transform. The shape of each volume curve fitted by Fourier transform was compared with the shape of the generated ideal curve. Curves fitted with the 3rd or more order harmonics were approximate to the ideal curve in shape during the systolic phase. The 6th to 10th order harmonics were suitable for the early diastole phase. As determined by peak ejection rate and peak filling rate (PFR), the 6th order harmonics was superior to the 3rd order harmonics in evaluating early diastolic abnormalities. In the clinical settings, there was no difference between the 3rd and 6th order harmonics in evaluating systolic abnormalities; however, the 6th order harmonics was more sensitive than the 3rd order harmonics in evaluating early diastolic abnormalities. The 6th order harmonics significantly reflected PFR in the group of hypertrophic cardiomyopathy (n=10) and time to PFR in the groups of old myocardial infarction (n=10) and angina pectoris (n=10). In conclusion, the 6th to 9th order harmonics of Fourier analysis may be useful in analyzing both systolic and early diastolic phases inf left ventricular volume curves obtained from ECG-gated cardiac blood pool scintigraphy. (Namekawa, K)
Application of the fractional Fourier transform to image reconstruction in MRI.
Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo
2012-07-01
The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.
Downhole Fluid Analyzer Development
Energy Technology Data Exchange (ETDEWEB)
Bill Turner
2006-11-28
A novel fiber optic downhole fluid analyzer has been developed for operation in production wells. This device will allow real-time determination of the oil, gas and water fractions of fluids from different zones in a multizone or multilateral completion environment. The device uses near infrared spectroscopy and induced fluorescence measurement to unambiguously determine the oil, water and gas concentrations at all but the highest water cuts. The only downhole components of the system are the fiber optic cable and windows. All of the active components--light sources, sensors, detection electronics and software--will be located at the surface, and will be able to operate multiple downhole probes. Laboratory testing has demonstrated that the sensor can accurately determine oil, water and gas fractions with a less than 5 percent standard error. Once installed in an intelligent completion, this sensor will give the operating company timely information about the fluids arising from various zones or multilaterals in a complex completion pattern, allowing informed decisions to be made on controlling production. The research and development tasks are discussed along with a market analysis.
Climate Model Diagnostic Analyzer
Lee, Seungwon; Pan, Lei; Zhai, Chengxing; Tang, Benyang; Kubar, Terry; Zhang, Zia; Wang, Wei
2015-01-01
The comprehensive and innovative evaluation of climate models with newly available global observations is critically needed for the improvement of climate model current-state representation and future-state predictability. A climate model diagnostic evaluation process requires physics-based multi-variable analyses that typically involve large-volume and heterogeneous datasets, making them both computation- and data-intensive. With an exploratory nature of climate data analyses and an explosive growth of datasets and service tools, scientists are struggling to keep track of their datasets, tools, and execution/study history, let alone sharing them with others. In response, we have developed a cloud-enabled, provenance-supported, web-service system called Climate Model Diagnostic Analyzer (CMDA). CMDA enables the physics-based, multivariable model performance evaluations and diagnoses through the comprehensive and synergistic use of multiple observational data, reanalysis data, and model outputs. At the same time, CMDA provides a crowd-sourcing space where scientists can organize their work efficiently and share their work with others. CMDA is empowered by many current state-of-the-art software packages in web service, provenance, and semantic search.
Lacunary Fourier Series and a Qualitative Uncertainty Principle for ...
Indian Academy of Sciences (India)
We define lacunary Fourier series on a compact connected semisimple Lie group . If f ∈ L 1 ( G ) has lacunary Fourier series and vanishes on a non empty open subset of , then we prove that vanishes identically. This result can be viewed as a qualitative uncertainty principle.
Bilaterally symmetric Fourier approximations of the skull outlines of ...
Indian Academy of Sciences (India)
Present work illustrates a scheme of quantitative description of the shape of the skull outlines of temnospondyl amphibians using bilaterally symmetric closed Fourier curves. Some special points have been identified on the Fourier fits of the skull outlines, which are the local maxima, or minima of the distances from the ...
Fourier transformations for difference analogs of the harmonic oscillator
International Nuclear Information System (INIS)
Askey, R.; Atakishiyev, N.M.
1995-01-01
The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs
The Fourier Transform for Certain HyperKähler Fourfolds
Shen, M.; Vial, C.
2016-01-01
Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle
Infrared Fourier spectres of pectin obtained from pumpkin
International Nuclear Information System (INIS)
Usmanova, S.R.; Dzhonmurodov, A.S.; Nazirova, Kh.I.; Mukhidinov, Z.K.
2015-01-01
Present article is devoted to infrared Fourier spectres of pectin obtained from pumpkin. The analysis of pectin obtained from pumpkin was conducted by means of infrared spectrophotometer with Fourier transformation. The infrared spectroscopic study of pectin polysaccharide fraction of pectin matter, as well as pectin helium and micro helium obtained by means of fast extraction was conducted.
Time-of-flight Fourier spectrometry of UCN
International Nuclear Information System (INIS)
Kulin, G.V.; Frank, A.I.; Goryunov, S.V.; Kustov, D.V.; Geltenbort, P.; Jentshel, M.; Strepetov, A.N.; Bushuev, V.A.
2014-01-01
The results of preliminary experiments on TOF Fourier UCN spectrometry are presented. The description of the new Fourier spectrometer that may be used for the measurement of the UCN spectra arising from diffraction by a moving grating is given. The results of preliminary experiments and Monte Carlo calculations give reason to hope for the success of the planned experiment.
Fourier path-integral Monte Carlo methods: Partial averaging
International Nuclear Information System (INIS)
Doll, J.D.; Coalson, R.D.; Freeman, D.L.
1985-01-01
Monte Carlo Fourier path-integral techniques are explored. It is shown that fluctuation renormalization techniques provide an effective means for treating the effects of high-order Fourier contributions. The resulting formalism is rapidly convergent, is computationally convenient, and has potentially useful variational aspects
Exploring Fourier Series and Gibbs Phenomenon Using Mathematica
Ghosh, Jonaki B.
2011-01-01
This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of…
Fourier transform in multimode systems in the Bargmann representation
International Nuclear Information System (INIS)
Lei, C; Vourdas, A
2007-01-01
A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag-Leffler states are discussed
Revisiting the quantum harmonic oscillator via unilateral Fourier transforms
International Nuclear Information System (INIS)
Nogueira, Pedro H F; Castro, Antonio S de
2016-01-01
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)
First order deformations of the Fourier matrix
Energy Technology Data Exchange (ETDEWEB)
Banica, Teodor, E-mail: teo.banica@gmail.com [Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise (France)
2014-01-15
The N × N complex Hadamard matrices form a real algebraic manifold C{sub N}. The singularity at a point H ∈ C{sub N} is described by a filtration of cones T{sub H}{sup ×}C{sub N}⊂T{sub H}{sup ∘}C{sub N}⊂T{sub H}C{sub N}⊂T{sup ~}{sub H}C{sub N}, coming from the trivial, affine, smooth, and first order deformations. We study here these cones in the case where H = F{sub N} is the Fourier matrix, (w{sup ij}) with w = e{sup 2πi/N}, our main result being a simple description of T{sup ~}{sub H}C{sub N}. As a consequence, the rationality conjecture dim{sub R}(T{sup ~}{sub H}C{sub N})=dim{sub Q}(T{sup ~}{sub H}C{sub N}∩M{sub N}(Q)) holds at H = F{sub N}.
Three dimensional image reconstruction in the Fourier domain
International Nuclear Information System (INIS)
Stearns, C.W.; Chesler, D.A.; Brownell, G.L.
1987-01-01
Filtered backprojection reconstruction algorithms are based upon the relationship between the Fourier transform of the imaged object and the Fourier transforms of its projections. A new reconstruction algorithm has been developed which performs the image assembly operation in Fourier space, rather than in image space by backprojection. This represents a significant decrease in the number of operations required to assemble the image. The new Fourier domain algorithm has resolution comparable to the filtered backprojection algorithm, and, after correction by a pointwise multiplication, demonstrates proper recovery throughout image space. Although originally intended for three-dimensional imaging applications, the Fourier domain algorithm can also be developed for two-dimensional imaging applications such as planar positron imaging systems
The relationship between shock response spectrum and fast Fourier transform
International Nuclear Information System (INIS)
Zola, Maurizio
2001-01-01
In this paper the basic relationship between response spectrum and fast Fourier transform is laid down. Since a long time the response spectrum has been used by structural engineers in the seismic domain and nowadays it is going to be used to define transient motions. This way to define the excitation is more general and more real than the use of classical shape pulses for the reproduction of real environment. Nevertheless the response spectrum of a real excitation represents a loss of some information with respect to the Fourier transform. A useful discussion could arise from these observations. Appendix A gives the relationship between the mathematic Fourier transform and the digital Fourier transform given by computers, while Appendix B gives some examples of response spectra and Fourier transforms of simple functions. (author)
Mathematical principles of signal processing Fourier and wavelet analysis
Brémaud, Pierre
2002-01-01
Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...
Solution of 3-dimensional diffusion equation by finite Fourier transformation
International Nuclear Information System (INIS)
Krishnani, P.D.
1978-01-01
Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)
The morphing of geographical features by Fourier transformation.
Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang
2018-01-01
This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.
Double Fourier analysis for Emotion Identification in Voiced Speech
International Nuclear Information System (INIS)
Sierra-Sosa, D.; Bastidas, M.; Ortiz P, D.; Quintero, O.L.
2016-01-01
We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented. (paper)
Digital Microfluidics Sample Analyzer
Pollack, Michael G.; Srinivasan, Vijay; Eckhardt, Allen; Paik, Philip Y.; Sudarsan, Arjun; Shenderov, Alex; Hua, Zhishan; Pamula, Vamsee K.
2010-01-01
Three innovations address the needs of the medical world with regard to microfluidic manipulation and testing of physiological samples in ways that can benefit point-of-care needs for patients such as premature infants, for which drawing of blood for continuous tests can be life-threatening in their own right, and for expedited results. A chip with sample injection elements, reservoirs (and waste), droplet formation structures, fluidic pathways, mixing areas, and optical detection sites, was fabricated to test the various components of the microfluidic platform, both individually and in integrated fashion. The droplet control system permits a user to control droplet microactuator system functions, such as droplet operations and detector operations. Also, the programming system allows a user to develop software routines for controlling droplet microactuator system functions, such as droplet operations and detector operations. A chip is incorporated into the system with a controller, a detector, input and output devices, and software. A novel filler fluid formulation is used for the transport of droplets with high protein concentrations. Novel assemblies for detection of photons from an on-chip droplet are present, as well as novel systems for conducting various assays, such as immunoassays and PCR (polymerase chain reaction). The lab-on-a-chip (a.k.a., lab-on-a-printed-circuit board) processes physiological samples and comprises a system for automated, multi-analyte measurements using sub-microliter samples of human serum. The invention also relates to a diagnostic chip and system including the chip that performs many of the routine operations of a central labbased chemistry analyzer, integrating, for example, colorimetric assays (e.g., for proteins), chemiluminescence/fluorescence assays (e.g., for enzymes, electrolytes, and gases), and/or conductometric assays (e.g., for hematocrit on plasma and whole blood) on a single chip platform.
International Nuclear Information System (INIS)
Zhang Duanming; Li, Li; Li Zhihua; Guan Li; Tan Xinyu
2005-01-01
A non-Fourier conduction model with heat source term is presented to study the target temperature evolvement when the target is radiated by high power (the laser intensity is above 10 9 w/cm 2 ) and ultra short (the pulse width is less than 150 ps) pulsed laser. By Laplace transform, the analytical expression of the space- and time-dependence of temperature is derived. Then as an example of aluminum target, the target temperature evolvement is simulated. Compared with the results of Fourier conduction model and non-Fourier model without heat source term, it is found that the effect of non-Fourier conduction is notable and the heat source plays an important role during non-Fourier conduction which makes surface temperature ascending quickly with time. Meanwhile, the corresponding physical mechanism is analyzed theoretically
Multiple wall-reflection effect in adaptive-array differential-phase reflectometry on QUEST
International Nuclear Information System (INIS)
Idei, H.; Fujisawa, A.; Nagashima, Y.; Onchi, T.; Hanada, K.; Zushi, H.; Mishra, K.; Hamasaki, M.; Hayashi, Y.; Yamamoto, M.K.
2016-01-01
A phased array antenna and Software-Defined Radio (SDR) heterodyne-detection systems have been developed for adaptive array approaches in reflectometry on the QUEST. In the QUEST device considered as a large oversized cavity, standing wave (multiple wall-reflection) effect was significantly observed with distorted amplitude and phase evolution even if the adaptive array analyses were applied. The distorted fields were analyzed by Fast Fourier Transform (FFT) in wavenumber domain to treat separately the components with and without wall reflections. The differential phase evolution was properly obtained from the distorted field evolution by the FFT procedures. A frequency derivative method has been proposed to overcome the multiple-wall reflection effect, and SDR super-heterodyned components with small frequency difference for the derivative method were correctly obtained using the FFT analysis
Choi, Yong-Kyu; Hosoya, Kenta; Lee, Chung Ghiu; Hanawa, Masanori; Park, Chang-Soo
2011-03-28
We propose and experimentally demonstrate a hybrid WDM/OCDMA ring with a dynamic add/drop function based on Fourier code for local area networks. Dynamic function is implemented by mechanically tuning the Fourier encoder/decoder for optical code division multiple access (OCDMA) encoding/decoding. Wavelength division multiplexing (WDM) is utilized for node assignment and 4-chip Fourier code recovers the matched signal from the codes. For an optical source well adapted to WDM channels and its short optical pulse generation, reflective semiconductor optical amplifiers (RSOAs) are used with a fiber Bragg grating (FBG) and gain-switched. To demonstrate we experimentally investigated a two-node hybrid WDM/OCDMA ring with a 4-chip Fourier encoder/decoder fabricated by cascading four FBGs with the bit error rate (BER) of <10(-9) for the node span of 10.64 km at 1.25 Gb/s.
The Scope Of Fourier Transform Infrared (FTIR)
Hirschfeld, T.
1981-10-01
Three auarters of a century after its inception, a generation after its advantages were recognized, and a decade after its first commercialization, FT-IR dominates the growth of the IR market, and reigns alone over its high performance end. What lies ahead for FT-IR now? On one hand, the boundary between it and the classical scanning spectrometers is becoming fuzzy, as gratings attempt to use as much of FT-IR's computer technology as they can handle, and smaller FT systems invade the medium cost instrument range. On the other hand, technology advances in IR detectors, non-Fourier interference devices, and the often announced tunable laser are at long last getting set to make serious inroads in the field (although not necessarily in the manner most of us expected). However, the dominance of FT-IR as the leading edge of IR spectroscopy seems assured for a good many years. The evolution of FT-IR will be dominated by demands not yet fully satisfied such as rapid sample turnover, better quantitation, automated interpretation, higher GC-IR sensitivity, improved LC-IR, and, above all else, reliability and ease of use. These developments will be based on multiple small advances in hardware, large advances in the way systems are put together, and the traditional yearly revolutionary advances of the computer industry. The big question in the field will, however, still be whether our ambition and our skill can continue to keep up with the advances of our tools. It will be fun.
Fourier transform based scalable image quality measure.
Narwaria, Manish; Lin, Weisi; McLoughlin, Ian; Emmanuel, Sabu; Chia, Liang-Tien
2012-08-01
We present a new image quality assessment (IQA) algorithm based on the phase and magnitude of the 2D (twodimensional) Discrete Fourier Transform (DFT). The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the Human Visual Systems (HVSs) sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of nonuniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Lastly, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is therefore further scalable for RR scenarios. We report extensive experimental results using a total of 9 publicly available databases: 7 image (with a total of 3832 distorted images with diverse distortions) and 2 video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing fullreference (FR) algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar.
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
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.
SPICA/SAFARI Fourier transform spectrometer mechanism evolutionary design
van den Dool, Teun C.; Kruizinga, Bob; Braam, Ben C.; Hamelinck, Roger F. M. M.; Loix, Nicolas; Van Loon, Dennis; Dams, Johan
2012-09-01
TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI1 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 Programme2 in 2022. JAXA3 leads the development of the SPICA satellite and SRON is the prime investigator of the Safari instrument. The FTS scanning mechanism (FTSM) has to meet a 35 mm stroke requirement with an Optical Path Difference resolution of less then 15 nm and must fit in a small volume. It consists of two back-to-back roof-top mirrors mounted on a small carriage, which is moved using a magnetic bearing linear guiding system in combination with a magnetic linear motor serving as the OPD actuator. The FTSM will be used at cryogenic temperatures of 4 Kelvin inducing challenging requirements on the thermal power dissipation and heat leak. The magnetic bearing enables movements over a scanning stroke of 35.5 mm in a small volume. It supports the optics in a free-floating way with no friction, or other non-linearities, with sub-nanometer accuracy. This solution is based on the design of the breadboard ODL (Optical Delay Line) developed for the ESA Darwin mission4 and the MABE mechanism developed by Micromega Dynamics. During the last couple of years the initial design of the SAFARI instrument, as described in an earlier SPIE 2010 paper5, was adapted by the SAFARI team in an evolutionary way to meet the changing requirements of the SPICA payload module. This presentation will focus on the evolution of the FTSM to meet these changing requirements. This work is supported by the Netherlands Space Office (NSO).
Anderson, Lorin W.
1979-01-01
Schools have devised several ways to adapt instruction to a wide variety of student abilities and needs. Judged by criteria for what adaptive education should be, most learning for mastery programs look good. (Author/JM)
Kim, Jaehee; Ogden, Robert Todd; Kim, Haseong
2013-10-18
Time course gene expression experiments are an increasingly popular method for exploring biological processes. Temporal gene expression profiles provide an important characterization of gene function, as biological systems are both developmental and dynamic. With such data it is possible to study gene expression changes over time and thereby to detect differential genes. Much of the early work on analyzing time series expression data relied on methods developed originally for static data and thus there is a need for improved methodology. Since time series expression is a temporal process, its unique features such as autocorrelation between successive points should be incorporated into the analysis. This work aims to identify genes that show different gene expression profiles across time. We propose a statistical procedure to discover gene groups with similar profiles using a nonparametric representation that accounts for the autocorrelation in the data. In particular, we first represent each profile in terms of a Fourier basis, and then we screen out genes that are not differentially expressed based on the Fourier coefficients. Finally, we cluster the remaining gene profiles using a model-based approach in the Fourier domain. We evaluate the screening results in terms of sensitivity, specificity, FDR and FNR, compare with the Gaussian process regression screening in a simulation study and illustrate the results by application to yeast cell-cycle microarray expression data with alpha-factor synchronization.The key elements of the proposed methodology: (i) representation of gene profiles in the Fourier domain; (ii) automatic screening of genes based on the Fourier coefficients and taking into account autocorrelation in the data, while controlling the false discovery rate (FDR); (iii) model-based clustering of the remaining gene profiles. Using this method, we identified a set of cell-cycle-regulated time-course yeast genes. The proposed method is general and can be
Toward a soft x-ray Fourier-transform spectrometer
International Nuclear Information System (INIS)
Howells, M.R.; Frank, K.; Hussain, Z.; Moler, E.J.; Reich, T.; Moeller, D.
1993-01-01
The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range ±1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330
Corrected Fourier series and its application to function approximation
Directory of Open Access Journals (Sweden)
Qing-Hua Zhang
2005-01-01
Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.
During a field study in the summer of 2000 in the Research Triangle Park (RTP), aerosol samples were collected using a five stage cascade impactor and subsequently analyzed using Fourier Transform Infrared Spectroscopy (FTIR). The impaction surfaces were stainless steel disks....
Analysis of the Interference Modulation Depth in the Fourier Transform Spectrometer
Directory of Open Access Journals (Sweden)
Rilong Liu
2015-01-01
Full Text Available Based on the principle of the Michelson interferometer, the paper briefly describes the theoretical significance and calculates and deduces three expressions of the interference modulation depth. The influence of the surface shape error of plane mirror on modulation depth is analyzed, and the tolerance of error is also pointed out. Moreover, the dependence of modulation depth on the reflectance change of beam splitter interface is also analyzed, and the curve is given. It is concluded that this paper is of general significance for the Fourier transform spectrometer based on the principle of the Michelson two-beam interference.
Residual Stress Studies Using the Cairo Fourier Diffractometer Facility
International Nuclear Information System (INIS)
Maayouf, R.M.A.; El-Shaer, Y.H.
2002-01-01
The present paper deals with residual stress studies using the Cairo Fourier diffractometer facility CFDF. The CFDF is a reverse - time of -flight (RTOF) diffractometer; applies a Fourier chopper. The measurements were performed for copper samples in order to study the residual stress after welding. The maximum modulation of the Fourier chopper during the measurements was 136 khz; leading to a time resolution half-width of about 7 μ s. It has been found from the present measurements that, the resulting diffraction spectra could be successfully used for studying the residual stress; in the wavelength range between 0.7-2.9 A degree at ∼ 0.45 % relative resolution
From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
2001-01-01
A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm
The application and improvement of Fourier transform spectrometer experiment
Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning
2017-08-01
According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.
Image reconstruction from pairs of Fourier-transform magnitude
International Nuclear Information System (INIS)
Hunt, B.R.; Overman, T.L.; Gough, P.
1998-01-01
The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms. copyright 1998 Optical Society of America
Principle and analysis of a rotational motion Fourier transform infrared spectrometer
Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning
2017-09-01
Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.
Singularities of affine fibrations in the regularity theory of Fourier integral operators
International Nuclear Information System (INIS)
Ruzhansky, M V
2000-01-01
We consider regularity properties of Fourier integral operators in various function spaces. The most interesting case is the L p spaces, for which survey of recent results is given. For example, sharp orders are known for operators satisfying the so-called smooth factorization condition. Here this condition is analyzed in both real and complex settings. In the letter case, conditions for the continuity of Fourier integral operators are related to singularities of affine fibrations in C n (or subsets of C n ) specified by the kernels of Jacobi matrices of holomorphic maps. Singularities of such fibrations are analyzed in this paper in the general case. In particular, it is shown that if the dimension n or the rank of the Jacobi matrix is small, then all singularities of an affine fibration are removable. The fibration associated with a Fourier integral operator is given by the kernels of the Hessian of the phase function of the operator. On the basis of an analysis of singularities for operators commuting with translations we show in a number of cases that the factorization condition is satisfied, which leads to L p estimates for operators. In other cases, examples are given in which the factorization condition fails. The results are applied to deriving L p estimates for solutions of the Cauchy problem for hyperbolic partial differential operators
Fourier transform spectroscopy of semiconductor materials
International Nuclear Information System (INIS)
Jonak-Auer, I.
1996-11-01
In order to determine the type of charge carriers, i.e. electrons or holes, participating in optical transitions, cyclotron resonance experiments using circularly polarized radiation were performed on strained-layer [111]-oriented InGaAs/(Al)GaAs multiple quantum wells and on a [100]-oriented InAs/GaSb double-heterostructure. Because of the rather complicated band-structures of these samples it is a priori unknown which carriers take part in transitions. The measurements yield the surprising result, that for the InGaAs/GaAs multiple quantum well the experimentally observed cyclotron resonance appears in the electron-active polarization in the frequency-regime of the Far Infrared (FIR), but in the hole-active polarization in the range of millimeter waves, whereas for the InGaAs/AlGaAs sample the resonance is caused by holes also in the FIR. Since by theoretical considerations the possibility of electrons causing the FIR cyclotron resonance could be excluded, the measurements are interpreted as being caused by holes due to broken selection rules. In the InAs/GaSb sample hole cyclotron resonance could for the first time be measured on a double-heterostructure. As for the application oriented measurements, they comprised a study of the hydrogen content of amorphous silicon nitride layers, and were performed in collaboration with Austria Mikro Systeme International AG. Fourier spectroscopy is a fast and non-destructive means for determining impurity concentrations. Radiation in the Mid Infrared regime stimulates N-H and Si-H stretching vibrations which lead to absorption peaks and can directly be attributed to the hydrogen concentration via calibration factors taken from the literature. In comparison with recommended procedures in the literature, a much higher accuracy in determining the areas of the absorption peaks could be gained in the course of this thesis by a proper polynomial fit of the background spectrum outside the absorption lines. The hydrogen content of
DEFF Research Database (Denmark)
Petersen, Kjell Yngve; Søndergaard, Karin; Kongshaug, Jesper
2015-01-01
Adaptive Lighting Adaptive lighting is based on a partial automation of the possibilities to adjust the colour tone and brightness levels of light in order to adapt to people’s needs and desires. IT support is key to the technical developments that afford adaptive control systems. The possibilities...... offered by adaptive lighting control are created by the ways that the system components, the network and data flow can be coordinated through software so that the dynamic variations are controlled in ways that meaningfully adapt according to people’s situations and design intentions. This book discusses...... differently into an architectural body. We also examine what might occur when light is dynamic and able to change colour, intensity and direction, and when it is adaptive and can be brought into interaction with its surroundings. In short, what happens to an architectural space when artificial lighting ceases...
Sheng, Ming; Gorzsás, András; Tuck, Simon
2016-01-01
Changes in intermediary metabolism have profound effects on many aspects of C. elegans biology including growth, development and behavior. However, many traditional biochemical techniques for analyzing chemical composition require relatively large amounts of starting material precluding the analysis of mutants that cannot be grown in large amounts as homozygotes. Here we describe a technique for detecting changes in the chemical compositions of C. elegans worms by Fourier transform infrared microspectroscopy. We demonstrate that the technique can be used to detect changes in the relative levels of carbohydrates, proteins and lipids in one and the same worm. We suggest that Fourier transform infrared microspectroscopy represents a useful addition to the arsenal of techniques for metabolic studies of C. elegans worms.
International Nuclear Information System (INIS)
Rebagay, T.V.; Dodd, D.A.
1992-07-01
The disposal of low-level radioactive liquid wastes at the Hanford Site near Richland, Washington, involves mixing the wastes with pozzolanic grout-forming solid blends. Checking the quality of each blend component and its mix ratio will ensure processibility of the blend and the long-term performance of the resulting waste grout. In earlier work at Hanford laboratories, Fourier transform infrared-transmission method (FTIR-TR) using KBr pellet was applied successfully in the analysis of blends consisting of cement, fly ash, and clays. This method involves time-consuming sample preparation resulting in slow turnaround for repetitive sampling. Because reflection methods do not require elaborate sample preparation, they have the potential to reduce turnaround analysis time. Neat samples may be examined making these methods attractive for quality control. This study investigates the capability of Fourier transform infrared-attenuated total reflectance method (FTIR-ATR) to analyze pozzolanic blends
Distributed ISAR Subimage Fusion of Nonuniform Rotating Target Based on Matching Fourier Transform.
Li, Yuanyuan; Fu, Yaowen; Zhang, Wenpeng
2018-06-04
In real applications, the image quality of the conventional monostatic Inverse Synthetic Aperture Radar (ISAR) for the maneuvering target is subject to the strong fluctuation of Radar Cross Section (RCS), as the target aspect varies enormously. Meanwhile, the maneuvering target introduces nonuniform rotation after translation motion compensation which degrades the imaging performance of the conventional Fourier Transform (FT)-based method in the cross-range dimension. In this paper, a method which combines the distributed ISAR technique and the Matching Fourier Transform (MFT) is proposed to overcome these problems. Firstly, according to the characteristics of the distributed ISAR, the multiple channel echoes of the nonuniform rotation target from different observation angles can be acquired. Then, by applying the MFT to the echo of each channel, the defocused problem of nonuniform rotation target which is inevitable by using the FT-based imaging method can be avoided. Finally, after preprocessing, scaling and rotation of all subimages, the noncoherent fusion image containing all the RCS information in all channels can be obtained. The accumulation coefficients of all subimages are calculated adaptively according to the their image qualities. Simulation and experimental data are used to validate the effectiveness of the proposed approach, and fusion image with improved recognizability can be obtained. Therefore, by using the distributed ISAR technique and MFT, subimages of high-maneuvering target from different observation angles can be obtained. Meanwhile, by employing the adaptive subimage fusion method, the RCS fluctuation can be alleviated and more recognizable final image can be obtained.
International Nuclear Information System (INIS)
Grigoriev, Yurii N; Meleshko, Sergey V; Suriyawichitseranee, Amornrat
2015-01-01
Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie group is reduced to a partial differential equation for the admitted source. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation with respect to a source function is given. The representation of invariant solutions and corresponding reduced equations for all obtained source functions are also presented. (paper)
CSIR Research Space (South Africa)
Fedotov, I
2006-07-01
Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...
Almost everywhere convergence over cubes of multiple trigonometric Fourier series
International Nuclear Information System (INIS)
Antonov, N Yu
2004-01-01
Under certain conditions on a function φ:[0,+∞)→[0,+∞) we prove a theorem asserting that the convergence almost everywhere of trigonometric Fourier series for all functions of class φ(L) [-π,π) implies the convergence over cubes of the multiple Fourier series and all its conjugates for an arbitrary function f element of φ(L)(log + L) d-1 ) [-π,π) d , d element of N. It follows from this and an earlier result of the author on the convergence almost everywhere of Fourier series of functions of one variable and class L(log + L)(log + log + log + L)) [-π,π) that if f element of L(log + L) d (log + log + log + L)) [-π,π) d , d element of N, then the Fourier series of f and all its conjugates converge over cubes almost everywhere
On the Equisummability of Hermite and Fourier Expansions
Indian Academy of Sciences (India)
We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.
q-Generalization of the inverse Fourier transform
International Nuclear Information System (INIS)
Jauregui, M.; Tsallis, C.
2011-01-01
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.
On Sums of Numerical Series and Fourier Series
Pavao, H. Germano; de Oliveira, E. Capelas
2008-01-01
We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)
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...
Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
Said-Houari, Belkacem
2013-02-01
In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo\\'s laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier\\'s law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U0 ∈ Hs(ℝ) ∩ L1(ℝ). In addition, by restricting the initial data to U0 ∈ Hs(ℝ) ∩ L1,γ(ℝ) and γ ∈ [0, 1], we can derive faster decay estimates with the decay rate improvement by a factor of t-γ/2. © 2013 Copyright Taylor and Francis Group, LLC.
Extending Single-Molecule Microscopy Using Optical Fourier Processing
2015-01-01
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862
Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
Said-Houari, Belkacem
2013-01-01
In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent
A fourier transform quality measure for iris images
CSIR Research Space (South Africa)
Makinana, S
2014-08-01
Full Text Available to ensure that good quality images are selected for feature extraction, in order to improve iris recognition system. In addition, this research proposes a measure of iris image quality using a Fourier Transform. The experimental results demonstrate...
Error Analysis for Fourier Methods for Option Pricing
Hä ppö lä , Juho
2016-01-01
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE
Surface Fourier-transform lens using a metasurface
International Nuclear Information System (INIS)
Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun
2015-01-01
We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)
Fourier-Based Transmit Beampattern Design Using MIMO Radar
Lipor, John; Ahmed, Sajid; Alouini, Mohamed-Slim
2014-01-01
a constant-envelope or drawing from a finite alphabet. In this paper, a closed-form method to design for a uniform linear array is proposed that utilizes the discrete Fourier transform (DFT) coefficients and Toeplitz matrices. The resulting
The Fourier law in a momentum-conserving chain
Giardinà, C.; Kurchan, J.
2005-01-01
We introduce a family of models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases the Fourier law is verified in one dimension.
Innovative design method of automobile profile based on Fourier descriptor
Gao, Shuyong; Fu, Chaoxing; Xia, Fan; Shen, Wei
2017-10-01
Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.
Fourier analysis in dynamic non periodic phenomena in nuclear medicine
International Nuclear Information System (INIS)
Constantinesco, A.; Lallot, C.
1984-01-01
The success of Fourier analysis in assessing cardiac function has led us to investigate other possible uses of this technique. We show that phase analysis applied to dynamic non periodic activity changes gives useful parametric functional images. The phase image is comparable to a transit time image, the amplitude image is comparable to the maximum variations of activity and the mean image corresponds to a normalized sum of images. Exemples of this powerful application of Fourier analysis are discussed [fr
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.
A New Nonlinear Unit Root Test with Fourier Function
Güriş, Burak
2017-01-01
Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an Exponential Smooth Threshold Autore...
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.
Self-Fourier functions and coherent laser combination
International Nuclear Information System (INIS)
Corcoran, C J; Pasch, K A
2004-01-01
The Gaussian and Comb functions are generally quoted as being the two basic functions that are their own Fourier transforms. In 1991, Caola presented a recipe for generating functions that are their own Fourier transforms by symmetrizing any transformable function and then adding its own Fourier transform to it. In this letter, we present a new method for generating a set of functions that are exactly their own Fourier transforms, and which have direct application to laser cavity design for a wide variety of applications. The generated set includes the Gaussian and Comb functions as special cases and forms a continuous bridge of functions between them. The new generating method uses the Gaussian and Comb functions as bases and does not rely on the Fourier operator itself. This self-Fourier function promises to be particularly useful in high-power laser design through coherent laser beam combination. Although these results are presented in a single dimension as with a linear array, the results are equally valid in two dimensions. (letter to the editor)
Li, Shu-Nan; Cao, Bing-Yang
2017-09-01
The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.
Rajačić, M M; Todorović, D J; Krneta Nikolić, J D; Janković, M M; Djurdjević, V S
2016-09-01
Air sample monitoring in Serbia, Belgrade started in the 1960s, while (7)Be activity in air and total (dry and wet) deposition has been monitored for the last 22 years by the Environment and Radiation Protection Department of the Institute for Nuclear Sciences, Vinca. Using this data collection, the changes of the (7)Be activity in the air and the total (wet and dry) deposition samples, as well as their correlation with meteorological parameters (temperature, pressure, cloudiness, sunshine duration, precipitation and humidity) that affect (7)Be concentration in the atmosphere, were mathematically described using the Fourier analysis. Fourier analysis confirmed the expected; the frequency with the largest intensity in the harmonic spectra of the (7)Be activity corresponds to a period of 1 year, the same as the largest intensity frequency in Fourier series of meteorological parameters. To analyze the quality of the results produced by the Fourier analysis, we compared the measured values of the parameters with the values calculated according to the Fourier series. Absolute deviations between measured and predicted mean monthly values are in range from 0.02 mBq/m(3) to 0.7 mBq/m(3) for (7)Be activity in air, and 0.01 Bq/m(2) and 0.6 Bq/m(2) for (7)Be activity in deposition samples. Relatively good agreement of measured and predicted results offers the possibility of prediction of the (7)Be activity. Copyright © 2016 Elsevier Ltd. All rights reserved.
National Aeronautics and Space Administration — Advanced Diagnostics and Prognostics Testbed (ADAPT) Project Lead: Scott Poll Subject Fault diagnosis in electrical power systems Description The Advanced...
Multichannel analyzer development in CAMAC
International Nuclear Information System (INIS)
Nagy, J.Z.; Zarandy, A.
1988-01-01
The data acquisition in TOKAMAK experiments some CAMAC modules have been developed. The modules are the following: 64 K analyzer memory, 32 K analyzer memory, 6-channel pulse peak analyzer memory which contains the 32 K analyzer memory and eight AD-converters
Evolution of adaptation mechanisms: Adaptation energy, stress, and oscillating death.
Gorban, Alexander N; Tyukina, Tatiana A; Smirnova, Elena V; Pokidysheva, Lyudmila I
2016-09-21
In 1938, Selye proposed the notion of adaptation energy and published 'Experimental evidence supporting the conception of adaptation energy.' Adaptation of an animal to different factors appears as the spending of one resource. Adaptation energy is a hypothetical extensive quantity spent for adaptation. This term causes much debate when one takes it literally, as a physical quantity, i.e. a sort of energy. The controversial points of view impede the systematic use of the notion of adaptation energy despite experimental evidence. Nevertheless, the response to many harmful factors often has general non-specific form and we suggest that the mechanisms of physiological adaptation admit a very general and nonspecific description. We aim to demonstrate that Selye׳s adaptation energy is the cornerstone of the top-down approach to modelling of non-specific adaptation processes. We analyze Selye׳s axioms of adaptation energy together with Goldstone׳s modifications and propose a series of models for interpretation of these axioms. Adaptation energy is considered as an internal coordinate on the 'dominant path' in the model of adaptation. The phenomena of 'oscillating death' and 'oscillating remission' are predicted on the base of the dynamical models of adaptation. Natural selection plays a key role in the evolution of mechanisms of physiological adaptation. We use the fitness optimization approach to study of the distribution of resources for neutralization of harmful factors, during adaptation to a multifactor environment, and analyze the optimal strategies for different systems of factors. Copyright © 2016 Elsevier Ltd. All rights reserved.
Botanical cotton trash mixed with lint reduces cotton’s marketability and appearance. During cotton harvesting, ginning, and processing, trash size reduction occurs, thus complicating its removal and identification. This trash causes problems by increasing ends down in yarn formation and thus proce...
Adaptive Spectral Doppler Estimation
DEFF Research Database (Denmark)
Gran, Fredrik; Jakobsson, Andreas; Jensen, Jørgen Arendt
2009-01-01
. The methods can also provide better quality of the estimated power spectral density (PSD) of the blood signal. Adaptive spectral estimation techniques are known to pro- vide good spectral resolution and contrast even when the ob- servation window is very short. The 2 adaptive techniques are tested......In this paper, 2 adaptive spectral estimation techniques are analyzed for spectral Doppler ultrasound. The purpose is to minimize the observation window needed to estimate the spectrogram to provide a better temporal resolution and gain more flexibility when designing the data acquisition sequence...... and compared with the averaged periodogram (Welch’s method). The blood power spectral capon (BPC) method is based on a standard minimum variance technique adapted to account for both averaging over slow-time and depth. The blood amplitude and phase estimation technique (BAPES) is based on finding a set...
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.
DEFF Research Database (Denmark)
Møller Larsen, Marcus; Lyngsie, Jacob
2017-01-01
We investigate the connection between contract duration, relational mechanisms, and premature relationship termination. Based on an analysis of a large sample of exchange relationships in the global service-provider industry, we argue that investments in either longer contract duration or more in...... ambiguous reference points for adaption and thus increase the likelihood of premature termination by restricting the parties' set of adaptive actions....
Kinzig, Ann P.
2015-03-01
This paper is intended as a brief introduction to climate adaptation in a conference devoted otherwise to the physics of sustainable energy. Whereas mitigation involves measures to reduce the probability of a potential event, such as climate change, adaptation refers to actions that lessen the impact of climate change. Mitigation and adaptation differ in other ways as well. Adaptation does not necessarily have to be implemented immediately to be effective; it only needs to be in place before the threat arrives. Also, adaptation does not necessarily require global, coordinated action; many effective adaptation actions can be local. Some urban communities, because of land-use change and the urban heat-island effect, currently face changes similar to some expected under climate change, such as changes in water availability, heat-related morbidity, or changes in disease patterns. Concern over those impacts might motivate the implementation of measures that would also help in climate adaptation, despite skepticism among some policy makers about anthropogenic global warming. Studies of ancient civilizations in the southwestern US lends some insight into factors that may or may not be important to successful adaptation.
Chandramouli, Rajarathnam; Li, Grace; Memon, Nasir D.
2002-04-01
Steganalysis techniques attempt to differentiate between stego-objects and cover-objects. In recent work we developed an explicit analytic upper bound for the steganographic capacity of LSB based steganographic techniques for a given false probability of detection. In this paper we look at adaptive steganographic techniques. Adaptive steganographic techniques take explicit steps to escape detection. We explore different techniques that can be used to adapt message embedding to the image content or to a known steganalysis technique. We investigate the advantages of adaptive steganography within an analytical framework. We also give experimental results with a state-of-the-art steganalysis technique demonstrating that adaptive embedding results in a significant number of bits embedded without detection.
DEFF Research Database (Denmark)
Petersen, Kjell Yngve; Søndergaard, Karin; Kongshaug, Jesper
2015-01-01
the investigations of lighting scenarios carried out in two test installations: White Cube and White Box. The test installations are discussed as large-scale experiential instruments. In these test installations we examine what could potentially occur when light using LED technology is integrated and distributed......Adaptive Lighting Adaptive lighting is based on a partial automation of the possibilities to adjust the colour tone and brightness levels of light in order to adapt to people’s needs and desires. IT support is key to the technical developments that afford adaptive control systems. The possibilities...... differently into an architectural body. We also examine what might occur when light is dynamic and able to change colour, intensity and direction, and when it is adaptive and can be brought into interaction with its surroundings. In short, what happens to an architectural space when artificial lighting ceases...
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.
Fast Fourier single-pixel imaging via binary illumination.
Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang
2017-09-20
Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.
Ballooning modes or Fourier modes in a toroidal plasma?
International Nuclear Information System (INIS)
Connor, J.W.; Taylor, J.B.
1987-01-01
The relationship between two different descriptions of eigenmodes in a torus is investigated. In one the eigenmodes are similar to Fourier modes in a cylinder and are highly localized near a particular rational surface. In the other they are the so-called ballooning modes that extend over many rational surfaces. Using a model that represents both drift waves and resistive interchanges the transition from one of these structures to the other is investigated. In this simplified model the transition depends on a single parameter which embodies the competition between toroidal coupling of Fourier modes (which enhances ballooning) and variation in frequency of Fourier modes from one rational surface to another (which diminishes ballooning). As the coupling is increased each Fourier mode acquires a sideband on an adjacent rational surface and these sidebands then expand across the radius to form the extended mode described by the conventional ballooning mode approximation. This analysis shows that the ballooning approximation is appropriate for drift waves in a tokamak but not for resistive interchanges in a pinch. In the latter the conventional ballooning effect is negligible but they may nevertheless show a ballooning feature. This is localized near the same rational surface as the primary Fourier mode and so does not lead to a radially extended structure
Screening retinal transplants with Fourier-domain OCT
Rao, Bin
2009-02-01
Transplant technologies have been studied for the recovery of vision loss from retinitis pigmentosa (RP) and age-related macular degeneration (AMD). In several rodent retinal degeneration models and in patients, retinal progenitor cells transplanted as layers to the subretinal space have been shown to restore or preserve vision. The methods for evaluation of transplants are expensive considering the large amount of animals. Alternatively, time-domain Stratus OCT was previously shown to be able to image the morphological structure of transplants to some extent, but could not clearly identify laminated transplants. The efficacy of screening retinal transplants with Fourier-domain OCT was studied on 37 S334ter line 3 rats with retinal degeneration 6-67 days after transplant surgery. The transplants were morphologically categorized as no transplant, detachment, rosettes, small laminated area and larger laminated area with both Fourier-domain OCT and histology. The efficacy of Fourier-domain OCT in screening retinal transplants was evaluated by comparing the categorization results with OCT and histology. Additionally, 4 rats were randomly selected for multiple OCT examinations (1, 5, 9, 14 and 21days post surgery) in order to determine the earliest image time of OCT examination since the transplanted tissue may need some time to show its tendency of growing. Finally, we demonstrated the efficacy of Fourier-domain OCT in screening retinal transplants in early stages and determined the earliest imaging time for OCT. Fourier-domain OCT makes itself valuable in saving resource spent on animals with unsuccessful transplants.
A tandem parallel plate analyzer
International Nuclear Information System (INIS)
Hamada, Y.; Fujisawa, A.; Iguchi, H.; Nishizawa, A.; Kawasumi, Y.
1996-11-01
By a new modification of a parallel plate analyzer the second-order focus is obtained in an arbitrary injection angle. This kind of an analyzer with a small injection angle will have an advantage of small operational voltage, compared to the Proca and Green analyzer where the injection angle is 30 degrees. Thus, the newly proposed analyzer will be very useful for the precise energy measurement of high energy particles in MeV range. (author)
Analysis of the physical simulation on Fourier transform infrared spectrometer
Yue, Peng-yuan; Wan, Yu-xi; Zhao, Zhen
2017-10-01
A kind of oscillating arm type Fourier Transform Infrared Spectrometer (FTS) which based on the corner cube retroreflector is presented, and its principle and properties are studied. It consists of a pair of corner cube retroreflector, beam splitter and compensator. The optical path difference(OPD) is created by oscillating reciprocating motion of the moving corner cube pair, and the OPD value is four times the physical shift value of the moving corner cube pair. Due to the basic property of corner cube retroreflector, the oscillating arm type FTS has no tilt problems. It is almost ideal for very high resolution infrared spectrometer. However, there are some factors to reduce the FTS capability. First, wavefront aberration due to the figures of these surfaces will reduce modulation of FTS system; second, corner cube retroreflector consist of three plane mirror, and orthogonal to each other. When there is a deviation from right angle, it will reduced the modulation of system; third, the apexes of corner cube retroreflector are symmetric about the surface of beam splitter, if one or both of the corner cube retroreflector is displaced laterally from its nominal position, phase of off-axis rays returning from the two arms were difference, this also contributes to loss of modulation of system. In order to solve these problems, this paper sets up a non-sequential interference model, and a small amount of oscillating arm rotation is set to realize the dynamic simulation process, the dynamic interference energy data were acquired at different times, and calculated the modulation of the FTS system. In the simulation, the influence of wedge error of beam splitter, compensator or between them were discussed; effects of oscillating arm shaft deviation from the coplanar of beam splitter was analyzed; and compensation effect of corner cube retroreflector alignment on beam splitter, oscillating arm rotary shaft alignment error is analyzed. In addition, the adjustment procedure
International Nuclear Information System (INIS)
Niehaus, T A; Lopez, R; Rico, J F
2008-01-01
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be numerically stable for a wide range of geometrical parameters and momenta. Details of the implementation are presented together with benchmark data for representative integrals. We also discuss the assets and drawbacks of alternative algorithms available and analyze the numerical efficiency of the new scheme
Modeling laser-driven electron acceleration using WARP with Fourier decomposition
Energy Technology Data Exchange (ETDEWEB)
Lee, P., E-mail: patrick.lee@u-psud.fr [LPGP, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France); Audet, T.L. [LPGP, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France); Lehe, R.; Vay, J.-L. [Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Maynard, G.; Cros, B. [LPGP, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)
2016-09-01
WARP is used with the recent implementation of the Fourier decomposition algorithm to model laser-driven electron acceleration in plasmas. Simulations were carried out to analyze the experimental results obtained on ionization-induced injection in a gas cell. The simulated results are in good agreement with the experimental ones, confirming the ability of the code to take into account the physics of electron injection and reduce calculation time. We present a detailed analysis of the laser propagation, the plasma wave generation and the electron beam dynamics.
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.
Liu, Zhengjun; Chen, Hang; Blondel, Walter; Shen, Zhenmin; Liu, Shutian
2018-06-01
A novel image encryption method is proposed by using the expanded fractional Fourier transform, which is implemented with a pair of lenses. Here the centers of two lenses are separated at the cross section of axis in optical system. The encryption system is addressed with Fresnel diffraction and phase modulation for the calculation of information transmission. The iterative process with the transform unit is utilized for hiding secret image. The structure parameters of a battery of lenses can be used for additional keys. The performance of encryption method is analyzed theoretically and digitally. The results show that the security of this algorithm is enhanced markedly by the added keys.
Frost heave modelling of buried pipelines using non-linear Fourier finite elements
International Nuclear Information System (INIS)
Wan, R. G.; You, R.
1998-01-01
Numerical analysis of the response of a three-dimensional soil-pipeline system in a freezing environment using non-linear Fourier finite elements was described as an illustration of the effectiveness of this technique in analyzing plasticity problems. Plastic deformations occur when buried pipeline is under the action of non-uniform frost heave. The three-dimensional frost heave which develops over time including elastoplastic deformations of the soil and pipe are computed. The soil heave profile obtained in the numerical analysis was consistent with experimental findings for similar configurations. 8 refs., 8 figs
Fourier imaging of non-linear structure formation
International Nuclear Information System (INIS)
Brandbyge, Jacob; Hannestad, Steen
2017-01-01
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
Fourier imaging of non-linear structure formation
Energy Technology Data Exchange (ETDEWEB)
Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)
2017-04-01
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.
Fourier domain asymmetric cryptosystem for privacy protected multimodal biometric security
Choudhury, Debesh
2016-04-01
We propose a Fourier domain asymmetric cryptosystem for multimodal biometric security. One modality of biometrics (such as face) is used as the plaintext, which is encrypted by another modality of biometrics (such as fingerprint). A private key is synthesized from the encrypted biometric signature by complex spatial Fourier processing. The encrypted biometric signature is further encrypted by other biometric modalities, and the corresponding private keys are synthesized. The resulting biometric signature is privacy protected since the encryption keys are provided by the human, and hence those are private keys. Moreover, the decryption keys are synthesized using those private encryption keys. The encrypted signatures are decrypted using the synthesized private keys and inverse complex spatial Fourier processing. Computer simulations demonstrate the feasibility of the technique proposed.
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
The Fourier U(2 Group and Separation of Discrete Variables
Directory of Open Access Journals (Sweden)
Kurt Bernardo Wolf
2011-06-01
Full Text Available The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R, whose maximal compact subgroup is the Fourier group U(2_F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4. Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle coordinates, thus realizing one case of separation in two discrete coordinates. The N^2-vectors in this space are digital (pixellated images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.
Some applications of Fourier's great discovery for beginners
International Nuclear Information System (INIS)
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency ω = 2π/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students should be familiar with this subject. A suitable device for demonstrating spectra of electrical signals is a digital storage oscilloscope. Spectra of various waveforms and of AM and FM signals are demonstrated, as well as AM signals from a broadcasting station. Changes in the signals filtered by frequency-selective circuits are seen by comparing the spectra of the input and output voltages. All the experiments are suitable for undergraduate laboratories and usable as classroom demonstrations. (paper)
On the Alignment of Shapes Represented by Fourier Descriptors
DEFF Research Database (Denmark)
Sjöstrand, Karl; Ericsson, Anders; Larsen, Rasmus
2006-01-01
The representation of shapes by Fourier descriptors is a time-honored technique that has received relatively little attention lately. Nevertheless, it has many benefits and is applicable for describing a range of medical structures in two dimensions. Delineations in medical applications often...... consist of continuous outlines of structures, where no information of correspondence between samples exist. In this article, we discuss an alignment method that works directly with the functional representation of Fourier descriptors, and that is optimal in a least-squares sense. With corresponding...... represented by common landmarks can be constructed in an automatic fashion. If the aligned Fourier descriptors are inverse transformed from the frequency domain to the spatial domain, a set of roughly aligned landmarks are obtained. The positions of these are then adjusted along the contour of the objects...
International conference Fourier Analysis and Pseudo-Differential Operators
Turunen, Ville; Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations
2014-01-01
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. This collection of 20 refereed articles is based on selected talks given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
Fourier analysis of the parametric resonance in neutrino oscillations
International Nuclear Information System (INIS)
Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe
2009-01-01
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.
Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.
Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda
2017-09-13
This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.
International Development Research Centre (IDRC) Digital Library (Canada)
Addressing Climate Change Adaptation in Africa through Participatory Action Research. A Regional Observatory ... while the average annual rainfall recorded between. 1968 and 1999 was .... the region of Thies. For sustainability reasons, the.
International Development Research Centre (IDRC) Digital Library (Canada)
By Reg'
adaptation to climate change from various regions of the Sahel. Their .... This simple system, whose cost and maintenance were financially sustainable, brought ... method that enables him to learn from experience and save time, which he ...
Directory of Open Access Journals (Sweden)
Yezid Torres Moreno
2007-06-01
Full Text Available La naturaleza periódica de las imágenes de tejido textil permite el uso de las técnicas de la transformación de Fourier rápida para su clasificación. Debido a los patrones de repetición dentro de las imágenes del tejido textil, es posible encontrar una forma relativamente fácil de descripción para su densidad espectral de energía. Un trabajo previamente publicado permite mostrar el uso de descriptores para el espectro de Fourier de las imágenes, en particular su eficiencia a la invarianza a la rotación, traslación y cambio de escala [1].Dichos descriptores mostraron ser muy efectivos para representar un tejido textil y pueden ser utilizados para caracterizar texturas cuasi¿periódicas mediante técnicas no destructivas en tiempo real e in situ. Muestras de texturas textiles son evaluadas con esta técnica de representación paramétrica con el propósito de analizar su robustez y reproducibilidad. Finalmente, un conjunto de tejidos textiles es sometido a este modelo con el objetivo de evaluar la posibilidad de utilizarlo para la clasificación, verificación y reconocimiento de formas.The periodic nature of the fabric images allows using fast Fourier transform techniques in image processing for its characterization. Due to the repetition of patterns inside the images of textile, is possible to ﬁnd a form relatively easy of description in their energy spectrum. A recent work outlines a group of geometric descriptors for the Fourier spectrum of the images; looking for this eﬃciency to rotation, translation and scale change invariance [1]. These descriptors showed to be very eﬀective to represent a textile fabric and can be used to characterize the quasi periodic textures in real time and in situ non destructive techniques. Samples of textile textures are tested to this technique of parametric representation with the purpose of analyzing their robustness and reproducibility. Finally, a set of textile fabrics is subjected to
Application of Fourier analysis to multispectral/spatial recognition
Hornung, R. J.; Smith, J. A.
1973-01-01
One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.
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
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
Fourier Multipliers on Anisotropic Mixed-Norm Spaces of Distributions
DEFF Research Database (Denmark)
Cleanthous, Galatia; Georgiadis, Athanasios; Nielsen, Morten
2018-01-01
A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operat......A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity...
A Fourier Optical Model for the Laser Doppler Velocimeter
DEFF Research Database (Denmark)
Lading, Lars
1972-01-01
The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. ldquodifferential moderdquo and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions. The particles are represented...... filtering ability vanishes as the aperture size converges towards zero. The results based on fourier optics are compared with the rough estimates obtainable by using the "antenna formular" for heterodyning (ArΩr≈λ2)....
From Fourier Series to Rapidly Convergent Series for Zeta(3)
DEFF Research Database (Denmark)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions on this such ......The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions...
Connection between Fourier coefficient and Discretized Cartesian path integration
International Nuclear Information System (INIS)
Coalson, R.D.
1986-01-01
The relationship between so-called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier-like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on-diagonal statistical density matrix elements for a number of prototypical 1-d potentials. A consistent convergence order among these prescriptions is established
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Decay of the Fourier transform analytic and geometric aspects
Iosevich, Alex
2014-01-01
The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
Dong, Rong; Long, Jinhua; Xu, Xiaoli; Zhang, Chunlin; Wen, Zongyao; Li, Long; Yao, Weijuan; Zeng, Zhu
2014-01-10
Dendritic cells are potent and specialized antigen presenting cells, which play a crucial role in initiating and amplifying both the innate and adaptive immune responses. The dendritic cell-based vaccination against cancer has been clinically achieved promising successes. But there are still many challenges in its clinical application, especially for how to identify the functional states. The CD14+ monocytes were isolated from human peripheral blood after plastic adherence and purified to approximately 98% with cocktail immunomagnetic beads. The immature dendritic cells and mature dendritic cells were induced by traditional protocols. The resulting dendritic cells were cocultured with normal cells and cancer cells. The functional state of dendritic cells including immature dendritic cells (imDCs) and mature dendritic cells (mDCs) under different conditioned microenvironments were investigated by Fourier transformed infrared spectroscopy (FTIR) and molecular biological methods. The results of Fourier transformed infrared spectroscopy showed that the gene transcription activity and energy states of dendritic cells were specifically suppressed by tumor cells (P Fourier transformed infrared spectroscopy at given wave numbers were closely correlated with the expression levels of NF-κB (R2:0.69 and R2:0.81, respectively). Our results confirmed that the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were positively correlated with the expression levels of NF-κB, suggesting that Fourier transformed infrared spectroscopy technology could be clinically applied to identify the functional states of dendritic cell when performing dendritic cell-based vaccination. It's significant for the simplification and standardization of dendritic cell-based vaccination clinical preparation protocols.
Directory of Open Access Journals (Sweden)
Yubo Wang
2017-06-01
Full Text Available It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC. In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976 ratio and outperforms existing methods such as short-time Fourier transfrom (STFT, continuous Wavelet transform (CWT and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Wang, Yubo; Veluvolu, Kalyana C
2017-06-14
It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval
Smith, Jeffrey Scott
2006-01-01
Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.
Directory of Open Access Journals (Sweden)
S. R. M. Tabugo-Rico
2017-12-01
Full Text Available Seahorses inhabit various ecosystems hence, had become a flagship species of the marine environment. The Philippines as a hot spot of biodiversity in Asia holds a number of species of seahorses. This serve as an exploratory study to describe body shape variation of selected common seahorse species: Hippocampus comes, Hippocampus histrix, Hippocampus spinosissimus and Hippocampus kuda from Danajon bank using Elliptic Fourier Analysis. The method was done to test whether significant yet subtle differences in body shape variation can be species-specific, habitat-influenced and provide evidence of sexual dimorphism. It is hypothesized that phenotypic divergence may provide evidence for genetic differentiation or mere adaptations to habitat variation. Results show significant considerable differences in the body shapes of the five populations based on the canonical variate analysis (CVA and multivariate analysis of variance (MANOVA with significant p values. Populations were found to be distinct from each other suggesting that body shape variation is species-specific, habitat-influenced and provided evidence for sexual dimorphism. Results of discriminant analysis show further support for species specific traits and sexual dimorphism. This study shows the application of the method of geometric morphometrics specifically elliptic fourier analysis in describing subtle body shape variation of selected Hippocampus species.
Digital Multi Channel Analyzer Enhancement
International Nuclear Information System (INIS)
Gonen, E.; Marcus, E.; Wengrowicz, U.; Beck, A.; Nir, J.; Sheinfeld, M.; Broide, A.; Tirosh, D.
2002-01-01
A cement analyzing system based on radiation spectroscopy had been developed [1], using novel digital approach for real-time, high-throughput and low-cost Multi Channel Analyzer. The performance of the developed system had a severe problem: the resulted spectrum suffered from lack of smoothness, it was very noisy and full of spikes and surges, therefore it was impossible to use this spectrum for analyzing the cement substance. This paper describes the work carried out to improve the system performance
PM 3655 PHILIPS Logic analyzer
A logic analyzer is an electronic instrument that captures and displays multiple signals from a digital system or digital circuit. A logic analyzer may convert the captured data into timing diagrams, protocol decodes, state machine traces, assembly language, or may correlate assembly with source-level software. Logic Analyzers have advanced triggering capabilities, and are useful when a user needs to see the timing relationships between many signals in a digital system.
Is adaptation. Truly an adaptation? Is adaptation. Truly an adaptation?
Directory of Open Access Journals (Sweden)
Thais Flores Nogueira Diniz
2008-04-01
Full Text Available The article begins by historicizing film adaptation from the arrival of cinema, pointing out the many theoretical approaches under which the process has been seen: from the concept of “the same story told in a different medium” to a comprehensible definition such as “the process through which works can be transformed, forming an intersection of textual surfaces, quotations, conflations and inversions of other texts”. To illustrate this new concept, the article discusses Spike Jonze’s film Adaptation. according to James Naremore’s proposal which considers the study of adaptation as part of a general theory of repetition, joined with the study of recycling, remaking, and every form of retelling. The film deals with the attempt by the scriptwriter Charles Kaufman, cast by Nicholas Cage, to adapt/translate a non-fictional book to the cinema, but ends up with a kind of film which is by no means what it intended to be: a film of action in the model of Hollywood productions. During the process of creation, Charles and his twin brother, Donald, undergo a series of adventures involving some real persons from the world of film, the author and the protagonist of the book, all of them turning into fictional characters in the film. In the film, adaptation then signifies something different from itstraditional meaning. The article begins by historicizing film adaptation from the arrival of cinema, pointing out the many theoretical approaches under which the process has been seen: from the concept of “the same story told in a different medium” to a comprehensible definition such as “the process through which works can be transformed, forming an intersection of textual surfaces, quotations, conflations and inversions of other texts”. To illustrate this new concept, the article discusses Spike Jonze’s film Adaptation. according to James Naremore’s proposal which considers the study of adaptation as part of a general theory of repetition
Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua
2016-07-01
On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.
Environmental applications of the centrifugal fast analyzer
International Nuclear Information System (INIS)
Goldstein, G.; Strain, J.E.; Bowling, J.L.
1975-12-01
The centrifugal fast analyzer (GeMSAEC Fast Analyzer) was applied to the analysis of pollutants in air and water. Since data acquisition and processing are computer controlled, considerable effort went into devising appropriate software. A modified version of the standard FOCAL interpreter was developed which includes special machine language functions for data timing, acquisition, and storage, and also permits chaining together of programs stored on a disk. Programs were written and experimental procedures developed to implement spectrophotometric, turbidimetric, kinetic (including initial-rate, fixed-time, and variable-time techniques), and chemiluminescence methods of analysis. Analytical methods were developed for the following elements and compounds: SO 2 , O 3 , Ca, Cr, Cu, Fe, Mg, Se(IV), Zn, Cl - , I - , NO 2 - , PO 4 -3 , S -2 , and SO 4 -2 . In many cases, standard methods could be adapted to the centrifugal analyzer, in others new methods were employed. In general, analyses performed with the centrifugal fast analyzer were faster, more precise, and more accurate than with conventional instrumentation
Symmetries of the second-difference matrix and the finite Fourier transform
International Nuclear Information System (INIS)
Aguilar, A.; Wolf, K.B.
1979-01-01
The finite Fourier transformation is well known to diagonalize the second-difference matrix and has been thus applied extensively to describe finite crystal lattices and electric networks. In setting out to find all transformations having this property, we obtain a multiparameter class of them. While permutations and unitary scaling of the eigenvectors constitute the trivial freedom of choice common to all diagonalization processes, the second-difference matrix has a larger symmetry group among whose elements we find the dihedral manifest symmetry transformations of the lattice. The latter are nevertheless sufficient for the unique specification of eigenvectors in various symmetry-adapted bases for the constrained lattice. The free symmetry parameters are shown to lead to a complete set of conserved quantities for the physical lattice motion. (author)
Online Distributed Learning Over Networks in RKH Spaces Using Random Fourier Features
Bouboulis, Pantelis; Chouvardas, Symeon; Theodoridis, Sergios
2018-04-01
We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number of parameters as time iterations evolve. Besides complexity, this leads to an increased need of communication resources, in a distributed setting. In contrast, the proposed method approximates the solution as a fixed-size vector (of larger dimension than the input space) using Random Fourier Features. This paves the way to use standard linear combine-then-adapt techniques. To the best of our knowledge, this is the first time that a complete protocol for distributed online learning in RKHS is presented. Conditions for asymptotic convergence and boundness of the networkwise regret are also provided. The simulated tests illustrate the performance of the proposed scheme.
Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics
Wu, Yinghua; Herman, Michael F.; Batista, Victor S.
2005-03-01
A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuit/split-operator Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MP/SOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.
Thyroid lesions diagnosis by Fourier transformed infrared absorption spectroscopy (FTIR)
International Nuclear Information System (INIS)
Albero, Felipe Guimaraes
2009-01-01
Thyroid nodules are a common disorder, with 4-7% of incidence in the Brazilian population. Although the fine needle aspiration (FNA) is an accurate method for thyroid tumors diagnosis, the discrimination between benign and malignant neoplasm is currently not possible in some cases with high incidence of false negative diagnosis, leading to a surgical intervention due to the risk of carcinomas. The aim of this study was to verify if the Fourier Transform infrared spectroscopy (FTIR) can contribute to the diagnosis of thyroid carcinomas and goiters, using samples of tissue and aspirates. Samples of FNA, homogenates and tissues of thyroid nodules with histopathological diagnosis were obtained and prepared for FTIR spectroscopy analysis. The FNA and homogenates samples were measured by μ-FTIR (between 950 . 1750 cm -1 ), at a nominal resolution of 4 cm -1 and 120 scans). Tissue samples were analyzed directly by ATR-FTIR technique, at a resolution 2 cm -1 , with 60 scans in the same region. All spectra were corrected by the baseline and normalized by amides area (1550-1640 cm -1 ) in order to minimize variations of sample homogeneity. Then, spectra were converted into second derivatives using the Savitzk-Golay algorithm with a 13 points window. The Ward's minimum variance algorithm and Euclidean distances among the points were used for cluster analysis. Some FNA samples showed complex spectral pattern. All samples showed some cell pellets and large amount of hormone, represented by the bands of 1545 and 1655 cm -1 . Bands in 1409, 1412, 1414, 1578 and 1579 cm -1 were also found, indicating possible presence of sugar, DNA, citric acid or metabolic products. In this study, it was obtained an excellent separation between goiter and malign lesion for the samples of tissues, with 100% of specificity in specific cluster and 67% sensibility and 50 of specificity. In homogenate and FNA samples this sensibility and specificity were lower, because among these samples, it were
Multichannel analyzer type CMA-3
International Nuclear Information System (INIS)
Czermak, A.; Jablonski, J.; Ostrowicz, A.
1978-01-01
Multichannel analyzer CMA-3 is designed for two-parametric analysis with operator controlled logical windows. It is implemented in CAMAC standard. A single crate contains all required modules and is controlled by the PDP-11/10 minicomputer. Configuration of CMA-3 is shown. CMA-3 is the next version of the multichannel analyzer described in report No 958/E-8. (author)
Gajam, Niharika
2016-01-01
Traditionally analyzing data happens via batch-processing and interactive work on the terminal. The project aims to provide another way of analyzing data files: A cloud-based approach. It aims to make it a productive and interactive environment through the combination of FCC and SWAN software.
Transformation of a Free-Wilson matrix into Fourier coefficients
Czech Academy of Sciences Publication Activity Database
Holík, M.; Halámek, Josef
2002-01-01
Roč. 20, - (2002), s. 422 - 428 ISSN 0931-8771 Institutional research plan: CEZ:AV0Z2065902 Keywords : Free-Wilson matrix * Fourier transform * multivariate regression Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.558, year: 2002
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit ...
Application of Migration Velocity Using Fourier Transform Approach ...
African Journals Online (AJOL)
Application of velocity by Fourier transform to process 3-D unmigrated seismic sections has been carried out in Fabi Field, Niger Delta – Nigeria. Usually, all seismic events (sections) are characterized by spikes or noise (random or coherent), multiples and shear waves so that when a seismic bed is dipping, the apparent ...
Fourier-transform infrared spectroscopic studies of dithia ...
Indian Academy of Sciences (India)
Unknown
limited region 1000–1150 cm–1.10 Therefore, in the present paper we report and analyse Fourier-trans- form infrared (FT-IR) spectra of S2TPP and its chemically prepared cation. 2. Experimental. Dithia tetraphenyl porphyrine was received from. Professor A L Verma as a gift and used without fur- ther purification. However ...
Properties of the Simpson discrete fourier transform | Singh ...
African Journals Online (AJOL)
The Simpson discrete Fourier transform (SDFT) and its inverse are transformations relating the time and frequency domains. In this paper we state and prove the important properties of shift, circular convolution, conjugation, time reversal and Plancherel's theorem. In addition, we provide an alternative representation of the ...
Fourier transformation methods in the field of gamma spectrometry
Indian Academy of Sciences (India)
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.
A new analytical solution to the diffusion problem: Fourier series ...
African Journals Online (AJOL)
This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.
Embedding relations connected with strong approximation of Fourier ...
Indian Academy of Sciences (India)
ing only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl. 11(4) (2008) 749–756] which is a generalization of Tikhonov's results [Anal. Math. 31 (2005) 183–194]. We also ...
Fourier transform infrared spectrophotometry and X-ray powder ...
African Journals Online (AJOL)
This study aimed at demonstrating complementary roles offered by both Fourier transform infrared (FTIR) spectrophotometry and x-ray powder diffraction (XRPD) techniques in characterizing clay size fraction of kaolins. The clay size fraction of kaolin samples obtained from Kgwakgwe, Makoro, Lobatse and Serule kaolin ...
Multipliers for the Absolute Euler Summability of Fourier Series
Indian Academy of Sciences (India)
In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with multipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.
Novel properties of the Fourier decomposition of the sinogram
International Nuclear Information System (INIS)
Edholm, P.R.; Lewitt, R.M.; Lindholm, B.
1986-01-01
The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency ω (continuous) and angular harmonic number n (discrete). For absolute value of ω large, the Fourier coefficients on the line n=kω of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed
Fourier transform distribution function of relaxation times; application and limitations
Boukamp, Bernard A.
2015-01-01
A simple Fourier transform (FT) method is presented for obtaining a Distribution Function of Relaxation Times (DFRT) for electrochemical impedance spectroscopy (EIS) data. By using a special data extension procedure the FT is performed over the range from -∞ ≤ lnω ≤ + ∞. The integration procedure is
Beschrijving van een computerprogramma voor Fourier-analyse
Sannes, A.jr.
1975-01-01
During my practical work at the NIOZ Texel, from May until August 1974, I have been engaged with the Fourier- transformation. The direct motive was the problem of a guest-investigator who studied the regularity in the frequency of pulsations of the hearts of guillemots. A computerprogram that can
Power filtering of nth order in the fractional Fourier domain
International Nuclear Information System (INIS)
Alieva, Tatiana; Calvo, Maria Luisa; Bastiaans, Martin J.
2002-01-01
The main properties of the power filtering operation in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of linear power filtering for solving the phase retrieval problem from intensity distributions only is proposed. The optical configuration for the experimental realization of the method is discussed. (author)
Discrete frequency identification using the HP 5451B Fourier analyser
International Nuclear Information System (INIS)
Holland, L.; Barry, P.
1977-01-01
The frequency analysis by the HP5451B discrete frequency Fourier analyser is studied. The advantages of cross correlation analysis to identify discrete frequencies in a background noise are discussed in conjuction with the elimination of aliasing and wraparound error. Discrete frequency identification is illustrated by a series of graphs giving the results of analysing 'electrical' and 'acoustical' white noise and sinusoidal signals [pt
Prototypes and matrix relevance learning in complex fourier space
Straat, M.; Kaden, M.; Gay, M.; Villmann, T.; Lampe, Alexander; Seiffert, U.; Biehl, M.; Melchert, F.
2017-01-01
In this contribution, we consider the classification of time-series and similar functional data which can be represented in complex Fourier coefficient space. We apply versions of Learning Vector Quantization (LVQ) which are suitable for complex-valued data, based on the so-called Wirtinger
An introduction to non-harmonic Fourier series
Young, Robert M
2001-01-01
An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.
Fourier coefficientes computation in two variables, a distributional version
Directory of Open Access Journals (Sweden)
Carlos Manuel Ulate R.
2015-01-01
Full Text Available The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.
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
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.
The RC Circuit: An Approach with Fourier Transforms
Indian Academy of Sciences (India)
The RC Circuit: An Approach with Fourier Transforms. Classroom Volume 21 Issue 11 November 2016 pp 1029-1042 ... 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 ...
Fourier transform infrared (FTIR) spectroscopy for identification of ...
African Journals Online (AJOL)
Fourier transform infrared (FTIR) spectroscopy was used in this study to identify and determine spectral features of Chlorella vulgaris Beijerinck 1890 and Scenedesmus obliquus (Turpin) Kützing 1833. Two cultures were grown in a chemically-defined media under photoautotrophic culture conditions isolated from eutrophic ...
Testing a Fourier Accelerated Hybrid Monte Carlo Algorithm
Catterall, S.; Karamov, S.
2001-01-01
We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for dynamical fermion simulations of non-gauge models. We test the algorithm in supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice field theory. We find dramatic reductions in the autocorrelation time of the algorithm in comparison to standard HMC.
Critical points of multidimensional random Fourier series: variance estimates
Nicolaescu, Liviu I.
2013-01-01
To any positive number $\\varepsilon$ and any nonnegative even Schwartz function $w:\\mathbb{R}\\to\\mathbb{R}$ we associate the random function $u^\\varepsilon$ on the $m$-torus $T^m_\\varepsilon:=\\mathbb{R}^m/(\\varepsilon^{-1}\\mathbb{Z})^m$ defined as the real part of the random Fourier series $$ \\sum_{\
Closed contour fractal dimension estimation by the Fourier transform
International Nuclear Information System (INIS)
Florindo, J.B.; Bruno, O.M.
2011-01-01
Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.
HEART ABNORMALITY CLASSIFICATIONS USING FOURIER TRANSFORMS METHOD AND NEURAL NETWORKS
Directory of Open Access Journals (Sweden)
Endah Purwanti
2014-05-01
Full Text Available Health problems with cardiovascular system disorder are still ranked high globally. One way to detect abnormalities in the cardiovascular system especially in the heart is through the electrocardiogram (ECG reading. However, reading ECG recording needs experience and expertise, software-based neural networks has designed to help identify any abnormalities ofthe heart through electrocardiogram digital image. This image is processed using image processing methods to obtain ordinate chart which representing the heart’s electrical potential. Feature extraction using Fourier transforms which are divided into several numbers of coefficients. As the software input, Fourier transforms coefficient have been normalized. Output of this software is divided into three classes, namely heart with atrial fibrillation, coronary heart disease and normal. Maximum accuracy rate ofthis software is 95.45%, with the distribution of the Fourier transform coefficients 1/8 and number of nodes 5, while minimum accuracy rate of this software at least 68.18% by distribution of the Fourier transform coefficients 1/32 and the number of nodes 32. Overall result accuracy rate of this software has an average of86.05% and standard deviation of7.82.
Fourier coefficientes computation in two variables, a distributional version
Carlos Manuel Ulate R.
2015-01-01
The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.
Closed form fourier-based transmit beamforming for MIMO radar
Lipor, John J.; Ahmed, Sajid; Alouini, Mohamed-Slim
2014-01-01
-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform
Free Sixteen Harmonic Fourier Series Web App with Sound
Ruiz, Michael J.
2018-01-01
An online HTML5 Fourier synthesizer app is provided that allows students to manipulate sixteen harmonics and construct periodic waves. Students can set the amplitudes and phases for each harmonic, seeing the resulting waveforms and hearing the sounds. Five waveform presets are included: sine, triangle, square, ramp (sawtooth), and pulse train. The…
The linogram algorithm and direct fourier method with linograms
International Nuclear Information System (INIS)
Edholm, P.R.
1990-01-01
This text is an attempt to describe the linogram algorithm based on a somewhat simplified mathematical description of the algorithm which is also more similar to the actual digital implementation. Another algorithm with linograms, which may be called a direct fourier method is also presented. (K.A.E.)
Fourier beamformation of multistatic synthetic aperture ultrasound imaging
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2015-01-01
A new Fourier beamformation (FB) algorithm is presented for multistatic synthetic aperture ultrasound imaging. It can reduce the number of computations by a factor of 20 compared to conventional Delay-and-Sum (DAS) beamformers. The concept is based on the wavenumber algorithm from radar and sonar...
Synthetic aperture ultrasound Fourier beamformation using virtual sources
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2016-01-01
An efficient Fourier beamformation algorithm is presented for multistatic synthetic aperture ultrasound imaging using virtual sources (FBV). The concept is based on the frequency domain wavenumber algorithm from radar and sonar and is extended to a multi-element transmit/receive configuration using...
Grating-assisted superresolution of slow waves in Fourier space
DEFF Research Database (Denmark)
Thomas, N. Le; Houdré, R.; Frandsen, Lars Hagedorn
2007-01-01
with a high numerical aperture Fourier space imaging set-up. A high-resolution spectroscopy of the far-field emission diagram allows us to accurately and efficiently determine the dispersion curve and the group-index dispersion of planar photonic waveguides operating in the slow light regime....
Nonlinear Fourier transform for dual-polarization optical communication system
DEFF Research Database (Denmark)
Gaiarin, Simone
communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...
Grid-Independent Compressive Imaging and Fourier Phase Retrieval
Liao, Wenjing
2013-01-01
This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem. Many situations in optics, medical imaging and signal processing call…
Education and Utopia: Robert Owen and Charles Fourier
Leopold, David
2011-01-01
The aims of education, and the appropriate means of realising them, are a recurring preoccupation of utopian authors. The utopian socialists Robert Owen (1771-1858) and Charles Fourier (1772-1837) both place human nature at the core of their educational views, and both see education as central to their wider objective of social and political…
Adaptive Matrices and Filters for Color Texture Classification
Giotis, Ioannis; Bunte, Kerstin; Petkov, Nicolai; Biehl, Michael
In this paper we introduce an integrative approach towards color texture classification and recognition using a supervised learning framework. Our approach is based on Generalized Learning Vector Quantization (GLVQ), extended by an adaptive distance measure, which is defined in the Fourier domain,
Accelerated radial Fourier-velocity encoding using compressed sensing
International Nuclear Information System (INIS)
Hilbert, Fabian; Han, Dietbert
2014-01-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Accelerated radial Fourier-velocity encoding using compressed sensing
Energy Technology Data Exchange (ETDEWEB)
Hilbert, Fabian; Han, Dietbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wech, Tobias; Koestler, Herbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wuerzburg Univ. (Germany). Comprehensive Heart Failure Center (CHFC)
2014-10-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Accelerated radial Fourier-velocity encoding using compressed sensing.
Hilbert, Fabian; Wech, Tobias; Hahn, Dietbert; Köstler, Herbert
2014-09-01
Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. We imaged the femoral artery of healthy volunteers with ECG-triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6-fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity distribution in vessels in the order of the voxel size. Thus
DEFF Research Database (Denmark)
Andersen, Torben Juul
2015-01-01
This article provides an overview of theoretical contributions that have influenced the discourse around strategic adaptation including contingency perspectives, strategic fit reasoning, decision structure, information processing, corporate entrepreneurship, and strategy process. The related...... concepts of strategic renewal, dynamic managerial capabilities, dynamic capabilities, and strategic response capabilities are discussed and contextualized against strategic responsiveness. The insights derived from this article are used to outline the contours of a dynamic process of strategic adaptation....... This model incorporates elements of central strategizing, autonomous entrepreneurial behavior, interactive information processing, and open communication systems that enhance the organization's ability to observe exogenous changes and respond effectively to them....