Digital Fourier analysis fundamentals

CERN Document Server

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...

Fourier analysis an introduction

CERN Document Server

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

An L1-norm phase constraint for half-Fourier compressed sensing in 3D MR imaging.

Science.gov (United States)

Li, Guobin; Hennig, Jürgen; Raithel, Esther; Büchert, Martin; Paul, Dominik; Korvink, Jan G; Zaitsev, Maxim

2015-10-01

In most half-Fourier imaging methods, explicit phase replacement is used. In combination with parallel imaging, or compressed sensing, half-Fourier reconstruction is usually performed in a separate step. The purpose of this paper is to report that integration of half-Fourier reconstruction into iterative reconstruction minimizes reconstruction errors. The L1-norm phase constraint for half-Fourier imaging proposed in this work is compared with the L2-norm variant of the same algorithm, with several typical half-Fourier reconstruction methods. Half-Fourier imaging with the proposed phase constraint can be seamlessly combined with parallel imaging and compressed sensing to achieve high acceleration factors. In simulations and in in-vivo experiments half-Fourier imaging with the proposed L1-norm phase constraint enables superior performance both reconstruction of image details and with regard to robustness against phase estimation errors. The performance and feasibility of half-Fourier imaging with the proposed L1-norm phase constraint is reported. Its seamless combination with parallel imaging and compressed sensing enables use of greater acceleration in 3D MR imaging.

Fourier phase analysis on equilibrium gated radionuclide ventriculography: range of phase spread and cut-off limits in normal individuals

International Nuclear Information System (INIS)

Ramaiah, Vijayaraghavan L.; Harish, B.; Sunil, H.V.; Selvakumar, Job; Ravi Kishore, A.G.; Nair, Gopinathan

2011-01-01

To define the range of phase spread on equilibrium gated radionuclide ventriculography (ERNV) in normal individuals and derive the cut-off limit for the parameters to detect cardiac dyssynchrony. ERNV was carried out in 30 individuals (age 53±23 years, 25 males and 5 females) who had no history of cardiovascular disease. They all had normal left ventricular ejection fraction (LVEF 55-70%) as determined by echocardiography, were in sinus rhythm, with normal QRS duration (≤120 msec) and normal coronary angiography. First harmonic phase analysis was performed on scintigraphic data acquired in best septal view. Left and right ventricular standard deviation (LVSD and RVSD, respectively) and interventricular mechanical delay (IVMD), the absolute difference of mean phase angles of right and left ventricle, were computed and expressed in milliseconds. Mean + 3 standard deviation (SD) was used to derive the cut-off limits. Average LVEF and duration of cardiac cycle in the study group were 62.5%±5.44% and 868.9±114.5 msec, respectively. The observations of LVSD, RVSD and right and left ventricular mean phase angles were shown to be normally distributed by Shapiro-Wilk test. Cut-off limits for LVSD, RVSD and IVMD were calculated to be 80 msec, 85 msec and 75 msec, respectively. Fourier phase analysis on ERNV is an effective tool for the evaluation of synchronicity of cardiac contraction. The cut-off limits of parameters of dyssynchrony can be used to separate heart failure patients with cardiac dyssynchrony from those without. ERNV can be used to select patients for cardiac resynchronization therapy. (author)

360-degrees profilometry using strip-light projection coupled to Fourier phase-demodulation.

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Servin, Manuel; Padilla, Moises; Garnica, Guillermo

2016-01-11

360 degrees (360°) digitalization of three dimensional (3D) solids using a projected light-strip is a well-established technique in academic and commercial profilometers. These profilometers project a light-strip over the digitizing solid while the solid is rotated a full revolution or 360-degrees. Then, a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based light-strip centroid estimation, we propose to use Fourier phase-demodulation for 360° solid digitalization. The advantage of Fourier demodulation over strip-centroid estimation is that the accuracy of phase-demodulation linearly-increases with the fringe density, while in strip-light the centroid-estimation errors are independent. Here we proposed first to construct a carrier-frequency fringe-pattern by closely adding the individual light-strip images recorded while the solid is being rotated. Next, this high-density fringe-pattern is phase-demodulated using the standard Fourier technique. To test the feasibility of this Fourier demodulation approach, we have digitized two solids with increasing topographic complexity: a Rubik's cube and a plastic model of a human-skull. According to our results, phase demodulation based on the Fourier technique is less noisy than triangulation based on centroid light-strip estimation. Moreover, Fourier demodulation also provides the amplitude of the analytic signal which is a valuable information for the visualization of surface details.

Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

International Nuclear Information System (INIS)

Miao, J.; Sayre, D.; Chapman, H.N.

1998-01-01

It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2x in each dimension (i.e., oversampling by 4x for 2D and 8x for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop. copyright 1998 Optical Society of America

Handbook of Fourier analysis & its applications

CERN Document Server

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

The Fourier decomposition method for nonlinear and non-stationary time series analysis.

Science.gov (United States)

Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik

2017-03-01

for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

Quantification of wall motion and phase of contraction in tomographic gated blood pool studies using length-based Fourier analysis

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Nakajima, Kenichi; Bunko, Hisashi; Taki, Junichi; Nambu, Ichiro; Shiire, Yasushi; Tonami, Norihisa; Hisada, Kinichi; Tada, Akira; Kojima, Kazuhkio

1985-03-01

Length-based Fourier analysis, a new method for quantification of wall motion and timing of contraction, was applied to tomographic gated blood pool study. Two parameters, percent-length shortening (%LS) and length-based phase were calculated based on the time-length curves from a center to ventricular edges, and compared with the count-based method. In mathematical models for tomographic gated blood pool images, the severity of asynergy was easily determined by length-based method, and the accuracy of the parameters was good. As to the setting of the center, fixed center provided more reliable parameters than the method using movable center, i.e., when a center of gravity was determined in each frame. By length-based Fourier analysis, quantification of wall motion was easily performed, and the initial inward movement caused by the accessory conduction pathway was assessed in patients with Wolff-Parkinson-White syndrome. Length-based approach was considered to be reasonable and effective because the movements of the ventricular edges are essential in tomographic gated blood pool images.

Quantification of wall motion and phase of contraction in tomographic gated blood pool studies using length-based Fourier analysis

International Nuclear Information System (INIS)

Nakajima, Kenichi; Bunko, Hisashi; Taki, Junichi; Nambu, Ichiro; Shiire, Yasushi; Tonami, Norihisa; Hisada, Kinichi; Tada, Akira; Kojima, Kazuhiko.

1985-01-01

Length-based Fourier analysis, a new method for quantification of wall motion and timing of contraction, was applied to tomographic gated blood pool study. Two parameters, percent-length shortening (%LS) and length-based phase were calculated based on the time-length curves from a center to ventricular edges, and compared with the count-based method. In mathematical models for tomographic gated blood pool images, the severity of asynergy was easily determined by length-based method, and the accuracy of the parameters was good. As to the setting of the center, fixed center provided more reliable parameters than the method using movable center, i.e., when a center of gravity was determined in each frame. By length-based Fourier analysis, quantification of wall motion was easily performed, and the initial inward movement caused by the accessory conduction pathway was assessed in patients with Wolff-Parkinson-White syndrome. Length-based approach was considered to be reasonable and effective because the movements of the ventricular edges are essential in tomographic gated blood pool images. (author)

Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry.

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Toto-Arellano, Noel-Ivan; Rodriguez-Zurita, Gustavo; Meneses-Fabian, Cruz; Vazquez-Castillo, Jose F

2008-11-10

Among several techniques, phase shifting interferometry can be implemented with a grating used as a beam divider to attain several interference patterns around each diffraction order. Because each pattern has to show a different phase-shift, a suitable shifting technique must be employed. Phase gratings are attractive to perform the former task due to their higher diffraction efficiencies. But as is very well known, the Fourier coefficients of only-phase gratings are integer order Bessel functions of the first kind. The values of these real-valued functions oscillate around zero, so they can adopt negative values, thereby introducing phase shifts of pi at certain diffraction orders. Because this almost trivial fact seems to have been overlooked in the literature regarding its practical implications, in this communication such phase shifts are stressed in the description of interference patterns obtained with grating interferometers. These patterns are obtained by placing two windows in the object plane of a 4f system with a sinusoidal grating/grid in the Fourier plane. It is shown that the corresponding experimental observations of the fringe modulation, as well as the corresponding phase measurements, are all in agreement with the proposed description. A one-shot phase shifting interferometer is finally proposed taking into account these properties after proper incorporation of modulation of polarization.

Classical Fourier analysis

CERN Document Server

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...

Grid-Independent Compressive Imaging and Fourier Phase Retrieval

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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…

Fundamental and clinical evaluation of Fourier analysis for the detection of regional wall contraction abnormalities in the patients with myocardial infarction

International Nuclear Information System (INIS)

Murata, H.; Toyama, H.; Tabuchi, H.; Muraki, T.; Ohtake, E.; Chiba, K.; Yamada, H.

1982-01-01

The purpose of the present study are to evaluate fundamentally the method of Fourier analysis and to detect regional wall motion abnormality of the infarcted lesions by Fourier analysis. Fourier analyses were performed using the data obtained by first pass method in right anterior oblique projection (RAO) and by equilibrium method in left anterior oblique projection (LAO), and amplitude and phase were calculated. Amplitude and phase values needed to be corrected by R-R interval. On the detection of myocardial infarction, Fourier analyses in RAO and in LAO had same value for anterior infarctions. The analysis in RAO was more sensitive to detect infero-posterior lesions. On the other hand, the analysis in LAO was more sensitive for septal and lateral lesions

Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding.

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Wang, Xiaogang; Chen, Wen; Chen, Xudong

2014-09-22

We present a novel image hiding method based on phase retrieval algorithm under the framework of nonlinear double random phase encoding in fractional Fourier domain. Two phase-only masks (POMs) are efficiently determined by using the phase retrieval algorithm, in which two cascaded phase-truncated fractional Fourier transforms (FrFTs) are involved. No undesired information disclosure, post-processing of the POMs or digital inverse computation appears in our proposed method. In order to achieve the reduction in key transmission, a modified image hiding method based on the modified phase retrieval algorithm and logistic map is further proposed in this paper, in which the fractional orders and the parameters with respect to the logistic map are regarded as encryption keys. Numerical results have demonstrated the feasibility and effectiveness of the proposed algorithms.

All-optical WDM Regeneration of DPSK Signals using Optical Fourier Transformation and Phase Sensitive Amplification

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian

2015-01-01

We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time.......We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time....

Direct phase retrieval in double blind Fourier holography.

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Raz, Oren; Leshem, Ben; Miao, Jianwei; Nadler, Boaz; Oron, Dan; Dudovich, Nirit

2014-10-20

Phase measurement is a long-standing challenge in a wide range of applications, from X-ray imaging to astrophysics and spectroscopy. While in some scenarios the phase is resolved by an interferometric measurement, in others it is reconstructed via numerical optimization, based on some a-priori knowledge about the signal. The latter commonly use iterative algorithms, and thus have to deal with their convergence, stagnation, and robustness to noise. Here we combine these two approaches and present a new scheme, termed double blind Fourier holography, providing an efficient solution to the phase problem in two dimensions, by solving a system of linear equations. We present and experimentally demonstrate our approach for the case of lens-less imaging.

Harmonic analysis from Fourier to wavelets

CERN Document Server

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...

Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

Science.gov (United States)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

Fast fourier algorithms in spectral computation and analysis of vibrating machines

International Nuclear Information System (INIS)

Farooq, U.; Hafeez, T.; Khan, M.Z.; Amir, M.

2001-01-01

In this work we have discussed Fourier and its history series, relationships among various Fourier mappings, Fourier coefficients, transforms, inverse transforms, integrals, analyses, discrete and fast algorithms for data processing and analysis of vibrating systems. The evaluation of magnitude of the source signal at transmission time, related coefficient matrix, intensity, and magnitude at the receiving end (stations). Matrix computation of Fourier transform has been explained, and applications are presented. The fast Fourier transforms, new computational scheme. have been tested with an example. The work also includes digital programs for obtaining the frequency contents of time function. It has been explained that how the fast Fourier algorithms (FFT) has decreased computational work by several order of magnitudes and split the spectrum of a signal into two (even and odd modes) at every successive step. That fast quantitative processing for discrete Fourier transforms' computations as well as signal splitting and combination provides an efficient. and reliable tool for spectral analyses. Fourier series decompose the given variable into a sum of oscillatory functions each having a specific frequency. These frequencies, with their corresponding amplitude and phase angles, constitute the frequency contents of the original time functions. These fast processing achievements, signals decomposition and combination may be carried out by the principle of superposition and convolution for, even, signals of different frequencies. Considerable information about a machine or a structure can be derived from variable speed and frequency tests. (author)

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

International Nuclear Information System (INIS)

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

1987-01-01

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

Fourier analysis and stochastic processes

CERN Document Server

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...

Do's and don'ts in Fourier analysis of steady-state potentials.

Science.gov (United States)

Bach, M; Meigen, T

1999-01-01

Fourier analysis is a powerful tool in signal analysis that can be very fruitfully applied to steady-state evoked potentials (flicker ERG, pattern ERG, VEP, etc.). However, there are some inherent assumptions in the underlying discrete Fourier transform (DFT) that are not necessarily fulfilled in typical electrophysiological recording and analysis conditions. Furthermore, engineering software-packages may be ill-suited and/or may not fully exploit the information of steady-state recordings. Specifically: * In the case of steady-state stimulation we know more about the stimulus than in standard textbook situations (exact frequency, phase stability), so 'windowing' and calculation of the 'periodogram' are not necessary. * It is mandatory to choose an integer relationship between sampling rate and frame rate when employing a raster-based CRT stimulator. * The analysis interval must comprise an exact integer number (e.g., 10) of stimulus periods. * The choice of the number of stimulus periods per analysis interval needs a wise compromise: A high number increases the frequency resolution, but makes artifact removal difficult; a low number 'spills' noise into the response frequency. * There is no need to feel tied to a power-of-two number of data points as required by standard FFT, 'resampling' is an easy and efficient alternative. * Proper estimates of noise-corrected Fourier magnitude and statistical significance can be calculated that take into account the non-linear superposition of signal and noise. These aspects are developed in an intuitive approach with examples using both simulations and recordings. Proper use of Fourier analysis of our electrophysiological records will reduce recording time and/or increase the reliability of physiologic or pathologic interpretations.

Detection of cardiac wall motion defects with combined amplitude/phase analysis

International Nuclear Information System (INIS)

Bacharach, S.L.; Green, M.V.; Bonow, R.O.; Pace, L.; Brunetti, A.; Larson, S.M.

1985-01-01

Fourier phase images have been used with some success to detect and quantify left ventricular (LV) wall motion defects. In abnormal regions of the LV, wall motion asynchronies often cause the time activity curve (TAC) to be shifted in phase. Such regional shifts are detected by analysis of the distribution function of phase values over the LV. However, not all wall motion defects result in detectable regional phase abnormalities. Such abnormalities may cause a reduction in the magnitude of contraction (and hence TAC amplitude) without any appreciable change in TAC shape(and hence phase). In an attempt to improve the sensitivity of the Fourier phase method for the detection of wall motion defects the authors analyzed the distribution function of Fourier amplitude as well as phase. 26 individuals with normal cardiac function and no history of cardiac disease served as controls. The goal was to detect and quantify wall motion as compared to the consensus of 3 independent observers viewing the scintigraphic cines. 26 subjects with coronary artery disease and mild wall motion defects (22 with normal EF) were studied ate rest. They found that analysis of the skew of thew amplitude distribution function improved the sensitivity for the detection of wall motion abnormalities at rest in the group from 65% to 85% (17/26 detected by phase alone, 22/26 by combined phase and amplitude analysis) while retaining a 0 false positive rate in the normal group. The authors conclude that analysis of Fourier amplitude distribution functions can significantly increase the sensitivity of phase imaging for detection of wall motion abnormalities

Fourier analysis in several complex variables

CERN Document Server

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

Methods of Fourier analysis and approximation theory

CERN Document Server

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.

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)

Applied Fourier analysis from signal processing to medical imaging

CERN Document Server

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...

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

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

International Nuclear Information System (INIS)

Harasse, Sébastien; Yashiro, Wataru; Momose, Atsushi

2012-01-01

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

Mathematical principles of signal processing Fourier and wavelet analysis

CERN Document Server

Brémaud, Pierre

2002-01-01

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

16 channel WDM regeneration in a single phase-sensitive amplifier through optical Fourier transformation

DEFF Research Database (Denmark)

Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads

2016-01-01

We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...

Image/patient registration from (partial) projection data by the Fourier phase matching method

International Nuclear Information System (INIS)

Weiguo Lu; You, J.

1999-01-01

A technique for 2D or 3D image/patient registration, PFPM (projection based Fourier phase matching method), is proposed. This technique provides image/patient registration directly from sequential tomographic projection data. The method can also deal with image files by generating 2D Radon transforms slice by slice. The registration in projection space is done by calculating a Fourier invariant (FI) descriptor for each one-dimensional projection datum, and then registering the FI descriptor by the Fourier phase matching (FPM) method. The algorithm has been tested on both synthetic and experimental data. When dealing with translated, rotated and uniformly scaled 2D image registration, the performance of the PFPM method is comparable to that of the IFPM (image based Fourier phase matching) method in robustness, efficiency, insensitivity to the offset between images, and registration time. The advantages of the former are that subpixel resolution is feasible, and it is more insensitive to image noise due to the averaging effect of the projection acquisition. Furthermore, the PFPM method offers the ability to generalize to 3D image/patient registration and to register partial projection data. By applying patient registration directly from tomographic projection data, image reconstruction is not needed in the therapy set-up verification, thus reducing computational time and artefacts. In addition, real time registration is feasible. Registration from partial projection data meets the geometry and dose requirements in many application cases and makes dynamic set-up verification possible in tomotherapy. (author)

International conference Fourier Analysis and Pseudo-Differential Operators

CERN Document Server

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 and boundary value problems

CERN Document Server

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...

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

Science.gov (United States)

Smith, Jeffrey Scott

2006-01-01

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

Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.

Science.gov (United States)

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.

Multivariate analysis of attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopic data to confirm phase partitioning in methacrylate-based dentin adhesive.

Science.gov (United States)

Ye, Qiang; Parthasarathy, Ranganathan; Abedin, Farhana; Laurence, Jennifer S; Misra, Anil; Spencer, Paulette

2013-12-01

Water is ubiquitous in the mouths of healthy individuals and is a major interfering factor in the development of a durable seal between the tooth and composite restoration. Water leads to the formation of a variety of defects in dentin adhesives; these defects undermine the tooth-composite bond. Our group recently analyzed phase partitioning of dentin adhesives using high-performance liquid chromatography (HPLC). The concentration measurements provided by HPLC offered a more thorough representation of current adhesive performance and elucidated directions to be taken for further improvement. The sample preparation and instrument analysis using HPLC are, however, time-consuming and labor-intensive. The objective of this work was to develop a methodology for rapid, reliable, and accurate quantitative analysis of near-equilibrium phase partitioning in adhesives exposed to conditions simulating the wet oral environment. Analysis by Fourier transform infrared (FT-IR) spectroscopy in combination with multivariate statistical methods, including partial least squares (PLS) regression and principal component regression (PCR), were used for multivariate calibration to quantify the compositions in separated phases. Excellent predictions were achieved when either the hydrophobic-rich phase or the hydrophilic-rich phase mixtures were analyzed. These results indicate that FT-IR spectroscopy has excellent potential as a rapid method of detection and quantification of dentin adhesives that experience phase separation under conditions that simulate the wet oral environment.

Randomly displaced phase distribution design and its advantage in page-data recording of Fourier transform holograms.

Science.gov (United States)

Emoto, Akira; Fukuda, Takashi

2013-02-20

For Fourier transform holography, an effective random phase distribution with randomly displaced phase segments is proposed for obtaining a smooth finite optical intensity distribution in the Fourier transform plane. Since unitary phase segments are randomly distributed in-plane, the blanks give various spatial frequency components to an image, and thus smooth the spectrum. Moreover, by randomly changing the phase segment size, spike generation from the unitary phase segment size in the spectrum can be reduced significantly. As a result, a smooth spectrum including sidebands can be formed at a relatively narrow extent. The proposed phase distribution sustains the primary functions of a random phase mask for holographic-data recording and reconstruction. Therefore, this distribution is expected to find applications in high-density holographic memory systems, replacing conventional random phase mask patterns.

Symplectic geometry and Fourier analysis

CERN Document Server

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.

Quantitative heart scintigraphy using Fourier analysis of unformated list mode data

International Nuclear Information System (INIS)

Knopp, R.; Schmidt, H.; Reichmann, K.; Biersack, H.J.; Winkler, C.

1981-01-01

Fourier transformation in radioventriculography is used for smoothing of the left ventricular volume curves as well as for the evaluating of regional wall motions by means of amplitude and phase imaging. Our new method is based on Fourier transformation from unformatted list mode data, pixel by pixel. Determination of the Fourier coefficients of 4 harmonic waves as a maximum is performed and frame sequences are generated by Fourier resynthesis. As main advantages of the method can be regarded a) considerable improvement of the image quality and b) substantial reduction of time needed for data acquisition. (orig.) [de

Left ventricular wall motion abnormalities evaluated by factor analysis as compared with Fourier analysis

International Nuclear Information System (INIS)

Hirota, Kazuyoshi; Ikuno, Yoshiyasu; Nishikimi, Toshio

1986-01-01

Factor analysis was applied to multigated cardiac pool scintigraphy to evaluate its ability to detect left ventricular wall motion abnormalities in 35 patients with old myocardial infarction (MI), and in 12 control cases with normal left ventriculography. All cases were also evaluated by conventional Fourier analysis. In most cases with normal left ventriculography, the ventricular and atrial factors were extracted by factor analysis. In cases with MI, the third factor was obtained in the left ventricle corresponding to wall motion abnormality. Each case was scored according to the coincidence of findings of ventriculography and those of factor analysis or Fourier analysis. Scores were recorded for three items; the existence, location, and degree of asynergy. In cases of MI, the detection rate of asynergy was 94 % by factor analysis, 83 % by Fourier analysis, and the agreement in respect to location was 71 % and 66 %, respectively. Factor analysis had higher scores than Fourier analysis, but this was not significant. The interobserver error of factor analysis was less than that of Fourier analysis. Factor analysis can display locations and dynamic motion curves of asynergy, and it is regarded as a useful method for detecting and evaluating left ventricular wall motion abnormalities. (author)

Artefacts in geometric phase analysis of compound materials.

Science.gov (United States)

Peters, Jonathan J P; Beanland, Richard; Alexe, Marin; Cockburn, John W; Revin, Dmitry G; Zhang, Shiyong Y; Sanchez, Ana M

2015-10-01

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. Copyright © 2015 Elsevier B.V. All rights reserved.

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

International Nuclear Information System (INIS)

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

1989-01-01

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

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.

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.

Comparative analysis of imaging configurations and objectives for Fourier microscopy.

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Fujimoto, Yohei; Sasaki, Toshihiko; Miyazaki, Toshiyuki

2015-01-01

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

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

Monocular deprivation of Fourier phase information boosts the deprived eye's dominance during interocular competition but not interocular phase combination.

Science.gov (United States)

Bai, Jianying; Dong, Xue; He, Sheng; Bao, Min

2017-06-03

Ocular dominance has been extensively studied, often with the goal to understand neuroplasticity, which is a key characteristic within the critical period. Recent work on monocular deprivation, however, demonstrates residual neuroplasticity in the adult visual cortex. After deprivation of patterned inputs by monocular patching, the patched eye becomes more dominant. Since patching blocks both the Fourier amplitude and phase information of the input image, it remains unclear whether deprivation of the Fourier phase information alone is able to reshape eye dominance. Here, for the first time, we show that removing of the phase regularity without changing the amplitude spectra of the input image induced a shift of eye dominance toward the deprived eye, but only if the eye dominance was measured with a binocular rivalry task rather than an interocular phase combination task. These different results indicate that the two measurements are supported by different mechanisms. Phase integration requires the fusion of monocular images. The fused percept highly relies on the weights of the phase-sensitive monocular neurons that respond to the two monocular images. However, binocular rivalry reflects the result of direct interocular competition that strongly weights the contour information transmitted along each monocular pathway. Monocular phase deprivation may not change the weights in the integration (fusion) mechanism much, but alters the balance in the rivalry (competition) mechanism. Our work suggests that ocular dominance plasticity may occur at different stages of visual processing, and that homeostatic compensation also occurs for the lack of phase regularity in natural scenes. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.

Phase coherence among the Fourier modes and non-Gaussian characteristics in the Alfvén chaos system

Science.gov (United States)

Nariyuki, Yasuhiro; Sasaki, Makoto; Kasuya, Naohiro; Hada, Tohru; Yagi, Masatoshi

2017-03-01

Non-Gaussian characteristics in time series of the Alfvén chaos system are discussed. The phase coherence index, a measure defined by using the surrogate data method and the structure function, is used to evaluate the phase coherence among the Fourier modes. Through Monte Carlo significance testing, it is found that the phase coherence decays monotonically with increasing dissipative parameter and time scale. By applying the Mori projection operator method assuming the Markov process, a model equation for the time correlation function is derived from the generalized Langevin equation. As opposed to the result of the phase coherence analysis, it is concluded that the difference between the direct numerical simulation and the model equation becomes pronounced as the dissipative parameters are increased. This suggests that, even when the phase coherence index is not significant, the underlying physical system may be a non-Gaussian process.

Automatic picking of the first arrival event using the unwrapped-phase of the Fourier transformed wavefield

KAUST Repository

Choi, Yun Seok; Alkhalifah, Tariq Ali; Saragiotis, Christos

2011-01-01

an approach based on unwrapping the phase. We unwrap the phase by taking the derivative of the Fourier-transformed wavefield with respect to the angular frequency and isolate its amplitude component. To do so, we first apply a damping function to the seismic

Color image cryptosystem using Fresnel diffraction and phase modulation in an expanded fractional Fourier transform domain

Science.gov (United States)

Chen, Hang; Liu, Zhengjun; Chen, Qi; Blondel, Walter; Varis, Pierre

2018-05-01

In this letter, what we believe is a new technique for optical color image encryption by using Fresnel diffraction and a phase modulation in an extended fractional Fourier transform domain is proposed. Different from the RGB component separation based method, the color image is converted into one component by improved Chirikov mapping. The encryption system is addressed with Fresnel diffraction and phase modulation. A pair of lenses is placed into the fractional Fourier transform system for the modulation of beam propagation. The structure parameters of the optical system and parameters in Chirikov mapping serve as extra keys. Some numerical simulations are given to test the validity of the proposed cryptosystem.

From Fourier analysis to wavelets

CERN Document Server

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.

Advantages of Wavelet analysis compared to Fourier analysis for the interpretation of electrochemical noise

International Nuclear Information System (INIS)

Espada, L.; Sanjurjo, M.; Urrejola, S.; Bouzada, F.; Rey, G.; Sanchez, A.

2003-01-01

Given its simplicity and low cost compared to other types of methodologies, the measurement and interpretation of Electrochemical Noise, is consolidating itself as one of the analysis methods most frequently used for the interpretation of corrosion. As the technique is still evolving, standard treatment methodologies for data retrieved in experiments do not exist yet. To date, statistical analysis and the Fourier analysis are commonly used in order to establish the parameters that may characterize the recording of potential and current electrochemical noise. This study introduces a new methodology based on wavelet analysis and presents its advantages with regards to the Fourier analysis in distinguishes periodical and non-periodical variations in the signal power in time and frequency, as opposed to the Fourier analysis that only considers the frequency. (Author) 15 refs

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...

Discrete Fourier analysis of multigrid algorithms

NARCIS (Netherlands)

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

Validation of Fourier analysis of videokeratographic data.

Science.gov (United States)

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-Based Diffraction Analysis of Live Caenorhabditis elegans.

Science.gov (United States)

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.

Modern Fourier analysis

CERN Document Server

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...

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

Artefacts in geometric phase analysis of compound materials

Energy Technology Data Exchange (ETDEWEB)

Peters, Jonathan J.P., E-mail: j.j.p.peters@warwick.ac.uk [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom); Beanland, Richard; Alexe, Marin [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom); Cockburn, John W.; Revin, Dmitry G.; Zhang, Shiyong Y. [Department of Physics and Astronomy, University of Sheffield, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Sanchez, Ana M., E-mail: a.m.sanchez@warwick.ac.uk [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom)

2015-10-15

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. - Highlights: • GPA is shown to produce incorrect strains when applied to images of compound materials. • A mathematical description is laid out for why GPA can produce artefacts. • The artefact is demonstrated using experimental and simulated data. • A ‘rule’ is set to avoid this artefact in GPA.

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.

Time sequence analysis of flickering auroras. I - Application of Fourier analysis. [in atmosphere

Science.gov (United States)

Berkey, F. T.; Silevitch, M. B.; Parsons, N. R.

1980-01-01

Using a technique that enables one to digitize the brightness of auroral displays from individual fields of a video signal, we have analyzed the frequency content of flickering aurora. Through the application of Fourier analysis to our data, we have found that flickering aurora contains a wide range of enhanced frequencies, although the dominant frequency enhancement generally occurs in the range 6-12 Hz. Each incidence of flickering that we observed was associated with increased radio wave absorption. Furthermore, we have found that flickering occurs in bright auroral surges, the occurrence of which is not limited to the 'breakup' phase of auroral substorms. Our results are interpreted in terms of a recently proposed theory of fluctuating double layers that accounts for a number of the observational features.

Application of Fourier-wavelet regularized deconvolution for improving image quality of free space propagation x-ray phase contrast imaging.

Science.gov (United States)

Zhou, Zhongxing; Gao, Feng; Zhao, Huijuan; Zhang, Lixin

2012-11-21

New x-ray phase contrast imaging techniques without using synchrotron radiation confront a common problem from the negative effects of finite source size and limited spatial resolution. These negative effects swamp the fine phase contrast fringes and make them almost undetectable. In order to alleviate this problem, deconvolution procedures should be applied to the blurred x-ray phase contrast images. In this study, three different deconvolution techniques, including Wiener filtering, Tikhonov regularization and Fourier-wavelet regularized deconvolution (ForWaRD), were applied to the simulated and experimental free space propagation x-ray phase contrast images of simple geometric phantoms. These algorithms were evaluated in terms of phase contrast improvement and signal-to-noise ratio. The results demonstrate that the ForWaRD algorithm is most appropriate for phase contrast image restoration among above-mentioned methods; it can effectively restore the lost information of phase contrast fringes while reduce the amplified noise during Fourier regularization.

Fourier analysis of temporal NDVI in the Southern African and American continents

NARCIS (Netherlands)

Azzali, S.; Menenti, M.

1996-01-01

Results of applying Fourier analysis of temporal NDVI in southern Africa and southern America are summarized. The decomposition of complex time series of images in simpler periodic components by Fourier analysis allowed the factors that affect the vegetation cover to be analysed much easier. The

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

Science.gov (United States)

Park, J. H.

1984-01-01

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Single beam Fourier transform digital holographic quantitative phase microscopy

Energy Technology Data Exchange (ETDEWEB)

Anand, A., E-mail: arun-nair-in@yahoo.com; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V. [Optics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390001 (India); Faridian, A.; Pedrini, G.; Osten, W. [Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart (Germany); Dubey, S. K. [Siemens Technology and Services Pvt. Ltd, Corporate Technology—Research and Technology Centre, Bangalore 560100 (India); Javidi, B. [Department of Electrical and Computer Engineering, U-4157, University of Connecticut, Storrs, Connecticut 06269-2157 (United States)

2014-03-10

Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.

Fourier analysis of finite element preconditioned collocation schemes

Science.gov (United States)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

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

Fourier Analysis: Graphical Animation and Analysis of Experimental Data with Excel

Directory of Open Access Journals (Sweden)

Margarida Oliveira

2012-05-01

Full Text Available According to Fourier formulation, any function that can be represented in a graph may be approximated by the “sum” of infinite sinusoidal functions (Fourier series, termed as “waves”.The adopted approach is accessible to students of the first years of university studies, in which the emphasis is put on the understanding of mathematical concepts through illustrative graphic representations, the students being encouraged to prepare animated Excel-based computational modules (VBA-Visual Basic for Applications.Reference is made to the part played by both trigonometric and complex representations of Fourier series in the concept of discrete Fourier transform. Its connection with the continuous Fourier transform is demonstrated and a brief mention is made of the generalization leading to Laplace transform.As application, the example presented refers to the analysis of vibrations measured on engineering structures: horizontal accelerations of a one-storey building deriving from environment noise. This example is integrated in the curriculum of the discipline “Matemática Aplicada à Engenharia Civil” (Mathematics Applied to Civil Engineering, lectured at ISEL (Instituto Superior de Engenharia de Lisboa. In this discipline, the students have the possibility of performing measurements using an accelerometer and a data acquisition system, which, when connected to a PC, make it possible to record the accelerations measured in a file format recognizable by Excel.

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

International Nuclear Information System (INIS)

Oliveira, S.M.M. de.

1983-01-01

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

Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis

Science.gov (United States)

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.

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

Spatial-phase code-division multiple-access system with multiplexed Fourier holography switching for reconfigurable optical interconnection

Science.gov (United States)

Takasago, Kazuya; Takekawa, Makoto; Shirakawa, Atsushi; Kannari, Fumihiko

2000-05-01

A new, to our knowledge, space-variant optical interconnection system based on a spatial-phase code-division multiple-access technique with multiplexed Fourier holography is described. In this technique a signal beam is spread over wide spatial frequencies by an M -sequence pseudorandom phase code. At a receiver side a selected signal beam is properly decoded, and at the same time its spatial pattern is shaped with a Fourier hologram, which is recorded by light that is encoded with the same M -sequence phase mask as the desired signal beam and by light whose spatial beam pattern is shaped to a signal routing pattern. Using the multiplexed holography, we can simultaneously route multisignal flows into individually specified receiver elements. The routing pattern can also be varied by means of switching the encoding phase code or replacing the hologram. We demonstrated a proof-of-principle experiment with a doubly multiplexed hologram that enables simultaneous routing of two signal beams. Using a numerical model, we showed that the proposed scheme can manage more than 250 routing patterns for one signal flow with one multiplexed hologram at a signal-to-noise ratio of 5.

Beyond Fourier

Science.gov (United States)

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.

Fourier analysis: from cloaking to imaging

Science.gov (United States)

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.

Application of Fourier analysis to multispectral/spatial recognition

Science.gov (United States)

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

1973-01-01

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

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.

Gas phase ion/molecule reactions as studied by Fourier Transform Ion Cyclotron Resonance mass spectrometry

International Nuclear Information System (INIS)

Joergensen, S.I.

1985-01-01

The subject of this thesis is gas phase ion/molecule reactions as studied by Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry (chapter 2 contains a short description of this method). Three chapters are mainly concerned with mechanistic aspects of gas phase ion/molecule reactions. An equally important aspect of the thesis is the stability and reactivity of α-thio carbanions, dipole stabilized carbanions and homoenolate anions, dealt with in the other four chapters. (Auth.)

Fourier analysis for hydrostatic pressure sensing in a polarization-maintaining photonic crystal fiber

International Nuclear Information System (INIS)

Childs, Paul; Wong, Allan C. L.; Fu, H. Y.; Liao, Yanbiao; Tam, Hwayaw; Lu Chao; Wai, P. K. A.

2010-01-01

.We measured the hydrostatic pressure dependence of the birefringence and birefringent dispersion of a Sagnac interferometric sensor incorporating a length of highly birefringent photonic crystal fiber using Fourier analysis. Sensitivity of both the phase and chirp spectra to hydrostatic pressure is demonstrated. Using this analysis, phase-based measurements showed a good linearity with an effective sensitivity of 9.45nm/MPa and an accuracy of ±7.8kPa using wavelength-encoded data and an effective sensitivity of -55.7cm -1 /MPa and an accuracy of ±4.4kPa using wavenumber-encoded data. Chirp-based measurements, though nonlinear in response, showed an improvement in accuracy at certain pressure ranges with an accuracy of ±5.5kPa for the full range of measured pressures using wavelength-encoded data and dropping to within ±2.5kPa in the range of 0.17 to 0.4MPa using wavenumber-encoded data. Improvements of the accuracy demonstrated the usefulness of implementing chirp-based analysis for sensing purposes.

Beyond Fourier.

Science.gov (United States)

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.

Fourier phase retrieval with a single mask by Douglas-Rachford algorithms.

Science.gov (United States)

Chen, Pengwen; Fannjiang, Albert

2018-05-01

The Fourier-domain Douglas-Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution requires more than a single oversampled coded diffraction pattern, the extra information is imposed in either of the following forms: 1) the sector condition on the object; 2) another oversampled diffraction pattern, coded or uncoded. For both settings, the uniqueness of projected fixed point is proved and for setting 2) the local, geometric convergence is derived with a rate given by a spectral gap condition. Numerical experiments demonstrate global, power-law convergence of FDR from arbitrary initialization for both settings as well as for 3 or more coded diffraction patterns without oversampling. In practice, the geometric convergence can be recovered from the power-law regime by a simple projection trick, resulting in highly accurate reconstruction from generic initialization.

Error Analysis for Fourier Methods for Option Pricing

KAUST Repository

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 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)

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

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.

Science.gov (United States)

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

Utilization of a liquid crystal spatial light modulator in a gray scale detour phase method for Fourier holograms.

Science.gov (United States)

Makey, Ghaith; El-Daher, Moustafa Sayem; Al-Shufi, Kanj

2012-11-10

This paper introduces a new modification for the well-known binary detour phase method, which is largely used to represent Fourier holograms; the modification utilizes gray scale level control provided by a liquid crystal spatial light modulator to improve the traditional binary detour phase. Results are shown by both simulation and experiment.

Electro-optic imaging Fourier transform spectrometer

Science.gov (United States)

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.

Spatiotemporal Signal Analysis via the Phase Velocity Transform

International Nuclear Information System (INIS)

Mattor, Nathan

2000-01-01

The phase velocity transform (PVT) is an integral transform that divides a function of space and time into components that propagate at uniform phase velocities without distortion. This paper examines the PVT as a method to analyze spatiotemporal fluctuation data. The transform is extended to systems with discretely sampled data on a periodic domain, and applied to data from eight azimuthally distributed probes on the Sustained Spheromak Physics Experiment (SSPX). This reveals features not shown by Fourier analysis, particularly regarding nonsinusoidal mode structure. (c) 2000 The American Physical Society

Phase Error Caused by Speed Mismatch Analysis in the Line-Scan Defect Detection by Using Fourier Transform Technique

Directory of Open Access Journals (Sweden)

Eryi Hu

2015-01-01

Full Text Available The phase error caused by the speed mismatch issue is researched in the line-scan images capturing 3D profile measurement. The experimental system is constructed by a line-scan CCD camera, an object moving device, a digital fringe pattern projector, and a personal computer. In the experiment procedure, the detected object is moving relative to the image capturing system by using a motorized translation stage in a stable velocity. The digital fringe pattern is projected onto the detected object, and then the deformed patterns are captured and recorded in the computer. The object surface profile can be calculated by the Fourier transform profilometry. However, the moving speed mismatch error will still exist in most of the engineering application occasion even after an image system calibration. When the moving speed of the detected object is faster than the expected value, the captured image will be compressed in the moving direction of the detected object. In order to overcome this kind of measurement error, an image recovering algorithm is proposed to reconstruct the original compressed image. Thus, the phase values can be extracted much more accurately by the reconstructed images. And then, the phase error distribution caused by the speed mismatch is analyzed by the simulation and experimental methods.

A Fourier Collocation Approach for Transit-Time Ultrasonic Flowmeter Under Multi-Phase Flow Conditions

DEFF Research Database (Denmark)

Simurda, Matej; Lassen, Benny; Duggen, Lars

2017-01-01

A numerical model for a clamp-on transit-time ultrasonic flowmeter (TTUF) under multi-phase flow conditions is presented. The method solves equations of linear elasticity for isotropic heterogeneous materials with background flow where acoustic media are modeled by setting shear modulus to zero....... Spatial derivatives are calculated by a Fourier collocation method allowing the use of the fast Fourier transform (FFT) and time derivatives are approximated by a finite difference (FD) scheme. This approach is sometimes referred to as a pseudospectral time-domain method. Perfectly matched layers (PML......) are used to avoid wave-wrapping and staggered grids are implemented to improve stability and efficiency. The method is verified against exact analytical solutions and the effect of the time-staggering and associated lowest number of points per minimum wavelengths value is discussed. The method...

The quantum state vector in phase space and Gabor's windowed Fourier transform

International Nuclear Information System (INIS)

Bracken, A J; Watson, P

2010-01-01

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schroedinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.

The use of Fourier reverse transforms in crystallographic phase refinement

Energy Technology Data Exchange (ETDEWEB)

Ringrose, Sharon [Iowa State Univ., Ames, IA (United States)

1997-10-08

Often a crystallographer obtains an electron density map which shows only part of the structure. In such cases, the phasing of the trial model is poor enough that the electron density map may show peaks in some of the atomic positions, but other atomic positions are not visible. There may also be extraneous peaks present which are not due to atomic positions. A method for determination of crystal structures that have resisted solution through normal crystallographic methods has been developed. PHASER is a series of FORTRAN programs which aids in the structure solution of poorly phased electron density maps by refining the crystallographic phases. It facilitates the refinement of such poorly phased electron density maps for difficult structures which might otherwise not be solvable. The trial model, which serves as the starting point for the phase refinement, may be acquired by several routes such as direct methods or Patterson methods. Modifications are made to the reverse transform process based on several assumptions. First, the starting electron density map is modified based on the fact that physically the electron density map must be non-negative at all points. In practice a small positive cutoff is used. A reverse Fourier transform is computed based on the modified electron density map. Secondly, the authors assume that a better electron density map will result by using the observed magnitudes of the structure factors combined with the phases calculated in the reverse transform. After convergence has been reached, more atomic positions and less extraneous peaks are observed in the refined electron density map. The starting model need not be very large to achieve success with PHASER; successful phase refinement has been achieved with a starting model that consists of only 5% of the total scattering power of the full molecule. The second part of the thesis discusses three crystal structure determinations.

Studies of gas phase ion/molecule reactions by Fourier transform ion cyclotron resonance mass spectrometry

International Nuclear Information System (INIS)

Kleingeld, J.C.

1984-01-01

An important field in which Fourier-transform ion cyclotron resonance has useful applications is that of gas phase ion chemistry, the subject of this thesis. First, the general picture of ion-molecule reactions in the gas phase is discussed. Next, some positive ion-molecule reactions are described, whereas the remaining chapters deal with negative ion-molecule reactions. Most of these studies have been performed using the FT-ICR method. Reactions involving H 3 O - and NH 4 - ions are described whereas the other chapters deal with larger organic complexes. (Auth.)

Measurement of multi-bunch transfer functions using time-domain data and Fourier analysis

International Nuclear Information System (INIS)

Hindi, H.; Sapozhnikov, L.; Fox, J.; Prabhakar, S.; Oxoby, G.; Linscott, I.; Drago, A.

1993-12-01

Multi-bunch transfer functions are principal ingredients in understanding both the behavior of high-current storage rings as well as control of their instabilities. The measurement of transfer functions on a bunch-by-bunch basis is particularly important in the design of active feedback systems. Traditional methods of network analysis that work well in the single bunch case become difficult to implement for many bunches. We have developed a method for obtaining empirical estimates of the multi-bunch longitudinal transfer functions from the time-domain measurements of the bunches' phase oscillations. This method involves recording the response of the bunch of interest to a white-noise excitation. The transfer function can then be computed as the ratio of the fast Fourier transforms (FFTs) of the response and excitation sequences, averaged over several excitations. The calculation is performed off-line on bunch-phase data and is well-suited to the multi-bunch case. A description of this method and an analysis of its performance is presented with results obtained using the longitudinal quick prototype feedback system developed at SLAC

Combining Fourier phase encoding and broadband inversion toward J-edited spectra

Science.gov (United States)

Lin, Yulan; Guan, Quanshuai; Su, Jianwei; Chen, Zhong

2018-06-01

Nuclear magnetic resonance (NMR) spectra are often utilized for gathering accurate information relevant to molecular structures and composition assignments. In this study, we develop a homonuclear encoding approach based on imparting a discrete phase modulation of the targeted cross peaks, and combine it with a pure shift experiments (PSYCHE) based J-modulated scheme, providing simple 2D J-edited spectra for accurate measurement of scalar coupling networks. Chemical shifts and J coupling constants of protons coupled to the specific protons are demonstrated along the F2 and F1 dimensions, respectively. Polychromatic pulses by Fourier phase encoding were performed to simultaneously detect several coupling networks. Proton-proton scalar couplings are chosen by a polychromatic pulse and a PSYCHE element. Axis peaks and unwanted couplings are complete eradicated by incorporating a selective COSY block as a preparation period. The theoretical principles and the signal processing procedure are laid out, and experimental observations are rationalized on the basis of theoretical analyses.

Analysis of gamma-ray spectra by using fast Fourier transform

International Nuclear Information System (INIS)

Tominaga, Shoji; Nagata, Shojiro; Nayatani, Yoshinobu; Ueda, Isamu; Sasaki, Satoshi.

1977-01-01

In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform devised. The validity of the method was confirmed by a computer simulation for spectra of a NaI detector. The method uses the fact that spectral data can be represented by Fourier series with reduced number of terms. The estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features in the method and a general problem to be solved in a response matrix method are described. (auth.)

Use of fast Fourier transform in gamma-ray spectral analysis

International Nuclear Information System (INIS)

Tominaga, Shoji; Nayatani, Yoshinobu; Nagata, Shojiro; Sasaki, Takashi; Ueda, Isamu.

1978-01-01

In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform has been devised. The validity of the method has been confirmed by computer simulation for spectra of a NaI detector. First, it is shown that spectral data can be represented by Fourier series with a reduced number of terms. Then the estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features of the method and a general problem to be solved in relation to a response matrix method are described. (author)

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)

Generalized fiber Fourier optics.

Science.gov (United States)

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 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

Phase extracting algorithms analysis in the white-light spectral interferometry

Science.gov (United States)

Guo, Tong; Li, Bingtong; Li, Minghui; Chen, Jinping; Fu, Xing; Hu, Xiaotang

2018-01-01

As an optical testing method, white-light spectral interferometry has the characteristics of non-contact, high precision. The phase information can be obtained by analyzing the spectral interference signal of the tested sample, and then the absolute distance is calculated. Fourier transform method, temporal phase-shifting method, spatial phase-shifting method and envelope method can be used to extract the phase information of the spectral interference signal. In this paper, the performance of four methods to extract phase information is simulated and analyzed by using the ideal spectral interference signal. It turns out that temporal phase-shifting method has the performance of high precision, the results of Fourier transform method and envelop method are distorted at the edge of the signal, and spatial phase-shifting method has the worst precision. Adding different levels of white noise to the ideal signal, temporal phase-shifting method is most accurate, while Fourier transform method and envelope method are relatively poor. Finally, the absolute distance measurement experiment is carried out on the constructed test system, and the results are consistent with the simulation ones.

Closed fringe demodulation using phase decomposition by Fourier basis functions.

Science.gov (United States)

Kulkarni, Rishikesh; Rastogi, Pramod

2016-06-01

We report a new technique for the demodulation of a closed fringe pattern by representing the phase as a weighted linear combination of a certain number of linearly independent Fourier basis functions in a given row/column at a time. A state space model is developed with the weights of the basis functions as the elements of the state vector. The iterative extended Kalman filter is effectively utilized for the robust estimation of the weights. A coarse estimate of the fringe density based on the fringe frequency map is used to determine the initial row/column to start with and subsequently the optimal number of basis functions. The performance of the proposed method is evaluated with several noisy fringe patterns. Experimental results are also reported to support the practical applicability of the proposed method.

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

Science.gov (United States)

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Picometer registration of zinc impurity states in Bi2Sr2CaCu2O8+δ for phase determination in intra-unit-cell Fourier transform STM

International Nuclear Information System (INIS)

Hamidian, M H; Firmo, I A; Fujita, K; Mukhopadhyay, S; Davis, J C; Orenstein, J W; Eisaki, H; Uchida, S; Lawler, M J; Kim, E-A

2012-01-01

Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). By studying the Bragg peaks in Fourier transforms of electronic structure images and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit-cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such a Bragg-peak Fourier analysis. Exemplary of this challenge is the high-temperature superconductor Bi 2 Sr 2 CaCu 2 O 8+δ for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO 2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a ∼2%(2π) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unit-cell rotational symmetry breaking at the CuO 2 plane (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for the Bragg-peak Fourier analysis of intra-unit-cell symmetry. (paper)

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...

Suppressing carrier removal error in the Fourier transform method for interferogram analysis

International Nuclear Information System (INIS)

Fan, Qi; Yang, Hongru; Li, Gaoping; Zhao, Jianlin

2010-01-01

A new carrier removal method for interferogram analysis using the Fourier transform is presented. The proposed method can be used to suppress the carrier removal error as well as the spectral leakage error. First, the carrier frequencies are estimated with the spectral centroid of the up sidelobe of the apodized interferogram, and then the up sidelobe can be shifted to the origin in the frequency domain by multiplying the original interferogram by a constructed plane reference wave. The influence of the carrier frequencies without an integer multiple of the frequency interval and the window function for apodization of the interferogram can be avoided in our work. The simulation and experimental results show that this method is effective for phase measurement with a high accuracy from a single interferogram

Fourier domain image fusion for differential X-ray phase-contrast breast imaging

International Nuclear Information System (INIS)

Coello, Eduardo; Sperl, Jonathan I.; Bequé, Dirk; Benz, Tobias; Scherer, Kai; Herzen, Julia; Sztrókay-Gaul, Anikó; Hellerhoff, Karin; Pfeiffer, Franz; Cozzini, Cristina; Grandl, Susanne

2017-01-01

X-Ray Phase-Contrast (XPC) imaging is a novel technology with a great potential for applications in clinical practice, with breast imaging being of special interest. This work introduces an intuitive methodology to combine and visualize relevant diagnostic features, present in the X-ray attenuation, phase shift and scattering information retrieved in XPC imaging, using a Fourier domain fusion algorithm. The method allows to present complementary information from the three acquired signals in one single image, minimizing the noise component and maintaining visual similarity to a conventional X-ray image, but with noticeable enhancement in diagnostic features, details and resolution. Radiologists experienced in mammography applied the image fusion method to XPC measurements of mastectomy samples and evaluated the feature content of each input and the fused image. This assessment validated that the combination of all the relevant diagnostic features, contained in the XPC images, was present in the fused image as well.

Fourier domain image fusion for differential X-ray phase-contrast breast imaging

Energy Technology Data Exchange (ETDEWEB)

Coello, Eduardo, E-mail: eduardo.coello@tum.de [GE Global Research, Garching (Germany); Lehrstuhl für Informatikanwendungen in der Medizin & Augmented Reality, Institut für Informatik, Technische Universität München, Garching (Germany); Sperl, Jonathan I.; Bequé, Dirk [GE Global Research, Garching (Germany); Benz, Tobias [Lehrstuhl für Informatikanwendungen in der Medizin & Augmented Reality, Institut für Informatik, Technische Universität München, Garching (Germany); Scherer, Kai; Herzen, Julia [Lehrstuhl für Biomedizinische Physik, Physik-Department & Institut für Medizintechnik, Technische Universität München, Garching (Germany); Sztrókay-Gaul, Anikó; Hellerhoff, Karin [Institute for Clinical Radiology, Ludwig-Maximilians-University Hospital, Munich (Germany); Pfeiffer, Franz [Lehrstuhl für Biomedizinische Physik, Physik-Department & Institut für Medizintechnik, Technische Universität München, Garching (Germany); Cozzini, Cristina [GE Global Research, Garching (Germany); Grandl, Susanne [Institute for Clinical Radiology, Ludwig-Maximilians-University Hospital, Munich (Germany)

2017-04-15

X-Ray Phase-Contrast (XPC) imaging is a novel technology with a great potential for applications in clinical practice, with breast imaging being of special interest. This work introduces an intuitive methodology to combine and visualize relevant diagnostic features, present in the X-ray attenuation, phase shift and scattering information retrieved in XPC imaging, using a Fourier domain fusion algorithm. The method allows to present complementary information from the three acquired signals in one single image, minimizing the noise component and maintaining visual similarity to a conventional X-ray image, but with noticeable enhancement in diagnostic features, details and resolution. Radiologists experienced in mammography applied the image fusion method to XPC measurements of mastectomy samples and evaluated the feature content of each input and the fused image. This assessment validated that the combination of all the relevant diagnostic features, contained in the XPC images, was present in the fused image as well.

Application of phase correction to improve the interpretation of crude oil spectra obtained using 7 T Fourier transform ion cyclotron resonance mass spectrometry.

Science.gov (United States)

Cho, Yunju; Qi, Yulin; O'Connor, Peter B; Barrow, Mark P; Kim, Sunghwan

2014-01-01

In this study, a phase-correction technique was applied to the study of crude oil spectra obtained using a 7 T Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). 7 T FT-ICR MS had not been widely used for oil analysis due to the lower resolving power compared with high field FT-ICR MS. For low field instruments, usage of data that has not been phase-corrected results in an inability to resolve critical mass splits of C3 and SH4 (3.4 mDa), and (13)C and CH (4.5 mDa). This results in incorrect assignments of molecular formulae, and discontinuous double bond equivalents (DBE) and carbon number distributions of S1, S2, and hydrocarbon classes are obtained. Application of phase correction to the same data, however, improves the reliability of assignments and produces continuous DBE and carbon number distributions. Therefore, this study clearly demonstrates that phase correction improves data analysis and the reliability of assignments of molecular formulae in crude oil anlayses.

Ventricular emptying performance in patients with tetralogy of Fallot; Assessment with Fourier analysis of gated blood-pool data

Energy Technology Data Exchange (ETDEWEB)

Takeda, Kan; Maeda, Hisato; Nakagawa, Tsuyoshi; Ito, Tsunao; Yamaguchi, Nobuo; Matsuda, Akira (Mie Univ., Tsu (Japan). School of Medicine)

1989-12-01

Comparison of emptying patterns between left and right ventricles (LV, RV) was performed with Fourier analysis of gated blood-pool data in patients with tetralogy of Fallot (TF). Using global time-activity curves, the phase and amplitude at the first-harmonic component of Fourier series were calculated and emptying patterns of both ventricles were evaluated by phase difference {l brace}D(phase)=RV phase minus LV phase{r brace} and RV/LV amplitude ratio {l brace}R(amp){r brace}. In 20 patients with normal cardiac function, D(phase) was minimal (mean 2.0{plus minus}6.6 degrees) and R(amp) was less than 1.0 (mean 0.60{plus minus}0.19). In 11 patients with TF, D(phase) was significantly larger than normal, with a mean value of 24.3{plus minus}10.0 degrees (p<0.01) and became greater in a reversed proportion to the ratio of the pulmonary-to-systemic blood flow (p<0.01). In all but one cases with TF, R(amp) was greater than 1.0 with a mean value of 1.4{plus minus}0.4, significantly larger than normal (p<0.001). Furthermore, using time-activity curves approximated by terms up to the 3rd-harmonic component, the temporal difference in emptying patterns between both ventricles was investigated. In TF cases, the time from end-diastole to minimum count (T2) was significantly larger in RV than in LV (p<0.001). The elongated T2 interval of RV seemed to play an important role in producing RV phase lag. Thus, this non-invasive method is valuable for pathophysiologic investigation of patients with TF and can be of help in estimating the severity of their disease. (author).

Multimode vibration analysis with high-speed TV holography and a spatiotemporal 3D Fourier transform method.

Science.gov (United States)

Trillo, Cristina; Doval, Angel F; Mendoza-Santoyo, Fernando; Pérez-López, Carlos; de la Torre-Ibarra, Manuel; Deán, J Luis

2009-09-28

The combination of a high-speed TV holography system and a 3D Fourier-transform data processing is proposed for the analysis of multimode vibrations in plates. The out-of-plane displacement of the object under generic vibrational excitation is resolved in time by the fast acquisition rate of a high-speed camera, and recorded in a sequence of interferograms with spatial carrier. A full-field temporal history of the multimode vibration is thus obtained. The optical phase of the interferograms is extracted and subtracted from the phase of a reference state to yield a sequence of optical phase-change maps. Each map represents the change undergone by the object between any given state and the reference state. The sequence of maps is a 3D array of data (two spatial dimensions plus time) that is processed with a 3D Fourier-transform algorithm. The individual vibration modes are separated in the 3D frequency space due to their different vibration frequencies and, to a lesser extent, to the different spatial frequencies of the mode shapes. The contribution of each individual mode (or indeed the superposition of several modes) to the dynamic behaviour of the object can then be separated by means of a bandpass filter (or filters). The final output is a sequence of complex-valued maps that contain the full-field temporal history of the selected mode (or modes) in terms of its mechanical amplitude and phase. The proof-of-principle of the technique is demonstrated with a rectangular, fully clamped, thin metal plate vibrating simultaneously in several of its natural resonant frequencies under white-noise excitation.

Using analytic derivatives to assess the impact of phase function Fourier decomposition technique on the accuracy of a radiative transfer model

International Nuclear Information System (INIS)

Sanghavi, Suniti; Natraj, Vijay

2013-01-01

Fourier decomposition of the phase function is essential to decouple the azimuthal component of the radiative transfer equation for multiple scattering calculations. This decomposition can be carried out by means of a direct numerical method based on the definition of the Fourier transform (numFT), or by an expansion of the phase function in terms of spherical Legendre polynomials (sphFT). numFT requires interpolation of the phase function between discrete angles, leading to spurious errors in the final computations. This error is difficult to quantify by means of intensity-only computations, since it is hard to determine the absolute accuracy of any given approach. We show that a linearization (analytic computation of derivatives) of the intensity with respect to parameters governing the phase function can be compared against results using the finite difference method, thereby providing a self-consistency test for characterizing and quantifying the error. We have applied this approach to two linearized versions of the Matrix Operator Method, which are identical in all respects except that one uses numFT while the other uses sphFT. In both cases, we compute the derivatives of the intensity with respect to aerosol parameters governing scattering in the simulated atmosphere. Comparison of the derivatives against their finite difference estimates shows a reduction of error by several orders of magnitude when Legendre polynomials are employed. We have also examined the effect of the angular resolution of the phase function on the error due to the numFT technique. A general reduction of error is seen with increasing angular resolution, indicating that interpolation is indeed the major error source. Also, we have pointed out a related source of error in numFT computations that occurs when Fourier decomposition is carried out on the composite phase function of a layer consisting of more than one scatterer. We conclude that an expansion of the phase function in terms of

Subset geometric phase analysis method for deformation evaluation of HRTEM images

Energy Technology Data Exchange (ETDEWEB)

Zhang, Hongye [School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081 (China); Liu, Zhanwei, E-mail: liuzw@bit.edu.cn [School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081 (China); Wen, Huihui [School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081 (China); Xie, Huimin, E-mail: xiehm@mail.tsinghua.edu.cn [AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084 (China); Liu, Chao [Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China)

2016-12-15

Geometrical phase analysis (GPA) is typically a powerful tool to investigate the deformation in high resolution transmission electron microscopy images and has been used in various fields. The traditional GPA method using the fast Fourier transform, referred to as global-GPA (G-GPA) here, is based on the relationship between the displacement and the phase difference. In this paper, a subset-GPA (S-GPA) is introduced for further improvement. The S-GPA performs the windowed Fourier transform block by block in the image. The maximum strain measurement scale of the GPA method is theoretically analyzed on the basic of the phase spectrum extraction process. The upper limit is one third of the atomic spacing. The results of various numerical simulations verified that the S-GPA method performs better than the traditional G-GPA method in both the homogeneous and inhomogeneous deformation conditions, with the evaluation parameter of calculation reliability of S-GPA 10% higher than G-GPA. Specifically, the measurement accuracy of S-GPA is about three times higher than the G-GPA when calculating small strain (less than 2000με). For the large strain (greater than 150000με), the measurement accuracy of S-GPA is about 50% higher than that of the G-GPA. Besides, the S-GPA method can significantly eliminate the phase filling effect, while the G-GPA cannot. The S-GPA method has been successfully applied to analyze the strain field distribution in an lnGaAs/InAlAs supperlattice heterostructure. - Highlights: • A subset-GPA method, performing the windowed Fourier transform block by block in HRTEM image, is systematically introduced. • According to the theoretical analysis, the upper limit of absolute maximum strain of GPA method is 1/3. • The measurement accuracy of S-GPA is about three times higher than that of the G-GPA when calculating small strain. • The measurement capability of S-GPA is about 50 percent higher than that of the G-GPA when calculating large strain. �

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)

Study of the clinical utility and potential problems of quantitative phase analysis using multiple gated cardiac blood pool image

International Nuclear Information System (INIS)

Tabuchi, Hiromi

1987-01-01

The temporal Fourier fitting at the fundamental frequency (Fourier analysis) and the Chebyshev polynomials for order 9 (Chebyshev analysis) were performed in 24 patients with myocardial infarction (MI) and 10 normal subjects. Fourier analysis showed a significantly delayed regional phase values (RPV), only when corrected in R-R interval, in the MI group. In both Fourier and Chebyshev analyses, a significantly decreased regional ejection fraction was noted in the MI group. Regional ejection time calculated by Chebyshev analysis was significantly delayed as well in the MI group. Fourier and Chebyshev analyses were useful in early detecting and precisely analysing MI contraction abnormality, respectively, although the former method required the correction in R-R interval. The second series of Fourier analysis was made on 11 patients with right ventricular endocardial pacing (RVEP), 7 patients with left bundle branch block (LBBB), and 10 normal subjects. The LBBB group had markedly delayed RPV in the whole ventricular area. The RVEP group had initial contraction at the apex of right ventricle, with tendency for wave-like contraction spreading basal portions of both ventricles. Patients with type RS on QRS waves at pacing tended to have slight differences in RPV between the right and left ventricles. Fourier analysis was useful in evaluating ventricular contraction pattern in patients with miscellaneous cardiac diseases. (Namekawa, K.) 70 refs

Evaluation of gastric motility by Fourier analysis of condensed images

Energy Technology Data Exchange (ETDEWEB)

Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K. [Dept. of Nuclear Medicine, Univ. of Munich, Munich (Germany)

2000-10-01

In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)

Evaluation of gastric motility by Fourier analysis of condensed images

International Nuclear Information System (INIS)

Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K.

2000-01-01

In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)

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)

Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference

Science.gov (United States)

Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.

2016-09-01

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

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)

Fourier transform infrared spectroscopy of peptides.

Science.gov (United States)

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.

Optical image-hiding method with false information disclosure based on the interference principle and partial-phase-truncation in the fractional Fourier domain

International Nuclear Information System (INIS)

Dai, Chaoqing; Wang, Xiaogang; Zhou, Guoquan; Chen, Junlang

2014-01-01

An image-hiding method based on the optical interference principle and partial-phase-truncation in the fractional Fourier domain is proposed. The primary image is converted into three phase-only masks (POMs) using an analytical algorithm involved partial-phase-truncation and a fast random pixel exchange process. A procedure of a fake silhouette for a decryption key is suggested to reinforce the encryption and give a hint of the position of the key. The fractional orders of FrFT effectively enhance the security of the system. In the decryption process, the POM with false information and the other two POMs are, respectively, placed in the input and fractional Fourier planes to recover the primary image. There are no unintended information disclosures and iterative computations involved in the proposed method. Simulation results are presented to verify the validity of the proposed approach. (letters)

Renal geology (quantitative renal stone analysis) by 'Fourier transform infrared spectroscopy'.

Science.gov (United States)

Singh, Iqbal

2008-01-01

To prospectively determine the precise stone composition (quantitative analysis) by using infrared spectroscopy in patients with urinary stone disease presenting to our clinic. To determine an ideal method for stone analysis suitable for use in a clinical setting. After routine and a detailed metabolic workup of all patients of urolithiasis, stone samples of 50 patients of urolithiasis satisfying the entry criteria were subjected to the Fourier transform infrared spectroscopic analysis after adequate sample homogenization at a single testing center. Calcium oxalate monohydrate and dihydrate stone mixture was most commonly encountered in 35 (71%) followed by calcium phosphate, carbonate apatite, magnesium ammonium hexahydrate and xanthine stones. Fourier transform infrared spectroscopy allows an accurate, reliable quantitative method of stone analysis. It also helps in maintaining a computerized large reference library. Knowledge of precise stone composition may allow the institution of appropriate prophylactic therapy despite the absence of any detectable metabolic abnormalities. This may prevent and or delay stone recurrence.

Fourier analysis of intracranial aneurysms: towards an objective and quantitative evaluation of the shape of aneurysms

International Nuclear Information System (INIS)

Rohde, Stefan; Lahmann, Katharina; Nafe, Reinhold; Yan, Bernard; Berkefeld, Joachim; Beck, Juergen; Raabe, Andreas

2005-01-01

Shape irregularities of intracranial aneurysms may indicate an increased risk of rupture. To quantify morphological differences, Fourier analysis of the shape of intracranial aneurysms was introduced. We compared the morphology of 45 unruptured (UIA) and 46 ruptured intracranial aneurysms (RIA) in 70 consecutive patients on the basis of 3D-rotational angiography. Fourier analysis, coefficient of roundness and qualitative shape assessment were determined for each aneurysm. Morphometric analysis revealed significantly smaller coefficient of roundness (P<0.02) and higher values for Fourier amplitudes numbers 2, 3 and 7 (P<0.01) in the RIA group, indicating more complex and irregular morphology in RIA. Qualitative assessment from 3D-reconstructions showed surface irregularities in 78% of RIA and 42% of UIA (P<0.05). Our data have shown significant differences in shape between RIA and UIA, and further developments of Fourier analysis may provide an objective factor for the assessment of the risk of rupture. (orig.)

Improvements in image quality with pseudo-parallel imaging in the phase-scrambling fourier transform technique

International Nuclear Information System (INIS)

Ito, Satoshi; Kawawa, Yasuhiro; Yamada, Yoshifumi

2010-01-01

The signal obtained in the phase-scrambling Fourier transform (PSFT) imaging technique can be transformed to the signal described by the Fresnel transform of the objects, in which the amplitude of the PSFT presents some kind of blurred image of the objects. Therefore, the signal can be considered to exist in the object domain as well as the Fourier domain of the object. This notable feature makes it possible to assign weights to the reconstructed images by applying a weighting function to the PSFT signal after data acquisition, and as a result, pseudo-parallel image reconstruction using these aliased image data with different weights on the images is feasible. In this study, the improvements in image quality with such pseudo-parallel imaging were examined and demonstrated. The weighting function of the PSFT signal that provides a given weight on the image is estimated using the obtained image data and is iteratively updated after sensitivity encoding (SENSE)-based image reconstruction. Simulation studies showed that reconstruction errors were dramatically reduced and that the spatial resolution was also improved in almost all image spaces. The proposed method was applied to signals synthesized from MR image data with phase variations to verify its effectiveness. It was found that the image quality was improved and that images almost entirely free of aliasing artifacts could be obtained. (author)

Sensitivity analysis of a complex, proposed geologic waste disposal system using the Fourier Amplitude Sensitivity Test method

International Nuclear Information System (INIS)

Lu Yichi; Mohanty, Sitakanta

2001-01-01

The Fourier Amplitude Sensitivity Test (FAST) method has been used to perform a sensitivity analysis of a computer model developed for conducting total system performance assessment of the proposed high-level nuclear waste repository at Yucca Mountain, Nevada, USA. The computer model has a large number of random input parameters with assigned probability density functions, which may or may not be uniform, for representing data uncertainty. The FAST method, which was previously applied to models with parameters represented by the uniform probability distribution function only, has been modified to be applied to models with nonuniform probability distribution functions. Using an example problem with a small input parameter set, several aspects of the FAST method, such as the effects of integer frequency sets and random phase shifts in the functional transformations, and the number of discrete sampling points (equivalent to the number of model executions) on the ranking of the input parameters have been investigated. Because the number of input parameters of the computer model under investigation is too large to be handled by the FAST method, less important input parameters were first screened out using the Morris method. The FAST method was then used to rank the remaining parameters. The validity of the parameter ranking by the FAST method was verified using the conditional complementary cumulative distribution function (CCDF) of the output. The CCDF results revealed that the introduction of random phase shifts into the functional transformations, proposed by previous investigators to disrupt the repetitiveness of search curves, does not necessarily improve the sensitivity analysis results because it destroys the orthogonality of the trigonometric functions, which is required for Fourier analysis

Analysis of tokamak plasma confinement modes using the fast Fourier transformation

International Nuclear Information System (INIS)

Mirmoeini, S.R.; Salar Elahi, A.; Ghoranneviss, M.

2016-01-01

The Fourier analysis is a satisfactory technique for detecting plasma confinement modes in tokamaks. The confinement mode of tokamak plasma was analysed using the fast Fourier transformation (FFT). For this purpose, we used the data of Mirnov coils that is one of the identifying tools in the IR-T1 tokamak, with and without external field (electric biasing), and then compared it with each other. After the Fourier analysis of Mirnov coil data, the diagram of power spectrum density was depicted in different angles of Mirnov coils in the 'presence of external field' as well as in the 'absence of external field'. The power spectrum density (PSD) interprets the manner of power distribution of a signal with frequency. In this article, the number of plasma modes and the safety factor q were obtained by using the mode number of q = m/n (m is the mode number). The maximum MHD activity was obtained in 30-35 kHz frequency, using the density of the energy spectrum. In addition, the number of different modes across 0-35 ms time was compared with each other in the presence and absence of the external field. (author)

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

International Nuclear Information System (INIS)

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

2009-01-01

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

Temporal Fourier transform of digital angiograms for left ventricular regional wall motion analysis

International Nuclear Information System (INIS)

Katayama, Kazuhiro; Guth, B.D.; Widmann, T.F.; Lee, Jong-Dae; Seitelberger, R.; Peterson, K.L.

1988-01-01

To determine whether or not the first harmonic of a temporal Fourier transform, applied pixel-by-pixel on time-intensity curves, can detect the subtle wall motion abnormalities due to ischemia, 6 dogs were instrumented with a micromanometer in the left ventricles, a hydraulic cuff occluder around the circumflex coronary artery, and sonomicrometers on the inferior (ischemic) and anterior (non-ischemic) walls. Left ventricular images, obtained after contrast injection via the pulmonary artery, were compared with dimension signals in control and 3 progressive levels of coronary stenosis (Stenosis I, II and III). Normalized, digital functional images (512 x 512 matrix, 256 shades of gray/pixel) were divided into anterior, apical, and inferior areas to acquire regional mean phase (degrees) and amplitude (intensity units) values. After inducing stenosis, phase in ischemic region significantly increased at all 3 levels of stenosis, whereas amplitude significantly decreased at Stenosis II and III. However, amplitude images showed clearly the topographic site of ischemia. There was a progressive increase in phase and decrease in amplitude in ischemic areas as the percent wall thickening (%WTh) fell (phase vs. %WTh: r = -0.55, p < 0.005; amplitude vs. %WTh: r = 0.71, p < 0.001). Heart rate and peak systolic pressure showed no significant changes during stenoses. We conclude that quantitative functional images, generated from a temporal Fourier transform, are sensitive to the detection of left ventricular regional wall motion abnormalities during mild, moderate, and severe degrees of ischemia. (author)

Bladed wheels damage detection through Non-Harmonic Fourier Analysis improved algorithm

Science.gov (United States)

Neri, P.

2017-05-01

Recent papers introduced the Non-Harmonic Fourier Analysis for bladed wheels damage detection. This technique showed its potential in estimating the frequency of sinusoidal signals even when the acquisition time is short with respect to the vibration period, provided that some hypothesis are fulfilled. Anyway, previously proposed algorithms showed severe limitations in cracks detection at their early stage. The present paper proposes an improved algorithm which allows to detect a blade vibration frequency shift due to a crack whose size is really small compared to the blade width. Such a technique could be implemented for condition-based maintenance, allowing to use non-contact methods for vibration measurements. A stator-fixed laser sensor could monitor all the blades as they pass in front of the spot, giving precious information about the wheel health. This configuration determines an acquisition time for each blade which become shorter as the machine rotational speed increases. In this situation, traditional Discrete Fourier Transform analysis results in poor frequency resolution, being not suitable for small frequency shift detection. Non-Harmonic Fourier Analysis instead showed high reliability in vibration frequency estimation even with data samples collected in a short time range. A description of the improved algorithm is provided in the paper, along with a comparison with the previous one. Finally, a validation of the method is presented, based on finite element simulations results.

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.

Application of fast Fourier transform in thermo-magnetic convection analysis

International Nuclear Information System (INIS)

Pyrda, L

2014-01-01

Application of Fast Fourier Transform in thermo-magnetic convection is reported. Cubical enclosure filled with paramagnetic fluid heated from below and placed in the strong magnetic field gradients was investigated. The main aim of study was connected with identification of flow types, especially transition to turbulence. For this purpose the Fast Fourier Transform (FFT) analysis was applied. It was followed by the heat transfer characteristic for various values of magnetic induction gradient. The analysis was done at two Rayleigh numbers 7.89·10 5 and 1.86·10 6 with thermo-magnetic Rayleigh numbers up to 1.8·10 8 and 4.5·10 8 respectively. The presented results clearly indicate flow types and also demonstrate augmented heat transfer in dependence on magnetic induction gradient. Detailed analysis of flow transition to turbulent state was compared with transition line for natural convection reported in literature. The transition to turbulence in the case of thermo-magnetic convection of paramagnetic fluid was in very good agreement with transition in the case of natural convection.

Some studies on Fourier analysis in students experiment

OpenAIRE

大崎, 正雄

2016-01-01

Here we give some troubles in teaching and their solutions occured during the Software Science Experiment course, which is opened for the 4th semester in the Department of Software Science. One of the subjects of this experiment course is Fourier analysis using MyPC. Some students are not familiar with calculating the integration of sinusoidal function, and also some need support for drawing graphs with MS Excel. Typical mistakes and their settlements are given.

Least-squares calibration method based on a universal phase and height mapping formula in Fourier transform profilometry

International Nuclear Information System (INIS)

Wen, Yongfu; Cheng, Haobo; Gao, Ya; Zhang, Huijing; Feng, Yunpeng; Pan, Baozhu

2011-01-01

In Fourier transform profilometry (FTP), we perform a strict theoretical analysis of the phase–height mapping relationship and give a universal calculation formula in which the constraints on the experimental setup are removed. In that case, the projector and camera can be located arbitrarily to get better information on fringes, which makes the system easy to manipulate and improves the speed of measurement. As the relationship between the phase and height distribution depends on system parameters (such as the relative position of the projector and camera) which are difficult to obtain, we propose a least-squares calibration approach for FTP, which can avoid measuring the system parameters directly. Both the simulation and experimental results prove that the 3D shape of the tested objects can be reconstructed exactly by using the calculation formula and calibration method, and that the system has better universality

Fourier analysis of cerebrospinal fluid flow velocities: MR imaging study. The Scandinavian Flow Group

DEFF Research Database (Denmark)

Thomsen, C; Ståhlberg, F; Stubgaard, M

1990-01-01

images. The phase information in the resultant image was converted to flow velocity with a calibration curve with the slope 26.5 radian.m-1.sec. The velocity versus time function was Fourier transformed and a continuous curve was fitted to the measured data with use of the first three harmonics...

Fourier techniques in X-ray timing

NARCIS (Netherlands)

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

Fourier series, Fourier transform and their applications to mathematical physics

CERN Document Server

Serov, Valery

2017-01-01

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

Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.

Science.gov (United States)

Caple, Jodi; Byrd, John; Stephan, Carl N

2017-11-01

The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.

Fourier-transform ghost imaging with pure far-field correlated thermal light

International Nuclear Information System (INIS)

Liu Honglin; Shen Xia; Han Shensheng; Zhu Daming

2007-01-01

Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed

Aliasless fresnel transform image reconstruction in phase scrambling fourier transform technique by data interpolation

International Nuclear Information System (INIS)

Yamada, Yoshifumi; Liu, Na; Ito, Satoshi

2006-01-01

The signal in the Fresnel transform technique corresponds to a blurred one of the spin density image. Because the amplitudes of adjacent sampled signals have a high interrelation, the signal amplitude at a point between sampled points can be estimated with a high degree of accuracy even if the sampling is so coarse as to generate aliasing in the reconstructed images. In this report, we describe a new aliasless image reconstruction technique in the phase scrambling Fourier transform (PSFT) imaging technique in which the PSFT signals are converted to Fresnel transform signals by multiplying them by a quadratic phase term and are then interpolated using polynomial expressions to generate fully encoded signals. Numerical simulation using MR images showed that almost completely aliasless images are reconstructed by this technique. Experiments using ultra-low-field PSFT MRI were conducted, and aliasless images were reconstructed from coarsely sampled PSFT signals. (author)

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

Science.gov (United States)

Mohanan, Sharika; Srivastava, Atul

2014-04-10

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

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

Energy Technology Data Exchange (ETDEWEB)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net [NASA Ames Research Center, Astrobiology and Space Science Division, Moffett Field, CA 94035 (United States)

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

International Nuclear Information System (INIS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Image security based on iterative random phase encoding in expanded fractional Fourier transform domains

Science.gov (United States)

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.

Analysis of cigarette smoke by Fourier transform infrared spectrometry

Energy Technology Data Exchange (ETDEWEB)

Maddox, W.L. (Oak Ridge National Lab., TN); Mamantov, G.

1977-02-01

The application of Fourier transform infrared spectrometry (FT-IR) to the quantitative determination of several components in the gas phase of whole, dilute tobacco smoke was demonstrated. The 18-cm absorption cell was part of a cigarette smoking system similar to the intermittent inhalation exposure devices used in smoking and health research with rodents. Concentrations were measured for carbon monoxide, carbon dioxide, methane, ethylene, and methanol in 7 to 22% smoke. The precision of a measurement in 22% smoke ranged from 3% for carbon dioxide to 34% for ethylene. Absorbances measured for isoprene and hydrogen cyanide followed expected concentrations in different cigarette smokes. It was shown that the concentrations of these components remain constant during a 30-s hold-up following each puff on the cigarettes.

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

Science.gov (United States)

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

1999-01-01

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

Fourier-muunnoksesta

OpenAIRE

NIEMELÄ, EERO

2008-01-01

Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...

Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform

Directory of Open Access Journals (Sweden)

Zohreh Moghareh Abed

2010-01-01

Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.

Fourier X-ray line shape analysis of lattice defects from a single reflection

International Nuclear Information System (INIS)

Misra, N.K.; Bhanumurthy, K.

1981-01-01

A method of single reflection Fourier analysis has been described considering the fact that the rms strain (averaged over a distance) is not independent of averaging distance. Following the procedure of N.K. Misra and T.B. Ghosh (1976) and considering the initial slopes of dAsub(L)/dL against L curves, (Asub(L) is the Lsub(th) order Fourier coefficient) the effective size of the coherently diffracting domains and the rms strain in them are determined. The results of this analysis for pure Ti and Ag-3.55% Ga, Ag-15% In and Cu-12.46% Ge alloys compare fairly well with those obtained from different multiple reflections techniques. (author)

Elliptic Fourier analysis of crown shapes in Quercus petraea trees

Directory of Open Access Journals (Sweden)

Ovidiu Hâruţa

2011-02-01

Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage developmentof the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, mass center, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.

Elliptic Fourier analysis of crown shapes in Quercus petraea trees

Directory of Open Access Journals (Sweden)

Ovidiu Hâruţa

2011-06-01

Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage development of the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, centroid position, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations. 

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...

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 Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

Science.gov (United States)

Debnath, Lokenath

2012-01-01

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

ANALYSIS OF NON-FOURIER THERMAL BEHAVIOUR FOR MULTI-LAYER SKIN MODEL

Directory of Open Access Journals (Sweden)

Kuo-Chi Liu

2011-01-01

Full Text Available This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes' model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.

Automatic picking of the first arrival event using the unwrapped-phase of the Fourier transformed wavefield

KAUST Repository

Choi, Yun Seok

2011-01-01

First-arrival picking has long suffered from cycle skipping, especially when the first arrival is contaminated with noise or have experienced complex near surface phenomena. We propose a new algorithm for automatic picking of first arrivals using an approach based on unwrapping the phase. We unwrap the phase by taking the derivative of the Fourier-transformed wavefield with respect to the angular frequency and isolate its amplitude component. To do so, we first apply a damping function to the seismic trace, calculate the derivative of the wavefield with respect to the angular frequency, divide the derivative of wavefield by the wavefield itself, and finally take its imaginary part. We compare our derivative approach to the logarithmic one and show that the derivative approach does not suffer from the phase wrapping or cycle-skipping effects. Numerical examples show that our automatic picking algorithm gives convergent and reliable results for the noise-free synthetic data and noisy field data. © 2011 Society of Exploration Geophysicists.

Fourier spectral of PalmCode as descriptor for palmprint recognition

NARCIS (Netherlands)

Ruan, Qiuqi; Spreeuwers, Lieuwe Jan; Veldhuis, Raymond N.J.; Mu, Meiru

Study on automatic person recognition by palmprint is currently a hot topic. In this paper, we propose a novel palmprint recognition method by transforming the typical palmprint phase code feature into its Fourier frequency domain. The resulting real-valued Fourier spectral features are further

Vibrational analysis of Fourier transform spectrum of the B u )–X g ...

Indian Academy of Sciences (India)

improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and r-centroid values. Keywords. Fourier transform spectroscopy; electronic spectrum of selenium dimer; vibrational analysis; Franck–Condon factor; r-centroid values.

Extending Single-Molecule Microscopy Using Optical Fourier Processing

Science.gov (United States)

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

Quantization error of CCD cameras and their influence on phase calculation in fringe pattern analysis.

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Skydan, Oleksandr A; Lilley, Francis; Lalor, Michael J; Burton, David R

2003-09-10

We present an investigation into the phase errors that occur in fringe pattern analysis that are caused by quantization effects. When acquisition devices with a limited value of camera bit depth are used, there are a limited number of quantization levels available to record the signal. This may adversely affect the recorded signal and adds a potential source of instrumental error to the measurement system. Quantization effects also determine the accuracy that may be achieved by acquisition devices in a measurement system. We used the Fourier fringe analysis measurement technique. However, the principles can be applied equally well for other phase measuring techniques to yield a phase error distribution that is caused by the camera bit depth.

Adaptive synchrosqueezing based on a quilted short-time Fourier transform

Science.gov (United States)

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.

Spurious results from Fourier analysis of data with closely spaced frequencies

International Nuclear Information System (INIS)

Loumos, G.L.; Deeming, T.J.

1978-01-01

It is shown how erroneous results can occur using some period-finding methods, such as Fourier analysis, on data containing closely spaced frequencies. The frequency spacing accurately resolvable with data of length T is increased from the standard value of about 1/T quoted in the literature to approximately 1.5/T. (Auth.)

Image encryption based on fractal-structured phase mask in fractional Fourier transform domain

Science.gov (United States)

Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-04-01

We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.

Fourier Transform Mass Spectrometry

Science.gov (United States)

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

Chemical phase analysis of seed mediated synthesized anisotropic silver nanoparticles

International Nuclear Information System (INIS)

Bharti, Amardeep; Goyal, Navdeep; Singh, Suman; Singla, M. L.

2015-01-01

Noble-metal nanoparticles are of great interest because of its broad applications almost in every stream (i.e. biology, chemistry and engineering) due to their unique size/shape dependant properties. In this paper, chemical phase of seed mediated synthesized anisotropic silver nanoparticle (AgNPs) has been investigated via fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA). These nanaoparticles were synthesized by seed-growth method controlled by urea and dextrose results to highly stable 12-20 nm particle size revealed by zeta potential and transmission electron microscopy (TEM)

Microstructure imaging of the YBCO thin film/MgO substrate interface: HRTEM and Fourier analysis of the Moire fringe pattern

International Nuclear Information System (INIS)

Auzary, S.; Pailloux, F.; Denanot, M.F.; Gaboriaud, R.J.

1998-01-01

Detailed microstructural aspects of the interface between YBaCuO thin films and MgO substrate are studied by means of a Fourier analysis of Moire fringe pattern obtained from HRTEM investigations of plan view samples. The main features of the observations are large, well oriented crystallographic domains surrounded by wide boundaries. HRTEM investigations together with the Fourier analysis show evidence of both orthorhombic and pseudo-tetragonal structure in the YBaCuO film. An accommodation mechanism is suggested from the Fourier analysis of the Moire fringe pattern. (orig.)

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited].

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Takeda, Mitsuo

2013-01-01

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

Observation of superconducting fluxons by transmission electron microscopy: A Fourier space approach to calculate the electron optical phase shifts and images

International Nuclear Information System (INIS)

Beleggia, M.; Pozzi, G.

2001-01-01

An approach is presented for the calculation of the electron optical phase shift experienced by high-energy electrons in a transmission electron microscope, when they interact with the magnetic field associated with superconducting fluxons in a thin specimen tilted with respect to the beam. It is shown that by decomposing the vector potential in its Fourier components and by calculating the phase shift of each component separately, it is possible to obtain the Fourier transform of the electron optical phase shift, which can be inverted either analytically or numerically. It will be shown how this method can be used to recover the result, previously obtained by the real-space approach, relative to the case of a straight flux tube perpendicular to the specimen surfaces. Then the method is applied to the case of a London fluxon in a thin film, where the bending and the broadening of the magnetic-field lines due to the finite specimen thickness are now correctly taken into account and not treated approximately by means of a parabolic fit. Finally, it will be shown how simple models for the pancake structure of the fluxon can be analyzed within this framework and the main features of electron transmission images predicted

Evaluation of alias-less reconstruction by pseudo-parallel imaging in a phase-scrambling fourier transform technique

International Nuclear Information System (INIS)

Ito, Satoshi; Kawawa, Yasuhiro; Yamada, Yoshifumi

2010-01-01

We propose an image reconstruction technique in which parallel image reconstruction is performed based on the sensitivity encoding (SENSE) algorithm using only a single set of signals. The signal obtained in the phase-scrambling Fourier transform (PSFT) imaging technique can be transformed to the signal described by the Fresnel transform of the objects, which is known as the diffracted wave-front equation of the object in acoustics or optics. Since the Fresnel transform is a convolution integral on the object space, the space where the PSFT signal exists can be considered as both in the Fourier domain and in the object domain. This notable feature indicates that weighting functions corresponding to the sensitivity of radiofrequency (RF) coils can be approximately given in the PSFT signal space. Therefore, we can obtain two folded images from a single set of signals with different weighting functions, and image reconstruction based on the SENSE parallel imaging algorithm is possible using a series of folded images. Simulation and experimental studies showed that almost alias-free images can be synthesized using a single signal that does not satisfy the sampling theorem. (author)

Fourier series

CERN Document Server

Tolstov, Georgi P

1962-01-01

Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie

Non-Harmonic Fourier Analysis for bladed wheels damage detection

Science.gov (United States)

Neri, P.; Peeters, B.

2015-11-01

The interaction between bladed wheels and the fluid distributed by the stator vanes results in cyclic loading of the rotating components. Compressors and turbines wheels are subject to vibration and fatigue issues, especially when resonance conditions are excited. Even if resonance conditions can be often predicted and avoided, high cycle fatigue failures can occur, causing safety issues and economic loss. Rigorous maintenance programs are then needed, forcing the system to expensive shut-down. Blade crack detection methods are beneficial for condition-based maintenance. While contact measurement systems are not always usable in exercise conditions (e.g. high temperature), non-contact methods can be more suitable. One (or more) stator-fixed sensor can measure all the blades as they pass by, in order to detect the damaged ones. The main drawback in this situation is the short acquisition time available for each blade, which is shortened by the high rotational speed of the components. A traditional Discrete Fourier Transform (DFT) analysis would result in a poor frequency resolution. A Non-Harmonic Fourier Analysis (NHFA) can be executed with an arbitrary frequency resolution instead, allowing to obtain frequency information even with short-time data samples. This paper shows an analytical investigation of the NHFA method. A data processing algorithm is then proposed to obtain frequency shift information from short time samples. The performances of this algorithm are then studied by experimental and numerical tests.

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

Science.gov (United States)

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.

SU(2 and SU(1,1 Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms

Directory of Open Access Journals (Sweden)

Maurice R. Kibler

2010-07-01

Full Text Available We propose a group-theoretical approach to the generalized oscillator algebra Aκ recently investigated in J. Phys. A: Math. Theor. 2010, 43, 115303. The case κ ≥ 0 corresponds to the noncompact group SU(1,1 (as for the harmonic oscillator and the Pöschl-Teller systems while the case κ < 0 is described by the compact group SU(2 (as for the Morse system. We construct the phase operators and the corresponding temporally stable phase eigenstates for Aκ in this group-theoretical context. The SU(2 case is exploited for deriving families of mutually unbiased bases used in quantum information. Along this vein, we examine some characteristics of a quadratic discrete Fourier transform in connection with generalized quadratic Gauss sums and generalized Hadamard matrices.

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

Energy Technology Data Exchange (ETDEWEB)

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

1984-06-01

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

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

International Nuclear Information System (INIS)

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

1984-01-01

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

Short-time variations of the solar neutrino luminosity (Fourier analysis of the argon-37 production rate data)

International Nuclear Information System (INIS)

Haubold, H.J.; Gerth, E.

1985-01-01

We continue the Fourier analysis of the argon-37 production rate for runs 18--80 observed in Davis' well known solar neutrino experiment. The method of Fourier analysis with the unequally-spaced data of Davis and associates is described and the discovered periods we compare with our recently published results for the analysis of runs 18--69 (Haubold and Gerth, 1983). The harmonic analysis of the data of runs 18--80 shows time variations of the solar neutrino flux with periods π = 8.33; 5.26; 2.13; 1.56; 0.83; 0.64; 0.54; and 0.50 years, respectively, which confirms our earlier computations

Encoding plaintext by Fourier transform hologram in double random phase encoding using fingerprint keys

Science.gov (United States)

Takeda, Masafumi; Nakano, Kazuya; Suzuki, Hiroyuki; Yamaguchi, Masahiro

2012-09-01

It has been shown that biometric information can be used as a cipher key for binary data encryption by applying double random phase encoding. In such methods, binary data are encoded in a bit pattern image, and the decrypted image becomes a plain image when the key is genuine; otherwise, decrypted images become random images. In some cases, images decrypted by imposters may not be fully random, such that the blurred bit pattern can be partially observed. In this paper, we propose a novel bit coding method based on a Fourier transform hologram, which makes images decrypted by imposters more random. Computer experiments confirm that the method increases the randomness of images decrypted by imposters while keeping the false rejection rate as low as in the conventional method.

Encoding plaintext by Fourier transform hologram in double random phase encoding using fingerprint keys

International Nuclear Information System (INIS)

Takeda, Masafumi; Nakano, Kazuya; Suzuki, Hiroyuki; Yamaguchi, Masahiro

2012-01-01

It has been shown that biometric information can be used as a cipher key for binary data encryption by applying double random phase encoding. In such methods, binary data are encoded in a bit pattern image, and the decrypted image becomes a plain image when the key is genuine; otherwise, decrypted images become random images. In some cases, images decrypted by imposters may not be fully random, such that the blurred bit pattern can be partially observed. In this paper, we propose a novel bit coding method based on a Fourier transform hologram, which makes images decrypted by imposters more random. Computer experiments confirm that the method increases the randomness of images decrypted by imposters while keeping the false rejection rate as low as in the conventional method. (paper)

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

International Nuclear Information System (INIS)

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-01-01

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

Tomographic phase analysis to detect the site of accessory conduction pathway in Wolff-Parkinson-White syndrome

International Nuclear Information System (INIS)

Nakajima, K.; Bunko, H.; Tada, A.; Tonami, N.; Taki, J.; Nanbu, I.; Hisada, K.; Misaki, T.; Iwa, T.

1984-01-01

Phase analysis has been applied to Wolff-Parkinson-White syndrome (WPW) to detect the site of accessory conduction pathway (ACP); however, there was a limitation to estimate the precise location of ACP by planar phase analysis. In this study, the authors applied phase analysis to gated blood pool tomography. Twelve patients with WPW who underwent epicardial mapping and surgical division of ACP were studied by both of gated emission computed tomography (GECT) and routine gated blood pool study (GBPS). The GBPS was performed with Tc-99m red blood cells in multiple projections; modified left anterior oblique, right anterior oblique and/or left lateral views. In GECT, short axial, horizontal and vertical long axial blood pool images were reconstructed. Phase analysis was performed using fundamental frequency of the Fourier transform in both GECT and GBPS images, and abnormal initial contractions on both the planar and tomographic phase analysis were compared with the location of surgically confirmed ACPs. In planar phase analysis, abnormal initial phase was identified in 7 out of 12 (58%) patients, while in tomographic phase analysis, the localization of ACP was predicted in 11 out of 12 (92%) patients. Tomographic phase analysis is superior to planar phase images in 8 out of 12 patients to estimate the location of ACP. Phase analysis by GECT can avoid overlap of blood pool in cardiac chambers and has advantage to identify the propagation of phase three-dimensionally. Tomographic phase analysis is a good adjunctive method for patients with WPW to estimate the site of ACP

Tomographic phase analysis to detect the site of accessory conduction pathway in Wolff-Parkinson-White syndrome

Energy Technology Data Exchange (ETDEWEB)

Nakajima, K.; Bunko, H.; Tada, A.; Tonami, N.; Taki, J.; Nanbu, I.; Hisada, K.; Misaki, T.; Iwa, T.

1984-01-01

Phase analysis has been applied to Wolff-Parkinson-White syndrome (WPW) to detect the site of accessory conduction pathway (ACP); however, there was a limitation to estimate the precise location of ACP by planar phase analysis. In this study, the authors applied phase analysis to gated blood pool tomography. Twelve patients with WPW who underwent epicardial mapping and surgical division of ACP were studied by both of gated emission computed tomography (GECT) and routine gated blood pool study (GBPS). The GBPS was performed with Tc-99m red blood cells in multiple projections; modified left anterior oblique, right anterior oblique and/or left lateral views. In GECT, short axial, horizontal and vertical long axial blood pool images were reconstructed. Phase analysis was performed using fundamental frequency of the Fourier transform in both GECT and GBPS images, and abnormal initial contractions on both the planar and tomographic phase analysis were compared with the location of surgically confirmed ACPs. In planar phase analysis, abnormal initial phase was identified in 7 out of 12 (58%) patients, while in tomographic phase analysis, the localization of ACP was predicted in 11 out of 12 (92%) patients. Tomographic phase analysis is superior to planar phase images in 8 out of 12 patients to estimate the location of ACP. Phase analysis by GECT can avoid overlap of blood pool in cardiac chambers and has advantage to identify the propagation of phase three-dimensionally. Tomographic phase analysis is a good adjunctive method for patients with WPW to estimate the site of ACP.

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

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

Science.gov (United States)

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

2009-01-01

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

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

Science.gov (United States)

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

The fit of an X-ray diffraction profile by Fourier analysis

International Nuclear Information System (INIS)

Bourniquel, B.; Feron, J.

1985-01-01

The fast Fourier transform algorithm commonly used for line profile analysis requires a list of values of the diffracted intensity with constant sintheta step; raw data are usually obtained at constant 2theta step; to interpolate between the measured values an analytic expression of the profile function is very useful. Statistical estimation is used to fit an analytic function to data; the only assumption made is the continuity of this function and no critical initialization is needed. Three different expressions are used: a Fourier sum for the peak and two polynomials of a suitable variable for the tails; the algorithm provides continuity for the function and its first derivative. Simulated examples using a Lorentzian and a Gaussian function are given and several criteria of goodness of fit are examined. The program runs on a PDP 11/03 digital computer with only 45 kbytes available memory. (orig.)

Accounting for the Spatial Observation Window in the 2-D Fourier Transform Analysis of Shear Wave Attenuation.

Science.gov (United States)

Rouze, Ned C; Deng, Yufeng; Palmeri, Mark L; Nightingale, Kathryn R

2017-10-01

Recent measurements of shear wave propagation in viscoelastic materials have been analyzed by constructing the 2-D Fourier transform (2DFT) of the shear wave signal and measuring the phase velocity c(ω) and attenuation α(ω) from the peak location and full width at half-maximum (FWHM) of the 2DFT signal at discrete frequencies. However, when the shear wave is observed over a finite spatial range, the 2DFT signal is a convolution of the true signal and the observation window, and measurements using the FWHM can yield biased results. In this study, we describe a method to account for the size of the spatial observation window using a model of the 2DFT signal and a non-linear, least-squares fitting procedure to determine c(ω) and α(ω). Results from the analysis of finite-element simulation data agree with c(ω) and α(ω) calculated from the material parameters used in the simulation. Results obtained in a viscoelastic phantom indicate that the measured attenuation is independent of the observation window and agree with measurements of c(ω) and α(ω) obtained using the previously described progressive phase and exponential decay analysis. Copyright © 2017 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Fourier transform ion cyclotron resonance mass spectrometry

Science.gov (United States)

Marshall, Alan G.

1998-06-01

As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.

Fourier Transform Infrared Spectroscopy as a Tool in Analysis of Proteus mirabilis Endotoxins.

Science.gov (United States)

Żarnowiec, Paulina; Czerwonka, Grzegorz; Kaca, Wiesław

2017-01-01

Fourier transform infrared spectroscopy (FT-IR) was used to scan whole bacterial cells as well as lipopolysaccharides (LPSs, endotoxins) isolated from them. Proteus mirabilis cells, with chemically defined LPSs, served as a model for the ATR FT-IR method. The paper focuses on three steps of infrared spectroscopy: (1) sample preparation, (2) IR scanning, and (3) multivariate analysis of IR data (principal component analysis, PCA).

An Interactive System For Fourier Analysis Of Artichoke Flower Shape.

Science.gov (United States)

Impedovo, Sebastiano; Fanelli, Anna M.; Ligouras, Panagiotis

1984-06-01

In this paper we present an interactive system which allows the Fourier analysis of the artichoke flower-head profile. The system consistsof a DEC pdp 11/34 computer with both a a track-following device and a Tektronix 4010/1 graphic and alpha numeric display on-line. Some experiments have been carried out taking into account some different parental types of artichoke flower-head samples. It is shown here that a narrow band of only eight harmonics is sufficient to classify different artichoke flower shapes.

Vibrational analysis of Fourier transform spectrum of the B 3− u (0

Indian Academy of Sciences (India)

... microwave, was recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.035 cm-1. Vibrational constants were improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and -centroid values.

Evaluation of natural mandibular shape asymmetry: an approach by using elliptical Fourier analysis.

Science.gov (United States)

Niño-Sandoval, Tania C; Morantes Ariza, Carlos F; Infante-Contreras, Clementina; Vasconcelos, Belmiro Ce

2018-04-05

The purpose of this study was to demonstrate that asymmetry is a natural occurring phenomenon in the mandibular shape by using elliptical Fourier analysis. 164 digital orthopantomographs from Colombian patients of both sexes aged 18 to 25 years were collected. Curves from left and right hemimandible were digitized. An elliptical Fourier analysis was performed with 20 harmonics. In the general sexual dimorphism a principal component analysis (PCA) and a hotelling T 2 from the multivariate warp space were employed. Exploratory analysis of general asymmetry and sexual dimorphism by side was made with a Procrustes Fit. A non-parametric multivariate analysis of variance (MANOVA) was applied to assess differentiation of skeletal classes of each hemimandible, and a Procrustes analysis of variance (ANOVA) was applied to search any relation between skeletal class and side in both sexes. Significant values were found in general asymmetry, general sexual dimorphism, in dimorphism by side (p < 0.0001), asymmetry by sex, and differences between Class I, II, and III (p < 0.005). However, a relation of skeletal classes and side was not found. The mandibular asymmetry by shape is present in all patients and should not be articulated exclusively to pathological processes, therefore, along with sexual dimorphism and differences between skeletal classes must be taken into account for improving mandibular prediction systems.

Fourier analysis and its applications

CERN Document Server

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

The deconvolution of Doppler-broadened positron annihilation measurements using fast Fourier transforms and power spectral analysis

International Nuclear Information System (INIS)

Schaffer, J.P.; Shaughnessy, E.J.; Jones, P.L.

1984-01-01

A deconvolution procedure which corrects Doppler-broadened positron annihilation spectra for instrument resolution is described. The method employs fast Fourier transforms, is model independent, and does not require iteration. The mathematical difficulties associated with the incorrectly posed first order Fredholm integral equation are overcome by using power spectral analysis to select a limited number of low frequency Fourier coefficients. The FFT/power spectrum method is then demonstrated for an irradiated high purity single crystal sapphire sample. (orig.)

Evaluation of the response of a round hole scintillation camera collimator by the Fourier analysis method

International Nuclear Information System (INIS)

Hernandez, A.; Millan, S.; Yzuel, M.J.

1986-01-01

The Fourier analysis method was used to investigate the response of scintillation camera collimators with parallel holes. This method which takes into account the septal penetration was applied to the case of round hole collimators having a hexagonal distribution. Modulation transfer functions, MTF have been determined to verify the accuracy of the computed Fourier coefficients of the collimator function. Comparisons between the geometric and the penetrating plus geometric transfer function are shown for round and hexagonal holes. (author)

Some consequences of the Fourier analysis on the Lorentz group for relativistic quantum mechanics

International Nuclear Information System (INIS)

Mavrodiev, S.Ch.

1974-01-01

On the basis of the analogy between the nonrelativistic and relativistic Fourier analysis the uncertainty relation for rapidity and relativistic relative coordinate is formaly derived. A geometricla interpretation of the behaviour of the elastic scattering differential cross section is given too

CHARACTERIZATION OF AMBIENT PM2.5 AEROSOL AT A SOUTHEASTERN US SITE: FOURIER TRANSFORM INFRARED ANALYSIS OR PARTICLE PHASE

Science.gov (United States)

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....

The Fourier analysis applied to the relationship between (7)Be activity in the Serbian atmosphere and meteorological parameters.

Science.gov (United States)

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.

Analysis of the intergranular fracture surface by the Fourier spectrum method

Energy Technology Data Exchange (ETDEWEB)

Hao Yao; Tian Jifeng; Wang Zhongguang (National Lab. for Fatigue and Fracture of Materials, Inst. of Metal Research, Academia Sinica, Shen Yang (China))

1991-11-30

A quantitative analysis of the fracture surface of a 1045 steel was undertaken in order to relate important microstructural features to brittle intergranular fractures in the steel. It was found that the character of the profile was not random but periodic. There is a direct correspondence between the Fourier spectrum of the profile and the microstructure features. Utilization of secondary-electron line scanning facilitated the analysis of the fracture surface in this case. The results of the analysis from both the profile and the scanning line showed that the first autocorrelation length is related to the average grain size and that the total power corresponds to the impact energy of the fracture. (orig.).

The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne).

Science.gov (United States)

Harrison, John A

2008-09-04

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.

Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

OpenAIRE

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.

Detection of fast oscillating magnetic fields using dynamic multiple TR imaging and Fourier analysis.

Directory of Open Access Journals (Sweden)

Ki Hwan Kim

Full Text Available Neuronal oscillations produce oscillating magnetic fields. There have been trials to detect neuronal oscillations using MRI, but the detectability in in vivo is still in debate. Major obstacles to detecting neuronal oscillations are (i weak amplitudes, (ii fast oscillations, which are faster than MRI temporal resolution, and (iii random frequencies and on/off intervals. In this study, we proposed a new approach for direct detection of weak and fast oscillating magnetic fields. The approach consists of (i dynamic acquisitions using multiple times to repeats (TRs and (ii an expanded frequency spectral analysis. Gradient echo echo-planar imaging was used to test the feasibility of the proposed approach with a phantom generating oscillating magnetic fields with various frequencies and amplitudes and random on/off intervals. The results showed that the proposed approach could precisely detect the weak and fast oscillating magnetic fields with random frequencies and on/off intervals. Complex and phase spectra showed reliable signals, while no meaningful signals were observed in magnitude spectra. A two-TR approach provided an absolute frequency spectrum above Nyquist sampling frequency pixel by pixel with no a priori target frequency information. The proposed dynamic multiple-TR imaging and Fourier analysis are promising for direct detection of neuronal oscillations and potentially applicable to any pulse sequences.

Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain

Science.gov (United States)

Sui, Liansheng; Lu, Haiwei; Ning, Xiaojuan; Wang, Yinghui

2014-02-01

A double-image encryption scheme is proposed based on an asymmetric technique, in which the encryption and decryption processes are different and the encryption keys are not identical to the decryption ones. First, a phase-only function (POF) of each plain image is retrieved by using an iterative process and then encoded into an interim matrix. Two interim matrices are directly modulated into a complex image by using the convolution operation in the fractional Fourier transform (FrFT) domain. Second, the complex image is encrypted into the gray scale ciphertext with stationary white-noise distribution by using the FrFT. In the encryption process, three random phase functions are used as encryption keys to retrieve the POFs of plain images. Simultaneously, two decryption keys are generated in the encryption process, which make the optical implementation of the decryption process convenient and efficient. The proposed encryption scheme has high robustness to various attacks, such as brute-force attack, known plaintext attack, cipher-only attack, and specific attack. Numerical simulations demonstrate the validity and security of the proposed method.

Fourier-Hermite communications; where Fourier meets Hermite

NARCIS (Netherlands)

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

Fourier analysis of heart SPECT slices: from remodelation to function?

International Nuclear Information System (INIS)

Zigman, M.; Prpic, H.; Lokner, V.

1994-01-01

The aim of this study was to determine character of the spatial distribution of marked erythrocytes in heart chambers, lungs and great blood vessels in relation to function of the left and right heart. Investigation included total of 142 subjects, 28 of which were without subjective and clinical signs of heart disease as well as 56 after myocardial infarction (30 of anterior localization, 26 of inferior infarction), 35 with predominant left heart disease (aortic valve disease, dilatative myocardiopathy, etc.) and 23 with predominant right heart disease (atrial septal defect, mitral valve disease). Radionuclide ventriculography (RNV) at rest, and thorax SPECT were performed in all subjects with 740 MBq Tc-99m after in vivo erythrocyte labelling with pyrophosphate. Ultrasound investigation was performed on all the subjects with heart disease and 87 of them underwent invasive cardiac investigation. RNV analysis revealed scintigraphic data on left and right ventricle: global ejection fraction (GEF), end-systolic volume (ESV), end-diastolic volume (EDV), fast tilling rate (FFR), fast emptying rate (FER) as well as regional wall motion shortening. Reconstruction of 64x64x8 SPECT images resulted in 3x64 slices (transversal, coronal and sagittal slices). Fourier analysis of 20-32 reconstructed slices in all three dimensions gave amplitude image of the intensity distribution of marked erythrocytes in heart chambers lungs and great blood vessels as well as phase display of spatial localization of regional amplitude values. Results of joint ROC curves constructed for detection, localization and character of heart disease in all subjects revealed significant clinical information content of SPECT data. Evaluation of RI retention using amplitude images in 3D provides insight in regional changes of volume, particular for atrial and lung involvement. (author)

Fourier transforms in radar and signal processing

CERN Document Server

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

Radial artery pulse waveform analysis based on curve fitting using discrete Fourier series.

Science.gov (United States)

Jiang, Zhixing; Zhang, David; Lu, Guangming

2018-04-19

Radial artery pulse diagnosis has been playing an important role in traditional Chinese medicine (TCM). For its non-invasion and convenience, the pulse diagnosis has great significance in diseases analysis of modern medicine. The practitioners sense the pulse waveforms in patients' wrist to make diagnoses based on their non-objective personal experience. With the researches of pulse acquisition platforms and computerized analysis methods, the objective study on pulse diagnosis can help the TCM to keep up with the development of modern medicine. In this paper, we propose a new method to extract feature from pulse waveform based on discrete Fourier series (DFS). It regards the waveform as one kind of signal that consists of a series of sub-components represented by sine and cosine (SC) signals with different frequencies and amplitudes. After the pulse signals are collected and preprocessed, we fit the average waveform for each sample using discrete Fourier series by least squares. The feature vector is comprised by the coefficients of discrete Fourier series function. Compared with the fitting method using Gaussian mixture function, the fitting errors of proposed method are smaller, which indicate that our method can represent the original signal better. The classification performance of proposed feature is superior to the other features extracted from waveform, liking auto-regression model and Gaussian mixture model. The coefficients of optimized DFS function, who is used to fit the arterial pressure waveforms, can obtain better performance in modeling the waveforms and holds more potential information for distinguishing different psychological states. Copyright © 2018 Elsevier B.V. All rights reserved.

OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation

DEFF Research Database (Denmark)

Palushani, Evarist; Richter, T.; Ludwig, R.

2012-01-01

We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information.......We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information....

Fourier techniques for an analysis of eclipsing binary light curves. Pt. 6b

International Nuclear Information System (INIS)

Demircan, O.

1980-01-01

This is a continuation of a previous paper which appeared in this journal (Demircan, 1980b) and aims at ascertaining some other relations between the integral transforms of the light curves of eclipsing binary systems. The appropriate use of these relations should facilitate the numerical computations for an analysis of eclipsing binary light curves by different Fourier techniques. (orig.)

Fourier transform NMR

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

Directional absorption by phased arrays of plasmonic nanoantennae probed with time-reversed Fourier microscopy

International Nuclear Information System (INIS)

Lozano, Gabriel; Barten, Tommy; Grzela, Grzegorz; Rivas, Jaime Gómez

2014-01-01

We demonstrate that an ordered array of aluminum nanopyramids, behaving as a phased array of optical antennae, strongly modifies light absorption in thin layers of dye molecules. Photoluminescence measurements as a function of the illumination angle are performed using a time-reversed Fourier microscope. This technique enables a variable-angle plane-wave illumination of nanostructures in a microscope-based setup. Our measurements reveal an enhancement of the light conversion in certain directions of illumination, which indicate the efficient diffractive coupling between the free space radiation and the surface plasmons. Numerical simulations confirm that surface modes supported by the periodic array enhance the intensity of the pump field in the space between particles, where the dye molecules are located, yielding a directional plasmonic-mediated enhancement of the optical absorption. This combined experimental and numerical characterization of the angular dependence of light absorption in nanostructures can be beneficial for the design and optimization of devices in which the harvesting of light plays a major role. (paper)

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

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....

Floor response spectra for multi-degree-of-freedom systems by Fourier transform

International Nuclear Information System (INIS)

Scanlan, R.H.; Sachs, K.

1975-01-01

A method of generating floor response spectra from a given ground response spectrum is given. This time-saving approach makes use of Fourier spectrum techniques and the randomness of phase angles. In matrix form a structure having many degrees-of-freedom is described by the equation of motion with M, C, K as the mass-, damping-, and stiffness matrices and Z being the acceleration time history of the earthquake and I a direction vector. If the Fourier spectrum FZ of the ground motion is known, then by standard methods the Fourier spectrum of the equipment response can be obtained. The assumption of random phase angles for the synthetic time history Z seems reasonable. The response is then also a superposition of cosine waves. Good agreement with time history methods is obtained. This method is much faster than time history methods, which are being used in most applications

An investigation of two-phase flow instability using wavelet signal extraction technique

International Nuclear Information System (INIS)

Shang Zhi; Yang Ruichang; Cao Xuewu; Yang Yanhua

2004-01-01

When the oscillation periods of the instability of two-phase flow are sought with traditional methods of signal analysis, generally the Fourier transform must be employed and then the oscillation periods will be gotten at the location of the local maximum amplitude of frequency transform. However, Fourier transform will be difficult to clearly analyze the unsteady signals especially when the signals include many peaks and the noise interference is not generated by white noise in many areas of practical engineering like the oscillation of the instability of two-phase flow. The most effective solving method for the difficulty of Fourier transform is to analyze the signals directly in time domain. Wavelet analysis is able to search out the periods from time domain directly. It also has more excellent local characteristics than Fourier analysis in the both of time and frequency domains. In this paper, not only is a direct detecting method of the oscillation periods successfully applied based on the wavelet signal extraction techniques, but also the oscillation of density wave type of TYPE I is found as a kind of oscillations with a high-frequency harmonization

Fourier techniques and applications

CERN Document Server

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 analysis algorithm for the posterior corneal keratometric data: clinical usefulness in keratoconus.

Science.gov (United States)

Sideroudi, Haris; Labiris, Georgios; Georgantzoglou, Kimon; Ntonti, Panagiota; Siganos, Charalambos; Kozobolis, Vassilios

2017-07-01

To develop an algorithm for the Fourier analysis of posterior corneal videokeratographic data and to evaluate the derived parameters in the diagnosis of Subclinical Keratoconus (SKC) and Keratoconus (KC). This was a cross-sectional, observational study that took place in the Eye Institute of Thrace, Democritus University, Greece. Eighty eyes formed the KC group, 55 eyes formed the SKC group while 50 normal eyes populated the control group. A self-developed algorithm in visual basic for Microsoft Excel performed a Fourier series harmonic analysis for the posterior corneal sagittal curvature data. The algorithm decomposed the obtained curvatures into a spherical component, regular astigmatism, asymmetry and higher order irregularities for averaged central 4 mm and for each individual ring separately (1, 2, 3 and 4 mm). The obtained values were evaluated for their diagnostic capacity using receiver operating curves (ROC). Logistic regression was attempted for the identification of a combined diagnostic model. Significant differences were detected in regular astigmatism, asymmetry and higher order irregularities among groups. For the SKC group, the parameters with high diagnostic ability (AUC > 90%) were the higher order irregularities, the asymmetry and the regular astigmatism, mainly in the corneal periphery. Higher predictive accuracy was identified using diagnostic models that combined the asymmetry, regular astigmatism and higher order irregularities in averaged 3and 4 mm area (AUC: 98.4%, Sensitivity: 91.7% and Specificity:100%). Fourier decomposition of posterior Keratometric data provides parameters with high accuracy in differentiating SKC from normal corneas and should be included in the prompt diagnosis of KC. © 2017 The Authors Ophthalmic & Physiological Optics © 2017 The College of Optometrists.

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.

Instantaneous lineshape analysis of Fourier domain mode-locked lasers.

Science.gov (United States)

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

2011-04-25

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

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 infrared microspectroscopy for the analysis of the biochemical composition of C. elegans worms.

Science.gov (United States)

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.

Error Analysis for Fourier Methods for Option Pricing

KAUST Repository

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

On Fourier re-expansions

OpenAIRE

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.

Spirometrically gated 133Xe ventilation imaging and phase analysis for assessment of regional lung function

International Nuclear Information System (INIS)

Inoue, Tomio

1984-01-01

The purpose of this study is to develop the technique of performing spirometrically gated 133 Xe ventilation imaging and to evaluate its clinical usefulness for the assessmentof regional ventilatory function in various lung diseases. Patients rebreathe d 133 Xe gas through the system with constant rates signaled by a metronom. The trigger signals from the patients were recorded in a minicomputer for 60 respiratory cycles simultaneously with posterior lung images. Functional images (phase analysis images) indicating phase and amplitude of regional ventilation were constructed by the first harmonic Fourier analysis. Materials included 13 normal volunteers and patients with COPD (24), lung cancer (5), pulmonary embolism (4) and others (20). In normal controls, phase analysis images before respiratory motion correction revealed gradual decrease in amplitude from base to apex with uniform phase distribution. The amplitude and phase distribution after respiratory motion correction became even more uniform. In patients with COPD, phase analysis images showed asymmetrical and irregular amplitude distribution with non-uniform phase distribution. The standard deviation (S.D.) of phase histogram correlated well with FEVsub(1.0)% (r=0.71, p<0.001) and down slope of flowvolume curve (r=0.55, p<0.001), and less prominently with %VC (r=0.42, p<0.01). Mean S.D. in patients with COPD (12.3+-6.5 degree, mean+-1 s.d.) was significantly larger than in normal controls (6.3+-1.5). Amplitude profile curve analysis revealed 83% sensitivity for the detection of abnormal spirometric respiratory function test. Data aquisition and processing of present method are rapid and easy to perform. The phase analysis of the gated ventilation images should prove useful in the clinical evaluation of patients with uneven ventilation such as COPD. (J.P.N.)

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

Science.gov (United States)

Levnajić, Zoran; Mezić, Igor

2015-05-01

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.

Elliptic Fourier Analysis of body shape variation of Hippocampus spp. (seahorse in Danajon Bank, Philippines

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.

Accurate determination of the diffusion coefficient of proteins by Fourier analysis with whole column imaging detection.

Science.gov (United States)

Zarabadi, Atefeh S; Pawliszyn, Janusz

2015-02-17

Analysis in the frequency domain is considered a powerful tool to elicit precise information from spectroscopic signals. In this study, the Fourier transformation technique is employed to determine the diffusion coefficient (D) of a number of proteins in the frequency domain. Analytical approaches are investigated for determination of D from both experimental and data treatment viewpoints. The diffusion process is modeled to calculate diffusion coefficients based on the Fourier transformation solution to Fick's law equation, and its results are compared to time domain results. The simulations characterize optimum spatial and temporal conditions and demonstrate the noise tolerance of the method. The proposed model is validated by its application for the electropherograms from the diffusion path of a set of proteins. Real-time dynamic scanning is conducted to monitor dispersion by employing whole column imaging detection technology in combination with capillary isoelectric focusing (CIEF) and the imaging plug flow (iPF) experiment. These experimental techniques provide different peak shapes, which are utilized to demonstrate the Fourier transformation ability in extracting diffusion coefficients out of irregular shape signals. Experimental results confirmed that the Fourier transformation procedure substantially enhanced the accuracy of the determined values compared to those obtained in the time domain.

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.

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.

Mapping agroecological zones and time lag in vegetation growth by means of Fourier analysis of time series of NDVI images

Science.gov (United States)

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.

Application of Fourier analysis to the study of roughness profiles of eroded samples

International Nuclear Information System (INIS)

Bethencourt, M.; Botana, F.J.; Calvino, J.J.; Marcos, M.; Rodriguez-Chacon, M.A.

1998-01-01

Fourier transforms are applied to analyse surface roughness profiles recorded on samples coming from erosion-corrosion essays. The information retrieved using this method clearly complements that revealed by the more classical roughness amplitude parameters. The analysis procedure here proposed can be applied not only to characterise the surface of corroded samples but, in general, to evaluate the quality of any surface after application of finishing treatments. (Author) 7 refs

Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨ θ⟩ directly from ⟨ θ2D⟩ by Fourier analysis.

Science.gov (United States)

Søndergaard, Anders Aspegren; Shepperson, Benjamin; Stapelfeldt, Henrik

2017-07-07

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos 2 θ⟩, directly from its two-dimensional counterpart, ⟨cos 2 θ 2D ⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos 2 θ 2D ⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos 2 θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos 2 θ 2D ⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos 2 θ⟩ is obtained and, finally, ⟨cos 2 θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos 2 θ⟩ trace from a measured ⟨cos 2 θ 2D ⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos 2 θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I 2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos 2 θ 2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos 2 θ 2D ⟩ and ⟨cos 2 θ⟩ in general.

Comparative measurement of collagen bundle orientation by Fourier analysis and semiquantitative evaluation: reliability and agreement in Masson's trichrome, Picrosirius red and confocal microscopy techniques.

Science.gov (United States)

Marcos-Garcés, V; Harvat, M; Molina Aguilar, P; Ferrández Izquierdo, A; Ruiz-Saurí, A

2017-08-01

Measurement of collagen bundle orientation in histopathological samples is a widely used and useful technique in many research and clinical scenarios. Fourier analysis is the preferred method for performing this measurement, but the most appropriate staining and microscopy technique remains unclear. Some authors advocate the use of Haematoxylin-Eosin (H&E) and confocal microscopy, but there are no studies comparing this technique with other classical collagen stainings. In our study, 46 human skin samples were collected, processed for histological analysis and stained with Masson's trichrome, Picrosirius red and H&E. Five microphotographs of the reticular dermis were taken with a 200× magnification with light microscopy, polarized microscopy and confocal microscopy, respectively. Two independent observers measured collagen bundle orientation with semiautomated Fourier analysis with the Image-Pro Plus 7.0 software and three independent observers performed a semiquantitative evaluation of the same parameter. The average orientation for each case was calculated with the values of the five pictures. We analyzed the interrater reliability, the consistency between Fourier analysis and average semiquantitative evaluation and the consistency between measurements in Masson's trichrome, Picrosirius red and H&E-confocal. Statistical analysis for reliability and agreement was performed with the SPSS 22.0 software and consisted of intraclass correlation coefficient (ICC), Bland-Altman plots and limits of agreement and coefficient of variation. Interrater reliability was almost perfect (ICC > 0.8) with all three histological and microscopy techniques and always superior in Fourier analysis than in average semiquantitative evaluation. Measurements were consistent between Fourier analysis by one observer and average semiquantitative evaluation by three observers, with an almost perfect agreement with Masson's trichrome and Picrosirius red techniques (ICC > 0.8) and a strong

Fast Fourier transformation in vibration analysis of physically active systems

International Nuclear Information System (INIS)

Hafeez, T.; Amir, M.; Farooq, U.; Day, P.

2003-01-01

Vibration of all physical systems may be expressed as the summation of an infinite number of sine and cosine terms known as Fourier series. The basic vibration analysis tool used is the frequency 'spectrum' (a graph of vibration where the amplitude of vibration is plotted against frequency). When a particular rotating component begins to fail, its vibration tends to increase. Spectra graphs are powerful diagnostic tool for detecting components' degradation. Spectra obtained with accelerometers located at the various locations on the components and their analysis in practice from rotating machines enable early detecting of incipient failure. Consequence of unexpected failure can be catastrophic and costly. This study provides basis to relate defective component by its constituent frequencies and then to the known discrete frequency of its 'signature' or 'thumbprint' to predict and verify the sustained dynamic behavior of machine designs harmful effects of forced vibration. The spectra for gearbox of a vane with teeth damaged fault are presented here which signified the importance of FFT analysis as diagnostic tool. This may be helpful to predictive maintenance of the machinery. (author)

Spirometrically gated /sup 133/Xe ventilation imaging and phase analysis for assessment of regional lung function

Energy Technology Data Exchange (ETDEWEB)

Inoue, Tomio (Kanto Teishin Hospital, Tokyo (Japan))

1984-10-01

The purpose of this study is to develop the technique of performing spirometrically gated /sup 133/Xe ventilation imaging and to evaluate its clinical usefulness for the assessment of regional ventilatory function in various lung diseases. Patients rebreathed /sup 133/Xe gas through the system with constant rates signaled by a metronome. The trigger signals from the patients were recorded in a minicomputer for 60 respiratory cycles simultaneously with posterior lung images. Functional images (phase analysis images) indicating phase and amplitude of regional ventilation were constructed by the first harmonic Fourier analysis. Materials included 13 normal volunteers and patients with COPD (24), lung cancer (5), pulmonary embolism (4) and others (20). In normal controls, phase analysis images before respiratory motion correction revealed gradual decrease in amplitude from base to apex with uniform phase distribution. The amplitude and phase distribution after respiratory motion correction became even more uniform. In patients with COPD, phase analysis images showed asymmetrical and irregular amplitude distribution with non-uniform phase distribution. The standard deviation (S.D.) of phase histogram correlated well with FEVsub(1.0)% (r=0.71, p < 0.001) and down slope of flow-volume curve (r=0.55, p < 0.001), and less prominently with %VC (r=0.42, p < 0.01). Mean S.D. in patients with COPD (12.3 +- 6.5 degree, mean+-1 s.d.) was significantly larger than in normal controls (6.3 +- 1.5). Amplitude profile curve analysis revealed 83% sensitivity for the detection of abnormal spirometric respiratory function test. Data aquisition and processing of present method are rapid and easy to perform. The phase analysis of the gated ventilation images should prove useful in the clinical evaluation of patients with uneven ventilation such as COPD.

Angular acceptance analysis of an infrared focal plane array with a built-in stationary Fourier transform spectrometer.

Science.gov (United States)

Gillard, Frédéric; Ferrec, Yann; Guérineau, Nicolas; Rommeluère, Sylvain; Taboury, Jean; Chavel, Pierre

2012-06-01

Stationary Fourier transform spectrometry is an interesting concept for building reliable field or embedded spectroradiometers, especially for the mid- and far- IR. Here, a very compact configuration of a cryogenic stationary Fourier transform IR (FTIR) spectrometer is investigated, where the interferometer is directly integrated in the focal plane array (FPA). We present a theoretical analysis to explain and describe the fringe formation inside the FTIR-FPA structure when illuminated by an extended source positioned at a finite distance from the detection plane. The results are then exploited to propose a simple front lens design compatible with a handheld package.

An OTDM-To-WDM Converter Using Optical Fourier Transformation

OpenAIRE

Khin Su Myat Min; Zaw Myo Lwin; Hla Myo Tun

2015-01-01

We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements ar...

Fourier mode analysis of slab-geometry transport iterations in spatially periodic media

International Nuclear Information System (INIS)

Larsen, E W; Zika, M R

1999-01-01

We describe a Fourier analysis of the diffusion-synthetic acceleration (DSA) and transport-synthetic acceleration (TSA) iteration schemes for a spatially periodic, but otherwise arbitrarily heterogeneous, medium. Both DSA and TSA converge more slowly in a heterogeneous medium than in a homogeneous medium composed of the volume-averaged scattering ratio. In the limit of a homogeneous medium, our heterogeneous analysis contains eigenvalues of multiplicity two at ''resonant'' wave numbers. In the presence of material heterogeneities, error modes corresponding to these resonant wave numbers are ''excited'' more than other error modes. For DSA and TSA, the iteration spectral radius may occur at these resonant wave numbers, in which case the material heterogeneities most strongly affect iterative performance

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

Optical polarimeter based on Fourier analysis and electronic control

International Nuclear Information System (INIS)

Vilardy, J; Salas, V.; Torres, C.

2016-01-01

In this paper, we show the design and implementation of an optical polarimeter using electronic control and the Fourier analysis. The polarimeter prototype will be used as a main tool for the students of the Universidad Popular del Cesar that belong to the following university programs: Electronics engineering (optoelectronics area), Math and Physics degree and the Master in Physics Sciences, in order to learning the theory and experimental aspects of the state of optical polarization via the Stokes vector measurement. Using the electronic polarimeter proposed in this paper, the students will be able to observe (in an optical bench) and understand the different interactions of the states of optical polarization when the optical waves pass through to the polarizers and retarder waves plates. The electronic polarimeter has a software that captures the optical intensity measurement and evaluates the Stokes vector. (Author)

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.

Fourier series analysis of a cylindrical pressure vessel subjected to axial end load and external pressure

International Nuclear Information System (INIS)

Brar, Gurinder Singh; Hari, Yogeshwar; Williams, Dennis K.

2013-01-01

Pressure Vessel Code, Section VIII, Division 2 and ASME STS-1. -- Highlights: • Fourier series is used to predict the load carrying capacity of cylindrical vessel. • Reliability approach used for analysis as against the deterministic approach. • Cylindrical pressure vessel is subjected to axial end load and external pressure. • Axisymmetric and asymmetric analysis carried out for imperfect pressure vessels. • Results are compared to the recommendations laid out in ASME B and PV Code

Compact Microwave Fourier Spectrum Analyzer

Science.gov (United States)

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.

The application and improvement of Fourier transform spectrometer experiment

Science.gov (United States)

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.

An OTDM-To-WDM Converter Using Optical Fourier Transformation

Directory of Open Access Journals (Sweden)

Khin Su Myat Min

2015-08-01

Full Text Available We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements are expressed.

Live face detection based on the analysis of Fourier spectra

Science.gov (United States)

Li, Jiangwei; Wang, Yunhong; Tan, Tieniu; Jain, Anil K.

2004-08-01

Biometrics is a rapidly developing technology that is to identify a person based on his or her physiological or behavioral characteristics. To ensure the correction of authentication, the biometric system must be able to detect and reject the use of a copy of a biometric instead of the live biometric. This function is usually termed "liveness detection". This paper describes a new method for live face detection. Using structure and movement information of live face, an effective live face detection algorithm is presented. Compared to existing approaches, which concentrate on the measurement of 3D depth information, this method is based on the analysis of Fourier spectra of a single face image or face image sequences. Experimental results show that the proposed method has an encouraging performance.

Computing exact Fourier series coefficients of IC rectilinear polygons from low-resolution fast Fourier coefficients

Science.gov (United States)

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.

Micro-Texture Synthesis by Phase Randomization

Directory of Open Access Journals (Sweden)

Bruno Galerne

2011-09-01

Full Text Available This contribution is concerned with texture synthesis by example, the process of generating new texture images from a given sample. The Random Phase Noise algorithm presented here synthesizes a texture from an original image by simply randomizing its Fourier phase. It is able to reproduce textures which are characterized by their Fourier modulus, namely the random phase textures (or micro-textures.

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings.

Science.gov (United States)

Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.

Free Sixteen Harmonic Fourier Series Web App with Sound

Science.gov (United States)

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…

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

Introduction to partial differential equations from Fourier series to boundary-value problems

CERN Document Server

Broman, Arne

2010-01-01

This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.

Fractional finite Fourier transform.

Science.gov (United States)

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.

Development of a phase-sensitive Fourier domain optical coherence tomography system to measure mouse organ of Corti vibrations in two cochlear turns

Energy Technology Data Exchange (ETDEWEB)

Ramamoorthy, Sripriya [Oregon Hearing Research Center, Oregon Health & Science University, Portland, Oregon (United States); Zhang, Yuan; Jacques, Steven [Department of Biomedical Engineering, Oregon Health & Science University, Portland, Oregon (United States); Petrie, Tracy; Wang, Ruikang [Department of Bioengineering, University of Washington, Seattle, Washington (United States); Nuttall, Alfred L. [Oregon Hearing Research Center, Oregon Health & Science University, Portland, Oregon (United States); Kresge Hearing Research Institute, The University of Michigan, Ann Arbor, Michigan (United States)

2015-12-31

In this study, we have developed a phase-sensitive Fourier-domain optical coherence tomography system to simultaneously measure the in vivo inner ear vibrations in the hook area and second turn of the mouse cochlea. This technical development will enable measurement of intra-cochlear distortion products at ideal locations such as the distortion product generation site and reflection site. This information is necessary to un-mix the complex mixture of intra-cochlear waves comprising the DPOAE and thus leads to the non-invasive identification of the local region of cochlear damage.

Nycterohemeral eating and ruminating patterns in heifers fed grass or corn silage: analysis by finite Fourier transform.

Science.gov (United States)

Deswysen, A G; Dutilleul, P; Godfrin, J P; Ellis, W C

1993-10-01

Average daily and within-day nycterohemeral patterns of eating and ruminating behavior were determined in six Holstein-Friesian heifers (average BW = 427 kg) given ad libitum access to either corn or grass silage in a two-period crossover design. Rhythm components (number of cycles/24 h) were characterized by finite Fourier transform of the 24-h mastication activities as measured during 4 d by continuous jaw movement recordings. Average daily voluntary intake of corn silage was 8.2% greater (P = .05) than that for grass silage and was associated (P finite Fourier transform was reparameterized to express the amplitude (as periodograms) and phase of each rhythm component. Rhythm Components 1, 3, and 4 contributed primarily to explaining the total dispersion of the 24-h series of time spent eating and ruminating, for both silage types and individual heifers. Relative importance of Rhythm Component 1 of time spent eating, indicative of a main circadian pattern, was related positively to pedigree value for milk production (P = .01) and negatively to milk protein concentration (P = .09).(ABSTRACT TRUNCATED AT 250 WORDS)

Dataset of Fourier transform-infrared coupled with chemometric analysis used to distinguish accessions of Garcinia mangostana L. in Peninsular Malaysia

Directory of Open Access Journals (Sweden)

Sri A’jilah Samsir

2016-09-01

Full Text Available In this dataset, we distinguish 15 accessions of Garcinia mangostana from Peninsular Malaysia using Fourier transform-infrared spectroscopy coupled with chemometric analysis. We found that the position and intensity of characteristic peaks at 3600–3100 cm−1 in IR spectra allowed discrimination of G. mangostana from different locations. Further principal component analysis (PCA of all the accessions suggests the two main clusters were formed: samples from Johor, Melaka, and Negeri Sembilan (South were clustered together in one group while samples from Perak, Kedah, Penang, Selangor, Kelantan, and Terengganu (North and East Coast were in another clustered group. Keywords: Apomictic, Mangosteen, Fourier Transformed-Infrared, Peninsular Malaysia

Singular-value demodulation of phase-shifted holograms.

Science.gov (United States)

Lopes, Fernando; Atlan, Michael

2015-06-01

We report on phase-shifted holographic interferogram demodulation by singular-value decomposition. Numerical processing of optically acquired interferograms over several modulation periods was performed in two steps: (1) rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; and (2) eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.

Correcting sample drift using Fourier harmonics.

Science.gov (United States)

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.

Application of group analysis to the spatially homogeneous and isotropic Boltzmann equation with source using its Fourier image

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)

Clifford Fourier transform on vector fields.

Science.gov (United States)

Ebling, Julia; Scheuermann, Gerik

2005-01-01

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

Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics.

Science.gov (United States)

Monat, Christelle; Grillet, Christian; Corcoran, Bill; Moss, David J; Eggleton, Benjamin J; White, Thomas P; Krauss, Thomas F

2010-03-29

Using Fourier optics, we retrieve the wavevector dependence of the third-harmonic (green) light generated in a slow light silicon photonic crystal waveguide. We show that quasi-phase matching between the third-harmonic signal and the fundamental mode is provided in this geometry by coupling to the continuum of radiation modes above the light line. This process sustains third-harmonic generation with a relatively high efficiency and a substantial bandwidth limited only by the slow light window of the fundamental mode. The results give us insights into the physics of this nonlinear process in the presence of strong absorption and dispersion at visible wavelengths where bandstructure calculations are problematic. Since the characteristics (e.g. angular pattern) of the third-harmonic light primarily depend on the fundamental mode dispersion, they could be readily engineered.

Fourier analysis of multi-gated cardiac blood-pool data in patients with congenital heart diseases, (2). Assessment of diseases with complex cardiac anomalies, especially tetralogy of Fallot

Energy Technology Data Exchange (ETDEWEB)

Takeda, Kan; Maeda, Hisato; Yamaguchi, Nobuo; Nakamura, Kazuyoshi; Matsumura, Kaname; Nakagawa, Tsuyoshi; Sakurai, Minoru; Aoki, Kenzo

1985-04-01

The clinical usefulness of Fourier analysis of multi-gated cardiac blood-pool data was evaluated in 18 subjects with normal cardiac functions and 14 patients with complex cardiac anomalies (ten with tetralogy of Fallot, two with tricuspid atresia (TA), one with double-outlet right ventricle (DORV), and one with Ebstein's anomaly (EA)). Using global ventricular time-activity curves, the phase and amplitude at fundamental frequency were calculated, and emptying patterns of the left and right ventricles (LV, RV) were evaluated by phase difference (D(phase)=RV phase minus LV phase) and amplitude ratio of RV to LV (R(amp)). In patients with TOF, mean values of D (phase) and R(amp) were 25.3 +- 10.5 degrees and 13.5 +- 0.49 respectively and significantly larger than those of normal subjects. D (phase) became larger in inverse proportion to the ratio of pulmonary-to-systemic blood flow and there was an inverse linear correlation between these two variables. On visual interpretation of functional images, the dynamic property of hypoplastic ventricles could be easily estimated in patients with TA or DORV. In a case with EA, the atrialized RV was shown clearly as a hypokinetic, atrial phase area. This method is valuable for pathophysiologic investigation of diseases with complex cardiac anomalies. (author).

Fourier-Based Fast Multipole Method for the Helmholtz Equation

KAUST Repository

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.

Mathematical Methods for Engineers and Scientists 3 Fourier Analysis, Partial Differential Equations and Variational Methods

CERN Document Server

Tang, Kwong-Tin

2007-01-01

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

Fourier descriptors analysis of anisotropy and preferred Orientation in geological samples

International Nuclear Information System (INIS)

Santiago Buey, C. de

2011-01-01

This study focuses on the use of Fourier descriptors to evaluate and quantify two specific fabric characteristics of geological materials: anisotropy of particles or voids morphologies and particle orientation. To this end, a theoretical section of a rock was created, made of ellipses and rectangles of different axes ratios and different orientations. The Fourier descriptors method was applied to calculate the anisotropy and orientation of each particle and, finally, a rose diagram was constructed to represent the particles orientations distribution and to observe the presence or not of any preferred orientation. (Author) 15 refs.

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)

Reconstruction of on-axis lensless Fourier transform digital hologram with the screen division method

Science.gov (United States)

Jiang, Hongzhen; Liu, Xu; Liu, Yong; Li, Dong; Chen, Zhu; Zheng, Fanglan; Yu, Deqiang

2017-10-01

An effective approach for reconstructing on-axis lensless Fourier Transform digital hologram by using the screen division method is proposed. Firstly, the on-axis Fourier Transform digital hologram is divided into sub-holograms. Then the reconstruction result of every sub-hologram is obtained according to the position of corresponding sub-hologram in the hologram reconstruction plane with Fourier transform operation. Finally, the reconstruction image of on-axis Fourier Transform digital hologram can be acquired by the superposition of the reconstruction result of sub-holograms. Compared with the traditional reconstruction method with the phase shifting technology, in which multiple digital holograms are required to record for obtaining the reconstruction image, this method can obtain the reconstruction image with only one digital hologram and therefore greatly simplify the recording and reconstruction process of on-axis lensless Fourier Transform digital holography. The effectiveness of the proposed method is well proved with the experimental results and it will have potential application foreground in the holographic measurement and display field.

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

NARCIS (Netherlands)

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

2002-01-01

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

Fourier analysis of a new P1 synthetic acceleration for Sn transport equations

International Nuclear Information System (INIS)

Turcksin, B.; Ragusa, J. C.

2010-10-01

In this work, is derived a new P1 synthetic acceleration scheme (P1SA) for the S N transport equation and analyze its convergence properties through the means of a Fourier analysis. The Fourier analysis is carried out for both continuous (i.e., not spatially discretized) S N equations and linear discontinuous Fem discretization. We show, thanks to the continuous analysis, that the scheme is unstable when the anisotropy is important (μ - >0.5). However, the discrete analysis shows that when cells are large in comparison to the mean free path, the spectral radius decreases and the acceleration scheme becomes effective, even for highly anisotropic scattering. In charged particles transport, scattering is highly anisotropic and mean free paths are very small and, thus, this scheme could be of interest. To use the P1SA when cells are small and anisotropy is important, the scheme is modified by altering the update of the accelerated flux or by using either K transport sweeps before the application of P1SA. The update scheme performs well as long as μ - - ≥0.9, the modified update scheme is unstable. The multiple transport sweeps scheme is convergent with an arbitrary μ - but the spectral radius increases when scattering is isotropic. When anisotropic increases, the frequency of use of the acceleration scheme needs to be decreased. Even if the P1SA is used less often, the spectral radius is significantly smaller when compared with a method that does not use it for high anisotropy (μ - ≥0.5). It is interesting to notice that using P1SA every two iterations gives the same spectral radius than the update method when μ - ≥0.5 but it is much less efficient when μ - <0.5. (Author)

Phase-only optical encryption based on the zeroth-order phase-contrast technique

Science.gov (United States)

Pizolato, José Carlos; Neto, Luiz Gonçalves

2009-09-01

A phase-only encryption/decryption scheme with the readout based on the zeroth-order phase-contrast technique (ZOPCT), without the use of a phase-changing plate on the Fourier plane of an optical system based on the 4f optical correlator, is proposed. The encryption of a gray-level image is achieved by multiplying the phase distribution obtained directly from the gray-level image by a random phase distribution. The robustness of the encoding is assured by the nonlinearity intrinsic to the proposed phase-contrast method and the random phase distribution used in the encryption process. The experimental system has been implemented with liquid-crystal spatial modulators to generate phase-encrypted masks and a decrypting key. The advantage of this method is the easy scheme to recover the gray-level information from the decrypted phase-only mask applying the ZOPCT. An analysis of this decryption method was performed against brute force attacks.

Identification and characterization of historical pigments with x-ray diffraction analysis (XRD), x-ray fluorescence analysis (XRA) and Fourier transformed infrared spectroscopy (FTIR)

International Nuclear Information System (INIS)

Hochleitner, B.

2002-11-01

This thesis presents a systematic characterization of historical inorganic pigments with respect to their crystallographic structure, main components, and trade elements, utilizing three complementary methods. The results are compiled in a computer-database containing the experimentally obtained information. The specimens examined in this study originate from a collection of 19th and 20th century pigments, dyes and binders with a wide variety of colors and materials at the Institute of Natural Sciences and Technologies in Art of the Academy of Fine Arts in Vienna. Approximately 400 different inorganic pigments were analysed for this first study of its kind by combining the experimental techniques explained in the next paragraph. For analyzing the inorganic pigments three different methods were applied: x-ray diffraction (XRD), x-ray fluorescence (XRF) and fourier-transformed infrared spectroscopy (FTIR) proved to be suitable techniques to identify and characterize the composition of the materials. The experimental work was focused on x-ray diffraction to detect the main components and to perform phase analysis for the identification of the crystallographic structure. To facilitate the analysis of the diffractograms and investigate differences in the elemental composition, XRF-measurements were carried out and complemented by FTIR-spectroscopy. The latter technique supports the identification of organic components of the samples and both ease phase analysis. In some cases, the obtained results show remarkable differences in composition for pigments having the same trade name. These differences consist either with respect to the identified elements or added components, such as pure white pigments. However, in most cases the chemical structure of the phase determining the color of the relevant pigment group was similar. Knowledge of the composition of the originally used pigments is of great importance for the restoration and conservation of art objects. In order to

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.

Ion-cyclotron-resonance- and Fourier-transform-ion-cyclotron-resonance spectroscopy: technology and application

International Nuclear Information System (INIS)

Luederwald, I.

1977-01-01

Instrumentation and technology of Ion-Cyclotron-Resonance and Fourier-Transform-Ion-Cyclotron-Resonance Spectroscopy are described. The method can be applied to studies of ion/molecule reactions in gas phase, to obtain thermodynamic data as gas phase acidity or basicity, proton and electron affinity, and to establish reaction mechanisms and ion structures. (orig.) [de

Proposal of AAA-battery-size one-shot ATR Fourier spectroscopic imager for on-site analysis: Simultaneous measurement of multi-components with high accuracy

Science.gov (United States)

Hosono, Satsuki; Qi, Wei; Sato, Shun; Suzuki, Yo; Fujiwara, Masaru; Hiramatsu, Hiroyuki; Suzuki, Satoru; Abeygunawardhana, P. K. W.; Wada, Kenji; Nishiyama, Akira; Ishimaru, Ichiro

2015-03-01

For simultaneous measurement of multi-components on-site like factories, the ultra-compact (diameter: 9[mm], length: 45[mm], weight: 200[g]) one-shot ATR (Attenuated Total Reflection) Fourier spectroscopic imager was proposed. Because the proposed one-shot Fourier spectroscopic imaging is based on spatial-phase-shift interferometer, interferograms could be obtained with simple optical configurations. We introduced the transmission-type relativeinclined phase-shifter, that was constructed with a cuboid prism and a wedge prism, onto the optical Fourier transform plane of infinity corrected optical systems. And also, small light-sources and cameras in the mid-infrared light region, whose size are several millimeter on a side, are essential components for the ultra-compact spectroscopic configuration. We selected the Graphite light source (light source area: 1.7×1.7[mm], maker: Hawkeye technologies) whose radiation factor was high. Fortunately, in these days we could apply the cost-effective 2-dimensional light receiving device for smartphone (e.g. product name: LEPTON, maker: FLIR, price: around 400USD). In the case of alcoholic drinks factory, conventionally workers measure glucose and ethanol concentrations by bringing liquid solution back to laboratories every day. The high portable spectroscopy will make it possible to measure multi-components simultaneously on manufacturing scene. But we found experimentally that absorption spectrum of glucose and water and ethanol were overlapped each other in near infrared light region. But for mid-infrared light region, we could distinguish specific absorption peaks of glucose (@10.5[μm]) and ethanol (@11.5[μm]) independently from water absorption. We obtained standard curve between absorption (@9.6[μm]) and ethanol concentration with high correlation coefficient 0.98 successfully by ATR imaging-type 2-dimensional Fourier spectroscopy (wavelength resolution: 0.057[μm]) with the graphite light source (maker: Hawkeye

Análise de Fourier para detecção de defeitos localizados na camada de fibras nervosas da retina com a polarimetria a laser Fourier analysis for the detection of localized nerve fiber layer defects using scanning laser polarimetry

Directory of Open Access Journals (Sweden)

Felipe Andrade Medeiros

2003-12-01

this study, we performed Fourier analysis of retinal nerve fiber layer (RNFL thickness measurements obtained with scanning laser polarimetry and evaluated the ability of this method to detect localized nerve fiber layer defects in glaucomatous patients. METHODS: The study included 40 eyes of 40 glaucomatous patients with localized RNFL defects identified by slit-lamp biomicroscopy or RNFL photography and 43 eyes of 43 normal patients. The patients were submitted to RNFL thickness measurements using the GDx® - Nerve Fiber Analyzer. Fourier analysis was applied to the polarimetry data. Fourier coefficients and GDx parameters were compared between the two groups. A linear discriminant function was developed to identify and combine the most useful Fourier coefficients to separate the two groups. ROC curves were obtained for each measurement and sensitivity values (at fixed specificities were calculated. RESULTS: The combination of Fourier coefficients resulted in a sensitivity of 80% for a specificity set at higher than 90%. For the same specificity, the GDx parameters had sensitivities ranging from 15% to 48%. The area under the ROC curve (AUC for the combination of Fourier coefficients was 0.90, significantly higher than the AUC for the parameter The Number (0.76. CONCLUSION: Fourier analysis of RNFL polarimetry data had a better diagnostic performance than standard GDx parameters to identify localized retinal nerve fiber layer defects in glaucomatous patients.

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)

Vibrational analysis of Fourier transform spectrum of the A3Π0–X1Σ ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 73; Issue 5. Vibrational analysis of Fourier transform spectrum of the A 3 0 – X 1 ∑ + and B 3 1 – X 1 ∑ + transitions of indium monobromide. Renu Singh K N Uttam M D Saksena M N Deo. Volume 73 Issue 5 November 2009 pp 889-899 ...

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)

Quasilinear theory without the random phase approximation

International Nuclear Information System (INIS)

Weibel, E.S.; Vaclavik, J.

1980-08-01

The system of quasilinear equations is derived without making use of the random phase approximation. The fluctuating quantities are described by the autocorrelation function of the electric field using the techniques of Fourier analysis. The resulting equations posses the necessary conservation properties, but comprise new terms which hitherto have been lost in the conventional derivations

Phase analysis in the Wolff-Parkinson-White syndrome with surgically proven accessory conduction pathways: concise communication

International Nuclear Information System (INIS)

Nakajima, K.; Bunko, H.; Tada, A.; Taki, J.; Tonami, N.; Hisada, K.; Misaki, T.; Iwa, T.

1984-01-01

Twenty-one patients with the Wolff-Parkinson-White (WPW) syndrome who underwent surgical division of the accessory conduction pathway (ACP) were studied by gated blood-pool scintigraphy. In each case, a functional image of the phase was generated, based on the fundamental frequency of the Fourier transform. The location of the ACP was confirmed by electrophysiologic study, epicardial mapping, and surgery. Phase analysis identified the side of preexcitation correctly in 16 out of 20 patients with WPW syndrome with a delta wave. All patients with right-cardiac type (N=9) had initial contraction in the right ventricle (RV). In patients with left-cardiac type (N=10), six had initial movement in the left ventricle (LV); but in the other four the ACPs in the anterior or lateral wall of the left ventricle (LV) could not be detected. In patients with multiple ACPs (N=2), one right-cardiac type had initial contraction in the RV, while in the other (with an intermittent WPW syndrome) the ACP was not detected. These observations indicate that abnormal wall motion is associated with the conduction anomalies of the WPW syndrome. We conclude that phase analysis can correctly identify the side of initial contraction in the WPW syndrome before and after surgery. However, as a method of preoperative study, it seems difficult to determine the precise site of the ACP by phase analysis alone

Phase analysis in the Wolff-Parkinson-White syndrome with surgically proven accessory conduction pathways: concise communication

Energy Technology Data Exchange (ETDEWEB)

Nakajima, K.; Bunko, H.; Tada, A.; Taki, J.; Tonami, N.; Hisada, K.; Misaki, T.; Iwa, T.

1984-01-01

Twenty-one patients with the Wolff-Parkinson-White (WPW) syndrome who underwent surgical division of the accessory conduction pathway (ACP) were studied by gated blood-pool scintigraphy. In each case, a functional image of the phase was generated, based on the fundamental frequency of the Fourier transform. The location of the ACP was confirmed by electrophysiologic study, epicardial mapping, and surgery. Phase analysis identified the side of preexcitation correctly in 16 out of 20 patients with WPW syndrome with a delta wave. All patients with right-cardiac type (N=9) had initial contraction in the right ventricle (RV). In patients with left-cardiac type (N=10), six had initial movement in the left ventricle (LV); but in the other four the ACPs in the anterior or lateral wall of the left ventricle (LV) could not be detected. In patients with multiple ACPs (N=2), one right-cardiac type had initial contraction in the RV, while in the other (with an intermittent WPW syndrome) the ACP was not detected. These observations indicate that abnormal wall motion is associated with the conduction anomalies of the WPW syndrome. We conclude that phase analysis can correctly identify the side of initial contraction in the WPW syndrome before and after surgery. However, as a method of preoperative study, it seems difficult to determine the precise site of the ACP by phase analysis alone.

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

Science.gov (United States)

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

2009-12-01

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

Using Fourier and Taylor series expansion in semi-analytical deformation analysis of thick-walled isotropic and wound composite structures

Directory of Open Access Journals (Sweden)

Jiran L.

2016-06-01

Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.

Performance analysis of an all-optical OFDM system in presence of non-linear phase noise.

Science.gov (United States)

Hmood, Jassim K; Harun, Sulaiman W; Emami, Siamak D; Khodaei, Amin; Noordin, Kamarul A; Ahmad, Harith; Shalaby, Hossam M H

2015-02-23

The potential for higher spectral efficiency has increased the interest in all-optical orthogonal frequency division multiplexing (OFDM) systems. However, the sensitivity of all-optical OFDM to fiber non-linearity, which causes nonlinear phase noise, is still a major concern. In this paper, an analytical model for estimating the phase noise due to self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in an all-optical OFDM system is presented. The phase noise versus power, distance, and number of subcarriers is evaluated by implementing the mathematical model using Matlab. In order to verify the results, an all-optical OFDM system, that uses coupler-based inverse fast Fourier transform/fast Fourier transform without any nonlinear compensation, is demonstrated by numerical simulation. The system employs 29 subcarriers; each subcarrier is modulated by a 4-QAM or 16-QAM format with a symbol rate of 25 Gsymbol/s. The results indicate that the phase variance due to FWM is dominant over those induced by either SPM or XPM. It is also shown that the minimum phase noise occurs at -3 dBm and -1 dBm for 4-QAM and 16-QAM, respectively. Finally, the error vector magnitude (EVM) versus subcarrier power and symbol rate is quantified using both simulation and the analytical model. It turns out that both EVM results are in good agreement with each other.

Using Dynamic Fourier Analysis to Discriminate Between Seismic Signals from Natural Earthquakes and Mining Explosions

Directory of Open Access Journals (Sweden)

Maria C. Mariani

2017-08-01

Full Text Available A sequence of intraplate earthquakes occurred in Arizona at the same location where miningexplosions were carried out in previous years. The explosions and some of the earthquakes generatedvery similar seismic signals. In this study Dynamic Fourier Analysis is used for discriminating signalsoriginating from natural earthquakes and mining explosions. Frequency analysis of seismogramsrecorded at regional distances shows that compared with the mining explosions the earthquake signalshave larger amplitudes in the frequency interval ~ 6 to 8 Hz and significantly smaller amplitudes inthe frequency interval ~ 2 to 4 Hz. This type of analysis permits identifying characteristics in theseismograms frequency yielding to detect potentially risky seismic events.

Three phase active power filter with selective harmonics elimination

Directory of Open Access Journals (Sweden)

Sozański Krzysztof

2016-03-01

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

Iterative wave-front reconstruction in the Fourier domain.

Science.gov (United States)

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.

An improved model for whole genome phylogenetic analysis by Fourier transform.

Science.gov (United States)

Yin, Changchuan; Yau, Stephen S-T

2015-10-07

DNA sequence similarity comparison is one of the major steps in computational phylogenetic studies. The sequence comparison of closely related DNA sequences and genomes is usually performed by multiple sequence alignments (MSA). While the MSA method is accurate for some types of sequences, it may produce incorrect results when DNA sequences undergone rearrangements as in many bacterial and viral genomes. It is also limited by its computational complexity for comparing large volumes of data. Previously, we proposed an alignment-free method that exploits the full information contents of DNA sequences by Discrete Fourier Transform (DFT), but still with some limitations. Here, we present a significantly improved method for the similarity comparison of DNA sequences by DFT. In this method, we map DNA sequences into 2-dimensional (2D) numerical sequences and then apply DFT to transform the 2D numerical sequences into frequency domain. In the 2D mapping, the nucleotide composition of a DNA sequence is a determinant factor and the 2D mapping reduces the nucleotide composition bias in distance measure, and thus improving the similarity measure of DNA sequences. To compare the DFT power spectra of DNA sequences with different lengths, we propose an improved even scaling algorithm to extend shorter DFT power spectra to the longest length of the underlying sequences. After the DFT power spectra are evenly scaled, the spectra are in the same dimensionality of the Fourier frequency space, then the Euclidean distances of full Fourier power spectra of the DNA sequences are used as the dissimilarity metrics. The improved DFT method, with increased computational performance by 2D numerical representation, can be applicable to any DNA sequences of different length ranges. We assess the accuracy of the improved DFT similarity measure in hierarchical clustering of different DNA sequences including simulated and real datasets. The method yields accurate and reliable phylogenetic trees

Fourier transforms principles and applications

CERN Document Server

Hansen, Eric W

2014-01-01

Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods.  Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.

Non-linear adjustment to purchasing power parity: an analysis using Fourier approximations

OpenAIRE

Juan-Ángel Jiménez-Martín; M. Dolores Robles Fernández

2005-01-01

This paper estimates the dynamics of adjustment to long run purchasing power parity (PPP) using data for 18 mayor bilateral US dollar exchange rates, over the post-Bretton Woods period, in a non-linear framework. We use new unit root and cointegration tests that do not assume a specific non-linear adjustment process. Using a first-order Fourier approximation, we find evidence of non-linear mean reversion in deviations from both absolute and relative PPP. This first-order Fourier approximation...

Modeling and forecasting monthly movement of annual average solar insolation based on the least-squares Fourier-model

International Nuclear Information System (INIS)

Yang, Zong-Chang

2014-01-01

Highlights: • Introduce a finite Fourier-series model for evaluating monthly movement of annual average solar insolation. • Present a forecast method for predicting its movement based on the extended Fourier-series model in the least-squares. • Shown its movement is well described by a low numbers of harmonics with approximately 6-term Fourier series. • Predict its movement most fitting with less than 6-term Fourier series. - Abstract: Solar insolation is one of the most important measurement parameters in many fields. Modeling and forecasting monthly movement of annual average solar insolation is of increasingly importance in areas of engineering, science and economics. In this study, Fourier-analysis employing finite Fourier-series is proposed for evaluating monthly movement of annual average solar insolation and extended in the least-squares for forecasting. The conventional Fourier analysis, which is the most common analysis method in the frequency domain, cannot be directly applied for prediction. Incorporated with the least-square method, the introduced Fourier-series model is extended to predict its movement. The extended Fourier-series forecasting model obtains its optimums Fourier coefficients in the least-square sense based on its previous monthly movements. The proposed method is applied to experiments and yields satisfying results in the different cities (states). It is indicated that monthly movement of annual average solar insolation is well described by a low numbers of harmonics with approximately 6-term Fourier series. The extended Fourier forecasting model predicts the monthly movement of annual average solar insolation most fitting with less than 6-term Fourier series

Monitoring of PVD, PECVD and etching plasmas using Fourier components of RF voltage

International Nuclear Information System (INIS)

Dvorak, P; Vasina, P; Bursikova, V; Zemlicka, R

2010-01-01

Fourier components of discharge voltages were measured in two different reactive plasmas and their response to the creation or destruction of a thin film was studied. In reactive magnetron sputtering the effect of transition from the metallic to the compound mode accompanied by the creation of a compound film on the sputtered target was observed. Further, deposition and etching of a diamond-like carbon film and their effects on amplitudes of Fourier components of the discharge voltage were studied. It was shown that the Fourier components, including higher harmonic frequencies, sensitively react to the presence of a film. Therefore, they can be used as a powerful tool for the monitoring of deposition and etching processes. It was demonstrated that the behaviour of the Fourier components was caused in both experiments by the presence of the film. It was not caused by changes in the chemical composition of the gas phase induced by material etched from the film or decrease in gettering rate. Further, the observed behaviour was not affected by the film conductivity. The behaviour of the Fourier components can be explained by the difference between the coefficients of secondary electron emission of the film and its underlying material.

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

Science.gov (United States)

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)

Free sixteen harmonic Fourier series web app with sound

Science.gov (United States)

Ruiz, Michael J.

2018-03-01

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 program is free for non-commercial use and can also be downloaded for running offline.

Flow-through Fourier transform infrared sensor for total hydrocarbons determination in water.

Science.gov (United States)

Pérez-Palacios, David; Armenta, Sergio; Lendl, Bernhard

2009-09-01

A new flow-through Fourier transform infrared (FT-IR) sensor for oil in water analysis based on solid-phase spectroscopy on octadecyl (C18) silica particles has been developed. The C18 non-polar sorbent is placed inside the sensor and is able to retain hydrocarbons from water samples. The system does not require the use of chlorinated solvents, reducing the environmental impact, and the minimal sample handling stages serve to ensure sample integrity whilst reducing exposure of the analyst to any toxic hydrocarbons present within the samples. Fourier transform infrared (FT-IR) spectra were recorded by co-adding 32 scans at a resolution of 4 cm(-1) and the band located at 1462 cm(-1) due to the CH(2) bending was integrated from 1475 to 1450 cm(-1) using a baseline correction established between 1485 and 1440 cm(-1) using the areas as analytical signal. The technique, which provides a limit of detection (LOD) of 22 mg L(-1) and a precision expressed as relative standard deviation (RSD) lower than 5%, is considerably rapid and allows for a high level of automation.

Direct Fourier imaging of distortions in LaAlO{sub 3} films

Energy Technology Data Exchange (ETDEWEB)

Schlueter, Christoph; Zegenhagen, Joerg [ESRF, Grenoble (France); Lee, Tien-Lin [Diamond Light Source Ltd, Didcot (United Kingdom); Aruta, Carmela [CNR-SPIN, Naples (Italy)

2012-07-01

The formation of a quasi-2dimensional electron gas at interface of SrTiO{sub 3} (STO) and LaAlO{sub 3} (LAO) attracted considerable attention in the recent years. The polar LAO layer was expected to cause the build-up of an electric potential. Distortions in the overlayer are discussed as one possible response of the system. The highly sensitive X-ray standing wave (XSW) imaging technique is well suited to study theses films because of its chemical and spacial resolution. LAO thin films below and above the critical thickness for conductivity were studied at the hard X-ray photo electron spectroscopy end station of ID32 at the ESRF. The XSW modulated core level photo electron yield was recorded for the five elements present in film and substrate for seven different Bragg reflections. Subsequent analysis provided for each reflection and element the amplitude and phase of one Fourier coefficient of the elemental atomic distribution function. The three dimensional real space image of the atomic distribution for each of the elements is reconstructed by direct Fourier inversion. The reconstructed 3D images obtained by this model free approach reveal significant atomic displacements.

On the Fourier integral theorem

NARCIS (Netherlands)

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

Prediction of solar cycle 24 using fourier series analysis

International Nuclear Information System (INIS)

Khalid, M.; Sultana, M.; Zaidi, F.

2014-01-01

Predicting the behavior of solar activity has become very significant. It is due to its influence on Earth and the surrounding environment. Apt predictions of the amplitude and timing of the next solar cycle will aid in the estimation of the several results of Space Weather. In the past, many prediction procedures have been used and have been successful to various degrees in the field of solar activity forecast. In this study, Solar cycle 24 is forecasted by the Fourier series method. Comparative analysis has been made by auto regressive integrated moving averages method. From sources, January 2008 was the minimum preceding solar cycle 24, the amplitude and shape of solar cycle 24 is approximate on monthly number of sunspots. This forecast framework approximates a mean solar cycle 24, with the maximum appearing during May 2014 (+- 8 months), with most sunspot of 98 +- 10. Solar cycle 24 will be ending in June 2020 (+- 7 months). The difference between two consecutive peak values of solar cycles (i.e. solar cycle 23 and 24 ) is 165 months(+- 6 months). (author)

Fourier Transform Infrared Imaging analysis of dental pulp inflammatory diseases.

Science.gov (United States)

Giorgini, E; Sabbatini, S; Conti, C; Rubini, C; Rocchetti, R; Fioroni, M; Memè, L; Orilisi, G

2017-05-01

Fourier Transform Infrared microspectroscopy let characterize the macromolecular composition and distribution of tissues and cells, by studying the interaction between infrared radiation and matter. Therefore, we hypothesize to exploit this analytical tool in the analysis of inflamed pulps, to detect the different biochemical features related to various degrees of inflammation. IR maps of 13 irreversible and 12 hyperplastic pulpitis, together with 10 normal pulps, were acquired, compared with histological findings and submitted to multivariate (HCA, PCA, SIMCA) and statistical (one-way ANOVA) analysis. The fit of convoluted bands let calculate meaningful band area ratios (means ± s.d., P < 0.05). The infrared imaging analysis pin-pointed higher amounts of water and lower quantities of type I collagen in all inflamed pulps. Specific vibrational markers were defined for irreversible pulpitis (Lipids/Total Biomass, PhII/Total Biomass, CH 2 /CH 3 , and Ty/AII) and hyperplastic ones (OH/Total Biomass, Collagen/Total Biomass, and CH 3 Collagen/Total Biomass). The study confirmed that FTIR microspectroscopy let discriminate tissues' biological features. The infrared imaging analysis evidenced, in inflamed pulps, alterations in tissues' structure and composition. Changes in lipid metabolism, increasing amounts of tyrosine, and the occurrence of phosphorylative processes were highlighted in irreversible pulpitis, while high amounts of water and low quantities of type I collagen were detected in hyperplastic samples. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

The application of an optical Fourier spectrum analyzer on detecting defects in mass-produced satellite photographs

Science.gov (United States)

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.

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.)

Metasurface Enabled Wide-Angle Fourier Lens.

Science.gov (United States)

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.

Two-dimensional fourier transform spectrometer

Science.gov (United States)

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

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

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)

Binary multiplexing and the phase-retrieval problem

International Nuclear Information System (INIS)

Ghiglia, D.C.

1982-01-01

A binary-mask multiplexing method is developed that provides a means of recovering phase information unambiguously from measurements of the modulus of masked complex waves in the object and image planes, respectively. The technique is developed from Fourier-transform theory and combinatorial analysis and is derived for both the continuous case (optical-digital-hybrid implementation) and the totally discrete case (digital computer simulation). Computer simulations provide unambiguous recovery of phase information and indicate that the matrix equations are reasonably well conditioned for cases of practical significance

Data characteristic analysis of air conditioning load based on fast Fourier transform

Science.gov (United States)

Li, Min; Zhang, Yanchi; Xie, Da

2018-04-01

With the development of economy and the improvement of people's living standards, air conditioning equipment is more and more popular. The influence of air conditioning load for power grid is becoming more and more serious. In this context it is necessary to study the characteristics of air conditioning load. This paper analyzes the data of air conditioning power consumption in an office building. The data is used for Fast Fourier Transform by data analysis software. Then a series of maps are drawn for the transformed data. The characteristics of each map were analyzed separately. The hidden rules of these data are mined from the angle of frequency domain. And these rules are hard to find in the time domain.

Phase Coherence of Large Amplitude MHD Waves in the Earth's Foreshock: Geotail Observations

International Nuclear Information System (INIS)

Hada, Tohru; Koga, Daiki; Yamamoto, Eiko

2003-01-01

Large amplitude MHD turbulence is commonly found in the earth's foreshock region. It can be represented as a superposition of Fourier modes with characteristic frequency, amplitude, and phase. Nonlinear interactions between the Fourier modes are likely to produce finite correlation among the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in quasi-linear theories) or they have a finite coherence. However, naive inspection of wave phases does not reveal anything, as the wave phase is sensitively related to the choice of origin of the coordinate, which should be arbitrary. Using a method based on a surrogate data technique and a fractal analysis, we analyzed Geotail magnetic field data to evaluate the phase coherence among the MHD waves in the earth's foreshock region. We show that the correlation of wave phases does exist, indicating that the nonlinear interactions between the waves is in progress. Furthermore, by introducing an index to represent the degree of the phase coherence, we discuss that the wave phases become more coherent as the turbulence amplitude increases, and also as the propagation angle of the most dominant wave mode becomes oblique. Details of the analysis as well as implications of the present results to transport processes of energetic particles will be discussed

Fourier transform digital holographic adaptive optics imaging system

Science.gov (United States)

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

Influences of overlap index on Fourier ptychography imaging

Science.gov (United States)

Wang, Honghong; Rong, Lu; Wang, Dayong; Zhang, Xu; Zhai, Changchao; Panezai, Spozmai; Wang, Yunxin; Zhao, Jie

2018-01-01

Fourier ptychography is a new type of synthetic aperture imaging technique based on phase retrieval method which can improve microscopeic imaging performance beyond the diffraction limit of the employed optical components by illuminating the object with oblique waves of different incident angles where the field of view remains unchanged. illumination angle and the overlap rate of spectrum will have a certain impact on the quality of reconstruction. In this paper, we study the effects of illumination angle and spectral overlap rate on the image quality of Fourier ptychography. The simulation results show that increasing the illumination angle and spectral overlap can improve the resolution, but there is a threshold for the key parameters of spectral overlap rate. The convergence rate decreases when the overlap rate exceeds 70%, and the reconstruction process is more time-consuming due to the high overlap rate. However the results of proposed study shows that an overlap of 60% is the optimal choice to acquire a high-quality recovery with high speed.

Research on effects of phase error in phase-shifting interferometer

Science.gov (United States)

Wang, Hongjun; Wang, Zhao; Zhao, Hong; Tian, Ailing; Liu, Bingcai

2007-12-01

Referring to phase-shifting interferometry technology, the phase shifting error from the phase shifter is the main factor that directly affects the measurement accuracy of the phase shifting interferometer. In this paper, the resources and sorts of phase shifting error were introduction, and some methods to eliminate errors were mentioned. Based on the theory of phase shifting interferometry, the effects of phase shifting error were analyzed in detail. The Liquid Crystal Display (LCD) as a new shifter has advantage as that the phase shifting can be controlled digitally without any mechanical moving and rotating element. By changing coded image displayed on LCD, the phase shifting in measuring system was induced. LCD's phase modulation characteristic was analyzed in theory and tested. Based on Fourier transform, the effect model of phase error coming from LCD was established in four-step phase shifting interferometry. And the error range was obtained. In order to reduce error, a new error compensation algorithm was put forward. With this method, the error can be obtained by process interferogram. The interferogram can be compensated, and the measurement results can be obtained by four-step phase shifting interferogram. Theoretical analysis and simulation results demonstrate the feasibility of this approach to improve measurement accuracy.

High-resolution wave-theory-based ultrasound reflection imaging using the split-step fourier and globally optimized fourier finite-difference methods

Science.gov (United States)

Huang, Lianjie

2013-10-29

Methods for enhancing ultrasonic reflection imaging are taught utilizing a split-step Fourier propagator in which the reconstruction is based on recursive inward continuation of ultrasonic wavefields in the frequency-space and frequency-wave number domains. The inward continuation within each extrapolation interval consists of two steps. In the first step, a phase-shift term is applied to the data in the frequency-wave number domain for propagation in a reference medium. The second step consists of applying another phase-shift term to data in the frequency-space domain to approximately compensate for ultrasonic scattering effects of heterogeneities within the tissue being imaged (e.g., breast tissue). Results from various data input to the method indicate significant improvements are provided in both image quality and resolution.

Jean Baptiste Joseph Fourier

Science.gov (United States)

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.

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

Science.gov (United States)

Ochs, A L

1979-01-01

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

Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.

Science.gov (United States)

Volkov, V V; Han, M G; Zhu, Y

2013-11-01

We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. Published by Elsevier B.V.

High resolution integral holography using Fourier ptychographic approach.

Science.gov (United States)

Li, Zhaohui; Zhang, Jianqi; Wang, Xiaorui; Liu, Delian

2014-12-29

An innovative approach is proposed for calculating high resolution computer generated integral holograms by using the Fourier Ptychographic (FP) algorithm. The approach initializes a high resolution complex hologram with a random guess, and then stitches together low resolution multi-view images, synthesized from the elemental images captured by integral imaging (II), to recover the high resolution hologram through an iterative retrieval with FP constrains. This paper begins with an analysis of the principle of hologram synthesis from multi-projections, followed by an accurate determination of the constrains required in the Fourier ptychographic integral-holography (FPIH). Next, the procedure of the approach is described in detail. Finally, optical reconstructions are performed and the results are demonstrated. Theoretical analysis and experiments show that our proposed approach can reconstruct 3D scenes with high resolution.

Multichannel Dynamic Fourier-Transform IR Spectrometer

Science.gov (United States)

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.

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...

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

Quasi-static analysis of flexible pavements based on predicted frequencies using Fast Fourier Transform and Artificial Neural Network

Directory of Open Access Journals (Sweden)

Ali Reza Ghanizadeh

2018-01-01

Full Text Available New trend in design of flexible pavements is mechanistic-empirical approach. The first step for applying this method is analyzing the pavement structure for several times and computation of critical stresses and strains, which needs a fast analysis method with good accuracy. This paper aims to introduce a new rapid pavement analysis approach, which can consider the history of loading and rate effect. To this end, 1200 flexible pavement sections were analyzed, and equivalent frequencies (EF were calculated using Fast Fourier Transform (FFT method at various depths of asphalt layer. A nonlinear regression equation has been presented for determining EF at different depths of asphalt layer. For more accurate predicting of EF at low frequencies, a feed-forward Artificial Neural Network (ANN was employed, which allows accurate prediction of EF. The frequencies obtained by the proposed regression equation and ANN were compared with frequencies observed in Virginia Smart Road project, and it was found that there is a good agreement between observed and predicted frequencies. Comparison of quasi-static analysis of flexible pavements by frequencies obtained using FFT method and full dynamic analysis by 3D-Move program approves that the critical responses of pavement computed by proposed quasi-static analysis approach are comparable to critical responses computed using full dynamic analysis. Keywords: Equivalent frequency, Fast Fourier Transform (FFT, Pavement quasi-static analysis, Dynamic modulus, Artificial Neural Network (ANN

Detection of Life Threatening Ventricular Arrhythmia Using Digital Taylor Fourier Transform.

Science.gov (United States)

Tripathy, Rajesh K; Zamora-Mendez, Alejandro; de la O Serna, José A; Paternina, Mario R Arrieta; Arrieta, Juan G; Naik, Ganesh R

2018-01-01

Accurate detection and classification of life-threatening ventricular arrhythmia episodes such as ventricular fibrillation (VF) and rapid ventricular tachycardia (VT) from electrocardiogram (ECG) is a challenging problem for patient monitoring and defibrillation therapy. This paper introduces a novel method for detection and classification of life-threatening ventricular arrhythmia episodes. The ECG signal is decomposed into various oscillatory modes using digital Taylor-Fourier transform (DTFT). The magnitude feature and a novel phase feature namely the phase difference (PD) are evaluated from the mode Taylor-Fourier coefficients of ECG signal. The least square support vector machine (LS-SVM) classifier with linear and radial basis function (RBF) kernels is employed for detection and classification of VT vs. VF, non-shock vs. shock and VF vs. non-VF arrhythmia episodes. The accuracy, sensitivity, and specificity values obtained using the proposed method are 89.81, 86.38, and 93.97%, respectively for the classification of Non-VF and VF episodes. Comparison with the performance of the state-of-the-art features demonstrate the advantages of the proposition.

Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation.

Science.gov (United States)

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.

Differential dynamic optical microscopy for the characterization of soft matter: liquid crystal dynamics, volume phase transition of hydrogels, and phase transition of binary mixtures

Science.gov (United States)

Yoon, Beom-Jin; Park, Jung Ok; Srinivasarao, Mohan; Smith, Michael H.; Lyon, L. Andrew

2011-03-01

The structure and dynamics of soft matter were studied by differential dynamic optical microscopy. One can retrieve q-space information through image processing and Fourier analysis, even when the feature sizes in real space image are too small to be resolved or even visible in an optical microscope. The temporal sequence of real space images were Fourier transformed, and analyzed for the temporal and spatial fluctuations of power spectrum. Here, we present the results on liquid crystal dynamics and their elastic properties, volume phase transition of hydrogels when their dimensions are sub-micron, and critical opalescence of binary mixtures (water/2,6-lutidine).

Combustion stratification study of partially premixed combustion using Fourier transform analysis of OH* chemiluminescence images

KAUST Repository

Izadi Najafabadi, Mohammad

2017-11-06

A relatively high level of stratification (qualitatively: lack of homogeneity) is one of the main advantages of partially premixed combustion over the homogeneous charge compression ignition concept. Stratification can smooth the heat release rate and improve the controllability of combustion. In order to compare stratification levels of different partially premixed combustion strategies or other combustion concepts, an objective and meaningful definition of “stratification level” is required. Such a definition is currently lacking; qualitative/quantitative definitions in the literature cannot properly distinguish various levels of stratification. The main purpose of this study is to objectively define combustion stratification (not to be confused with fuel stratification) based on high-speed OH* chemiluminescence imaging, which is assumed to provide spatial information regarding heat release. Stratification essentially being equivalent to spatial structure, we base our definition on two-dimensional Fourier transforms of photographs of OH* chemiluminescence. A light-duty optical diesel engine has been used to perform the OH* bandpass imaging on. Four experimental points are evaluated, with injection timings in the homogeneous regime as well as in the stratified partially premixed combustion regime. Two-dimensional Fourier transforms translate these chemiluminescence images into a range of spatial frequencies. The frequency information is used to define combustion stratification, using a novel normalization procedure. The results indicate that this new definition, based on Fourier analysis of OH* bandpass images, overcomes the drawbacks of previous definitions used in the literature and is a promising method to compare the level of combustion stratification between different experiments.

Analytic and Unambiguous Phase-Based Algorithm for 3-D Localization of a Single Source with Uniform Circular Array

Directory of Open Access Journals (Sweden)

Le Zuo

2018-02-01

Full Text Available This paper presents an analytic algorithm for estimating three-dimensional (3-D localization of a single source with uniform circular array (UCA interferometers. Fourier transforms are exploited to expand the phase distribution of a single source and the localization problem is reformulated as an equivalent spectrum manipulation problem. The 3-D parameters are decoupled to different spectrums in the Fourier domain. Algebraic relations are established between the 3-D localization parameters and the Fourier spectrums. Fourier sampling theorem ensures that the minimum element number for 3-D localization of a single source with a UCA is five. Accuracy analysis provides mathematical insights into the 3-D localization algorithm that larger number of elements gives higher estimation accuracy. In addition, the phase-based high-order difference invariance (HODI property of a UCA is found and exploited to realize phase range compression. Following phase range compression, ambiguity resolution is addressed by the HODI of a UCA. A major advantage of the algorithm is that the ambiguity resolution and 3-D localization estimation are both analytic and are processed simultaneously, hence computationally efficient. Numerical simulations and experimental results are provided to verify the effectiveness of the proposed 3-D localization algorithm.

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)

Asymptotically stable phase synchronization revealed by autoregressive circle maps

Science.gov (United States)

Drepper, F. R.

2000-11-01

A specially designed of nonlinear time series analysis is introduced based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit estimation scheme for the potentially underlying autoregressive circle map (next phase map) guarantee the invertibility of reconstructed phase space trajectories to the original coordinates. The resulting Fourier approximated, invertibility enforcing phase space map allows us to detect conditional asymptotic stability of coupled phases. This comparatively general synchronization criterion unites two existing generalizations of the old concept and can successfully be applied, e.g., to phases obtained from electrocardiogram and airflow recordings characterizing cardiorespiratory interaction.

New Substrate-Guided Method of Predicting Slow Conducting Isthmuses of Ventricular Tachycardia: Preliminary Analysis to the Combined Use of Voltage Limit Adjustment and Fast-Fourier Transform Analysis.

Science.gov (United States)

Kuroki, Kenji; Nogami, Akihiko; Igarashi, Miyako; Masuda, Keita; Kowase, Shinya; Kurosaki, Kenji; Komatsu, Yuki; Naruse, Yoshihisa; Machino, Takeshi; Yamasaki, Hiro; Xu, Dongzhu; Murakoshi, Nobuyuki; Sekiguchi, Yukio; Aonuma, Kazutaka

2018-04-01

Several conducting channels of ventricular tachycardia (VT) can be identified using voltage limit adjustment (VLA) of substrate mapping. However, the sensitivity or specificity to predict a VT isthmus is not high by using VLA alone. This study aimed to evaluate the efficacy of the combined use of VLA and fast-Fourier transform analysis to predict VT isthmuses. VLA and fast-Fourier transform analyses of local ventricular bipolar electrograms during sinus rhythm were performed in 9 postinfarction patients who underwent catheter ablation for a total of 13 monomorphic VTs. Relatively higher voltage areas on an electroanatomical map were defined as high voltage channels (HVCs), and relatively higher fast-Fourier transform areas were defined as high-frequency channels (HFCs). HVCs were classified into full or partial HVCs (the entire or >30% of HVC can be detectable, respectively). Twelve full HVCs were identified in 7 of 9 patients. HFCs were located on 7 of 12 full HVCs. Five VT isthmuses (71%) were included in the 7 full HVC+/HFC+ sites, whereas no VT isthmus was found in the 5 full HVC+/HFC- sites. HFCs were identical to 9 of 16 partial HVCs. Eight VT isthmuses (89%) were included in the 9 partial HVC+/HFC+ sites, whereas no VT isthmus was found in the 7 partial HVC+/HFC- sites. All HVC+/HFC+ sites predicted VT isthmus with a sensitivity of 100% and a specificity of 80%. Combined use of VLA and fast-Fourier transform analysis may be a useful method to detect VT isthmuses. © 2018 American Heart Association, Inc.

Fourier transform infrared and fluorescence spectroscopy for analysis of vegetable oils

Directory of Open Access Journals (Sweden)

Nigri S.

2013-09-01

Full Text Available Fourier transform infrared (FTIR and fluorescence spectroscopy, combined with chemometric approaches have been developed to analysis of extra virgin olive oil adulterated with pomace olive oil. The measurements were made on pure vegetable oils: extra virgin oil, pomace olive oil and that adulterated with varying concentration of pomace olive oil. Today, the application of FTIR spectroscopy has increased in food studied, and particularly has become a powerful analytical tool in the study of edible oils and fats. The spectral regions where the variations were observed chosen for developing models and cross validation was used. The synchronous fluorescence spectrometry takes advantage of the hardware capability to vary both the excitation and emission wavelengths during the analysis with constant wavelength difference is maintained between the two. The region between 300 and 400 nm is attributed to the tocopherols and phenols, the derivatives of vitamin E are associated with the region 400–600 nm and the bands in the region of 600–700 nm are attributed to the chlorophyll and peophytin pigments. The results presented in this study suggest that FTIR and fluorescence may be a useful tool for analysis and detecting adulteration of extra virgin olive oil with pomace oil.

Quantitative comparison of tympanic membrane displacements using two optical methods to recover the optical phase

Science.gov (United States)

Santiago-Lona, Cynthia V.; Hernández-Montes, María del Socorro; Mendoza-Santoyo, Fernando; Esquivel-Tejeda, Jesús

2018-02-01

The study and quantification of the tympanic membrane (TM) displacements add important information to advance the knowledge about the hearing process. A comparative statistical analysis between two commonly used demodulation methods employed to recover the optical phase in digital holographic interferometry, namely the fast Fourier transform and phase-shifting interferometry, is presented as applied to study thin tissues such as the TM. The resulting experimental TM surface displacement data are used to contrast both methods through the analysis of variance and F tests. Data are gathered when the TMs are excited with continuous sound stimuli at levels 86, 89 and 93 dB SPL for the frequencies of 800, 1300 and 2500 Hz under the same experimental conditions. The statistical analysis shows repeatability in z-direction displacements with a standard deviation of 0.086, 0.098 and 0.080 μm using the Fourier method, and 0.080, 0.104 and 0.055 μm with the phase-shifting method at a 95% confidence level for all frequencies. The precision and accuracy are evaluated by means of the coefficient of variation; the results with the Fourier method are 0.06143, 0.06125, 0.06154 and 0.06154, 0.06118, 0.06111 with phase-shifting. The relative error between both methods is 7.143, 6.250 and 30.769%. On comparing the measured displacements, the results indicate that there is no statistically significant difference between both methods for frequencies at 800 and 1300 Hz; however, errors and other statistics increase at 2500 Hz.

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

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.

Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation

International Nuclear Information System (INIS)

Aldea, N; Pintea, S; Rednic, V; Matei, F; Hu Tiandou; Xie Yaning

2009-01-01

The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe 3 O 4 core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.

Development of Michelson interferometer based spatial phase-shift digital shearography

Science.gov (United States)

Xie, Xin

Digital shearography is a non-contact, full field, optical measurement method, which has the capability of directly measuring the gradient of deformation. For high measurement sensitivity, phase evaluation method has to be introduced into digital shearography by phase-shift technique. Catalog by phase-shift method, digital phase-shift shearography can be divided into Temporal Phase-Shift Digital Shearography (TPS-DS) and Spatial Phase-Shift Digital Shearography (SPS-DS). TPS-DS is the most widely used phase-shift shearography system, due to its simple algorithm, easy operation and good phase-map quality. However, the application of TPS-DS is only limited in static/step-by-step loading measurement situation, due to its multi-step shifting process. In order to measure the strain under dynamic/continuous loading situation, a SPS-DS system has to be developed. This dissertation aims to develop a series of Michelson Interferometer based SPS-DS measurement methods to achieve the strain measurement by using only a single pair of speckle pattern images. The Michelson Interferometer based SPS-DS systems utilize special designed optical setup to introduce extra carrier frequency into the laser wavefront. The phase information corresponds to the strain field can be separated on the Fourier domain using a Fourier Transform and can further be evaluated with a Windowed Inverse Fourier Transform. With different optical setups and carrier frequency arrangements, the Michelson Interferometer based SPS-DS method is capable to achieve a variety of measurement tasks using only single pair of speckle pattern images. Catalog by the aimed measurand, these capable measurement tasks can be divided into five categories: 1) measurement of out-of-plane strain field with small shearing amount; 2) measurement of relative out-of-plane deformation field with big shearing amount; 3) simultaneous measurement of relative out-of-plane deformation field and deformation gradient field by using multiple

Investigation of Cyprus thermal tenancy using nine year MODIS LST data and Fourier analysis

Science.gov (United States)

Skarlatos, D.; Miliaresis, G.; Georgiou, A.

2013-08-01

Land Surface Temperature (LST) is an extremely important parameter that controls the exchange of long wave radiation between surface and atmosphere. It is a good indicator of the energy balance at the Earth's surface and it is one of the key parameters in the physics of land-surface processes on regional as well as global scale. This paper utilizes monthly night and day averaged LST MODIS imagery over Cyprus for a 9 year period. Fourier analysis and Least squares estimation fitting are implemented to analyze mean daily data over Cyprus in an attempt to investigate possible temperature tenancy over these years and possible differences among areas with different land cover and land use, such as Troodos Mountain and Nicosia, the main city in the center of the island. The analysis of data over a long time period, allows questions such as whether there is a tenancy to temperature increase, to be answered in a statistically better way, provided that `noise' is removed correctly. Dealing with a lot of data, always provides a more accurate estimation, but on the other hand, more noise in implemented on the data, especially when dealing with temperature which is subject to daily and annual cycles. A brief description over semi-automated data acquisition and standardization using object-oriented programming and GIS-based techniques, will be presented. The paper fully describes the time series analysis implemented, the Fourier method and how it was used to analyze and filter mean daily data with high frequency. Comparison of mean monthly daily LST against day and night LSTs is also performed over the 9 year period in order to investigate whether use of the extended data series provide significant advantage over short.

A new BP Fourier algorithm and its application in English teaching evaluation

Science.gov (United States)

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.

Criteria for confirming sequence periodicity identified by Fourier transform analysis: application to GCR2, a candidate plant GPCR?

Science.gov (United States)

Illingworth, Christopher J R; Parkes, Kevin E; Snell, Christopher R; Mullineaux, Philip M; Reynolds, Christopher A

2008-03-01

Methods to determine periodicity in protein sequences are useful for inferring function. Fourier transformation is one approach but care is required to ensure the periodicity is genuine. Here we have shown that empirically-derived statistical tables can be used as a measure of significance. Genuine protein sequences data rather than randomly generated sequences were used as the statistical backdrop. The method has been applied to G-protein coupled receptor (GPCR) sequences, by Fourier transformation of hydrophobicity values, codon frequencies and the extent of over-representation of codon pairs; the latter being related to translational step times. Genuine periodicity was observed in the hydrophobicity whereas the apparent periodicity (as inferred from previously reported measures) in the translation step times was not validated statistically. GCR2 has recently been proposed as the plant GPCR receptor for the hormone abscisic acid. It has homology to the Lanthionine synthetase C-like family of proteins, an observation confirmed by fold recognition. Application of the Fourier transform algorithm to the GCR2 family revealed strongly predicted seven fold periodicity in hydrophobicity, suggesting why GCR2 has been reported to be a GPCR, despite negative indications in most transmembrane prediction algorithms. The underlying multiple sequence alignment, also required for the Fourier transform analysis of periodicity, indicated that the hydrophobic regions around the 7 GXXG motifs commence near the C-terminal end of each of the 7 inner helices of the alpha-toroid and continue to the N-terminal region of the helix. The results clearly explain why GCR2 has been understandably but erroneously predicted to be a GPCR.

On the role of spatial phase and phase correlation in vision, illusion, and cognition.

Science.gov (United States)

Gladilin, Evgeny; Eils, Roland

2015-01-01

Numerous findings indicate that spatial phase bears an important cognitive information. Distortion of phase affects topology of edge structures and makes images unrecognizable. In turn, appropriately phase-structured patterns give rise to various illusions of virtual image content and apparent motion. Despite a large body of phenomenological evidence not much is known yet about the role of phase information in neural mechanisms of visual perception and cognition. Here, we are concerned with analysis of the role of spatial phase in computational and biological vision, emergence of visual illusions and pattern recognition. We hypothesize that fundamental importance of phase information for invariant retrieval of structural image features and motion detection promoted development of phase-based mechanisms of neural image processing in course of evolution of biological vision. Using an extension of Fourier phase correlation technique, we show that the core functions of visual system such as motion detection and pattern recognition can be facilitated by the same basic mechanism. Our analysis suggests that emergence of visual illusions can be attributed to presence of coherently phase-shifted repetitive patterns as well as the effects of acuity compensation by saccadic eye movements. We speculate that biological vision relies on perceptual mechanisms effectively similar to phase correlation, and predict neural features of visual pattern (dis)similarity that can be used for experimental validation of our hypothesis of "cognition by phase correlation."

On the role of spatial phase and phase correlation in vision, illusion and cognition

Directory of Open Access Journals (Sweden)

Evgeny eGladilin

2015-04-01

Full Text Available Numerous findings indicate that spatial phase bears an important cognitive information. Distortion of phase affects topology of edge structures and makes images unrecognizable. In turn, appropriately phase-structured patterns give rise to various illusions of virtual image content and apparent motion. Despite a large body of phenomenological evidence not much is known yet about the role of phase information in neural mechanisms of visual perception and cognition. Here, we are concerned with analysis of the role of spatial phase in computational and biological vision, emergence of visual illusions and pattern recognition. We hypothesize that fundamental importance of phase information for invariant retrieval of structural image features and motion detection promoted development of phase-based mechanisms of neural image processing in course of evolution of biological vision. Using an extension of Fourier phase correlation technique, we show that the core functions of visual system such as motion detection and pattern recognition can be facilitated by the same basic mechanism. Our analysis suggests that emergence of visual illusions can be attributed to presence of coherently phase-shifted repetitive patterns as well as the effects of acuity compensation by saccadic eye movements. We speculate that biological vision relies on perceptual mechanisms effectively similar to phase correlation, and predict neural features of visual pattern (dissimilarity that can be used for experimental validation of our hypothesis of 'cognition by phase correlation'.

Lectures on harmonic analysis

CERN Document Server

Wolff, Thomas H; Shubin, Carol

2003-01-01

This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for fu...

Processing of gamma-ray spectra employing a Fourier deconvolver for the analysis of complex spectra

International Nuclear Information System (INIS)

Madan, V.K.; Rattan, S.S.

1996-01-01

Processing of a nuclear spectrum e.g. gamma ray spectrum is concerned with the estimation of energies and intensities of radiation. The processing involves filtering, peak detection and its significance, baseline delineation, the qualitative and the quantitative analysis of singlets and multiplets present in the spectrum. The methodology for the analysis of singlets is well established. However, the analysis of multiplets provides a challenge and is a extremely difficult problem. This report incorporates a Fourier deconvolver for the quantitative analysis of doublets separated by more than a full width at half maximum. The method is easy to implement. The report discusses the methodology, mathematical analysis, and the results obtained by analyzing both synthetic and observed spectra. A computer program, developed for the analysis of a nuclear spectrum, was verified by analyzing a 152 Eu gamma ray spectrum. The proposed technique compared favourably with SAMPO and MDFT method. (author). 16 refs., 3 tabs

Sample handling and contamination encountered when coupling offline normal phase high performance liquid chromatography fraction collection of petroleum samples to Fourier transform ion cyclotron resonance mass spectrometry.

Science.gov (United States)

Oro, Nicole E; Whittal, Randy M; Lucy, Charles A

2012-09-05

Normal phase high performance liquid chromatography (HPLC) is used to separate a gas oil petroleum sample, and the fractions are collected offline and analyzed on a high resolution Fourier Transform Ion Cyclotron Resonance Mass Spectrometer (FT-ICR MS). The separation prior to MS analysis dilutes the sample significantly; therefore the fractions need to be prepared properly to achieve the best signal possible. The methods used to prepare the HPLC fractions for MS analysis are described, with emphasis placed on increasing the concentration of analyte species. The dilution effect also means that contamination in the MS spectra needs to be minimized. The contamination from molecular sieves, plastics, soap, etc. and interferences encountered during the offline fraction collection process are described and eliminated. A previously unreported MS contamination of iron formate clusters with a 0.8 mass defect in positive mode electrospray is also described. This interference resulted from the stainless steel tubing in the HPLC system. Contamination resulting from what has tentatively been assigned as palmitoylglycerol and stearoylglycerol was also observed; these compounds have not previously been reported as contaminant peaks. Copyright © 2012 Elsevier B.V. All rights reserved.

Quadrature formulas for Fourier coefficients

KAUST Repository

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.

Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis

International Nuclear Information System (INIS)

Shimizu, Ryosuke; Edamatsu, Keiichi; Itoh, Tadashi

2006-01-01

We present one- and two-photon diffraction and interference experiments involving parametric down-converted photon pairs. By controlling the divergence of the pump beam in parametric down-conversion, the diffraction-interference pattern produced by an object changes from a quantum (perfectly correlated) case to a classical (uncorrelated) one. The observed diffraction and interference patterns are accurately reproduced by Fourier-optical analysis taking into account the quantum spatial correlation. We show that the relation between the spatial correlation and the object size plays a crucial role in the formation of both one- and two-photon diffraction-interference patterns

The fractional Fourier transform and applications

Science.gov (United States)

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.

Fourier Series Optimization Opportunity

Science.gov (United States)

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…

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

Directory of Open Access Journals (Sweden)

Sumarna Sumarna

2017-01-01

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

Dispersion analysis of spaced antenna scintillation measurement

Directory of Open Access Journals (Sweden)

M. Grzesiak

2009-07-01

Full Text Available We present a dispersion analysis of the phase of GPS signals received at high latitude. Basic theoretical aspects for spectral analysis of two-point measurement are given. To account for nonstationarity and statistical robustness a power distribution of the windowed Fourier transform cross-spectra as a function of frequency and phase is analysed using the Radon transform.

An introduction to non-harmonic Fourier series

CERN Document Server

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.

A study on the application of Fourier series in IMRT treatment planning.

Science.gov (United States)

Almeida-Trinidad, R; Garnica-Garza, H M

2007-12-01

In intensity-modulated radiotherapy, a set of x-ray fluence profiles is iteratively adjusted until a desired absorbed dose distribution is obtained. The purpose of this article is to present a method that allows the optimization of fluence profiles based on the Fourier series decomposition of an initial approximation to the profile. The method has the advantage that a new fluence profile can be obtained in a precise and controlled way with the tuning of only two parameters, namely the phase of the sine and cosine terms of one of the Fourier components, in contrast to the point-by-point tuning of the profile. Also, because the method uses analytical functions, the resultant profiles do not exhibit numerical artifacts. A test case consisting of a mathematical phantom with a target wrapped around a critical structure is discussed to illustrate the algorithm. It is shown that the degree of conformality of the absorbed dose distribution can be tailored by varying the number of Fourier terms made available to the optimization algorithm. For the test case discussed here, it is shown that the number of Fourier terms to be modified depends on the number of radiation beams incident on the target but it is in general in the order of 10 terms.

Does the entorhinal cortex use the Fourier transform?

Science.gov (United States)

Orchard, Jeff; Yang, Hao; Ji, Xiang

2013-01-01

Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4–12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed “theta precession.” Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415

Biological applications of phase-contrast electron microscopy.

Science.gov (United States)

Nagayama, Kuniaki

2014-01-01

Here, I review the principles and applications of phase-contrast electron microscopy using phase plates. First, I develop the principle of phase contrast based on a minimal model of microscopy, introducing a double Fourier-transform process to mathematically formulate the image formation. Next, I explain four phase-contrast (PC) schemes, defocus PC, Zernike PC, Hilbert differential contrast, and schlieren optics, as image-filtering processes in the context of the minimal model, with particular emphases on the Zernike PC and corresponding Zernike phase plates. Finally, I review applications of Zernike PC cryo-electron microscopy to biological systems such as protein molecules, virus particles, and cells, including single-particle analysis to delineate three-dimensional (3D) structures of protein and virus particles and cryo-electron tomography to reconstruct 3D images of complex protein systems and cells.

Analysis of geometric phase effects in the quantum-classical Liouville formalism.

Science.gov (United States)

Ryabinkin, Ilya G; Hsieh, Chang-Yu; Kapral, Raymond; Izmaylov, Artur F

2014-02-28

We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.

Analysis of geometric phase effects in the quantum-classical Liouville formalism

Energy Technology Data Exchange (ETDEWEB)

Ryabinkin, Ilya G.; Izmaylov, Artur F. [Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4 (Canada); Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada); Hsieh, Chang-Yu; Kapral, Raymond [Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)

2014-02-28

We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.

Analysis of the physical simulation on Fourier transform infrared spectrometer

Science.gov (United States)

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

Fourier power spectrum characteristics of face photographs: attractiveness perception depends on low-level image properties.

Science.gov (United States)

Menzel, Claudia; Hayn-Leichsenring, Gregor U; Langner, Oliver; Wiese, Holger; Redies, Christoph

2015-01-01

We investigated whether low-level processed image properties that are shared by natural scenes and artworks - but not veridical face photographs - affect the perception of facial attractiveness and age. Specifically, we considered the slope of the radially averaged Fourier power spectrum in a log-log plot. This slope is a measure of the distribution of special frequency power in an image. Images of natural scenes and artworks possess - compared to face images - a relatively shallow slope (i.e., increased high spatial frequency power). Since aesthetic perception might be based on the efficient processing of images with natural scene statistics, we assumed that the perception of facial attractiveness might also be affected by these properties. We calculated Fourier slope and other beauty-associated measurements in face images and correlated them with ratings of attractiveness and age of the depicted persons (Study 1). We found that Fourier slope - in contrast to the other tested image properties - did not predict attractiveness ratings when we controlled for age. In Study 2A, we overlaid face images with random-phase patterns with different statistics. Patterns with a slope similar to those in natural scenes and artworks resulted in lower attractiveness and higher age ratings. In Studies 2B and 2C, we directly manipulated the Fourier slope of face images and found that images with shallower slopes were rated as more attractive. Additionally, attractiveness of unaltered faces was affected by the Fourier slope of a random-phase background (Study 3). Faces in front of backgrounds with statistics similar to natural scenes and faces were rated as more attractive. We conclude that facial attractiveness ratings are affected by specific image properties. An explanation might be the efficient coding hypothesis.

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

Generalized functions and Fourier analysis dedicated to Stevan Pilipović on the occasion of his 65th birthday

CERN Document Server

Toft, Joachim; Vindas, Jasson; Wahlberg, Patrik

2017-01-01

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

Science.gov (United States)

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

Direct phase derivative estimation using difference equation modeling in holographic interferometry

International Nuclear Information System (INIS)

Kulkarni, Rishikesh; Rastogi, Pramod

2014-01-01

A new method is proposed for the direct phase derivative estimation from a single spatial frequency modulated carrier fringe pattern in holographic interferometry. The fringe intensity in a given row/column is modeled as a difference equation of intensity with spatially varying coefficients. These coefficients carry the information on the phase derivative. Consequently, the accurate estimation of the coefficients is obtained by approximating the coefficients as a linear combination of the predefined linearly independent basis functions. Unlike Fourier transform based fringe analysis, the method does not call for performing the filtering of the Fourier spectrum of fringe intensity. Moreover, the estimation of the carrier frequency is performed by applying the proposed method to a reference interferogram. The performance of the proposed method is insensitive to the fringe amplitude modulation and is validated with the simulation results. (paper)

Discrimination of handlebar grip samples by fourier transform infrared microspectroscopy analysis and statistics

Directory of Open Access Journals (Sweden)

Zeyu Lin

2017-01-01

Full Text Available In this paper, the authors presented a study on the discrimination of handlebar grip samples, to provide effective forensic science service for hit and run traffic cases. 50 bicycle handlebar grip samples, 49 electric bike handlebar grip samples, and 96 motorcycle handlebar grip samples have been randomly collected by the local police in Beijing (China. Fourier transform infrared microspectroscopy (FTIR was utilized as analytical technology. Then, target absorption selection, data pretreatment, and discrimination of linked samples and unlinked samples were chosen as three steps to improve the discrimination of FTIR spectrums collected from different handlebar grip samples. Principal component analysis and receiver operating characteristic curve were utilized to evaluate different data selection methods and different data pretreatment methods, respectively. It is possible to explore the evidential value of handlebar grip residue evidence through instrumental analysis and statistical treatments. It will provide a universal discrimination method for other forensic science samples as well.

Automated magnification calibration in transmission electron microscopy using Fourier analysis of replica images

International Nuclear Information System (INIS)

Laak, Jeroen A.W.M. van der; Dijkman, Henry B.P.M.; Pahlplatz, Martin M.M.

2006-01-01

The magnification factor in transmission electron microscopy is not very precise, hampering for instance quantitative analysis of specimens. Calibration of the magnification is usually performed interactively using replica specimens, containing line or grating patterns with known spacing. In the present study, a procedure is described for automated magnification calibration using digital images of a line replica. This procedure is based on analysis of the power spectrum of Fourier transformed replica images, and is compared to interactive measurement in the same images. Images were used with magnification ranging from 1,000x to 200,000x. The automated procedure deviated on average 0.10% from interactive measurements. Especially for catalase replicas, the coefficient of variation of automated measurement was considerably smaller (average 0.28%) compared to that of interactive measurement (average 3.5%). In conclusion, calibration of the magnification in digital images from transmission electron microscopy may be performed automatically, using the procedure presented here, with high precision and accuracy

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

Directory of Open Access Journals (Sweden)

Eduardo O. Cerqueira

2000-10-01

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

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

International Nuclear Information System (INIS)

Ardisasmita, M. Syamsa

1996-01-01

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

Design and Development of a compact and ruggest phase and flouresence microscope for space utilization, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — In this SBIR Phase 1 we propose to develop a novel microscope by integrating Fourier phase contrast microscopy (FPCM) and epi-fluorescence microscopy. In FPCM, the...

On fractional Fourier transform moments

NARCIS (Netherlands)

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

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

International Nuclear Information System (INIS)

Axelsson, C.

1994-01-01

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

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

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)

Study on a phase space representation of quantum theory

International Nuclear Information System (INIS)

Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.; Raboanary, R.

2013-01-01

A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.

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-Mellin moment-based intertwining map for image encryption

Science.gov (United States)

Kaur, Manjit; Kumar, Vijay

2018-03-01

In this paper, a robust image encryption technique that utilizes Fourier-Mellin moments and intertwining logistic map is proposed. Fourier-Mellin moment-based intertwining logistic map has been designed to overcome the issue of low sensitivity of an input image. Multi-objective Non-Dominated Sorting Genetic Algorithm (NSGA-II) based on Reinforcement Learning (MNSGA-RL) has been used to optimize the required parameters of intertwining logistic map. Fourier-Mellin moments are used to make the secret keys more secure. Thereafter, permutation and diffusion operations are carried out on input image using secret keys. The performance of proposed image encryption technique has been evaluated on five well-known benchmark images and also compared with seven well-known existing encryption techniques. The experimental results reveal that the proposed technique outperforms others in terms of entropy, correlation analysis, a unified average changing intensity and the number of changing pixel rate. The simulation results reveal that the proposed technique provides high level of security and robustness against various types of attacks.

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

A general theory of interference fringes in x-ray phase grating imaging

International Nuclear Information System (INIS)

Yan, Aimin; Wu, Xizeng; Liu, Hong

2015-01-01

Purpose: The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need. Methods: In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance. Results: The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints. Conclusions: In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers

A general theory of interference fringes in x-ray phase grating imaging.

Science.gov (United States)

Yan, Aimin; Wu, Xizeng; Liu, Hong

2015-06-01

The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need. In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance. The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints. In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers.

Electro-Optical Imaging Fourier-Transform Spectrometer

Science.gov (United States)

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.

The derivative-free Fourier shell identity for photoacoustics.

Science.gov (United States)

Baddour, Natalie

2016-01-01

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

Analysis of mineral phases in coal utilizing factor analysis

International Nuclear Information System (INIS)

Roscoe, B.A.; Hopke, P.K.

1982-01-01

The mineral phase inclusions of coal are discussed. The contribution of these to a coal sample are determined utilizing several techniques. Neutron activation analysis in conjunction with coal washability studies have produced some information on the general trends of elemental variation in the mineral phases. These results have been enhanced by the use of various statistical techniques. The target transformation factor analysis is specifically discussed and shown to be able to produce elemental profiles of the mineral phases in coal. A data set consisting of physically fractionated coal samples was generated. These samples were analyzed by neutron activation analysis and then their elemental concentrations examined using TTFA. Information concerning the mineral phases in coal can thus be acquired from factor analysis even with limited data. Additional data may permit the resolution of additional mineral phases as well as refinement of theose already identified

Fast process (Flash-SPECT) to extract three-dimensional scans of Fourier amplitude and phase of the heart by means of gated single photon emission computed tomography (GASPECT)

International Nuclear Information System (INIS)

Graf, G.; Heidenreich, P.; Clausen, M.; Henze, E.; Bitter, F.; Adam, W.E.

1989-01-01

The backprojection of Fourier-data like the average of the heart period and the sums of the cosinus- and sinusrow with the combined advantage of count statistics yield to high quality functional slices of the heart by only 15 minutes acquisition time. Reducing the data volumes of the functional slices for amplitudes and phases by transforming them in a bull's eye display, it results in superposition free and position independent detection of the leftventricular functional state, with adequate and direct comparison to 201 Tl-Myocard-ECT investigation. (orig.) [de

Implementation of quantum and classical discrete fractional Fourier transforms

Science.gov (United States)

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.

Science.gov (United States)

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.

The Fractional Fourier Transform and Its Application to Energy Localization Problems

Directory of Open Access Journals (Sweden)

ter Morsche Hennie G

2003-01-01

Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

Science.gov (United States)

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.

Dataset of Fourier transform-infrared coupled with chemometric analysis used to distinguish accessions of Garcinia mangostana L. in Peninsular Malaysia

OpenAIRE

Samsir, Sri A’jilah; Bunawan, Hamidun; Yen, Choong Chee; Noor, Normah Mohd

2016-01-01

In this dataset, we distinguish 15 accessions of Garcinia mangostana from Peninsular Malaysia using Fourier transform-infrared spectroscopy coupled with chemometric analysis. We found that the position and intensity of characteristic peaks at 3600–3100 cm−1 in IR spectra allowed discrimination of G. mangostana from different locations. Further principal component analysis (PCA) of all the accessions suggests the two main clusters were formed: samples from Johor, Melaka, and Negeri Sembilan (S...

Applications of Fourier transforms to generalized functions

CERN Document Server

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...

Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.

Science.gov (United States)

Mikkonen, Jopi J W; Raittila, Jussi; Rieppo, Lassi; Lappalainen, Reijo; Kullaa, Arja M; Myllymaa, Sami

2016-09-01

Saliva provides a valuable tool for assessing oral and systemic diseases, but concentrations of salivary components are very small, calling the need for precise analysis methods. In this work, Fourier transform infrared (FT-IR) spectroscopy using transmission and photoacoustic (PA) modes were compared for quantitative analysis of saliva. The performance of these techniques was compared with a calibration series. The linearity of spectrum output was verified by using albumin-thiocyanate (SCN(-)) solution at different SCN(-) concentrations. Saliva samples used as a comparison were obtained from healthy subjects. Saliva droplets of 15 µL were applied on the silicon sample substrate, 6 drops for each specimen, and dried at 37 ℃ overnight. The measurements were carried out using an FT-IR spectrometer in conjunction with an accessory unit for PA measurements. The findings with both transmission and PA modes mirror each other. The major bands presented were 1500-1750 cm(-1) for proteins and 1050-1200 cm(-1) for carbohydrates. In addition, the distinct spectral band at 2050 cm(-1) derives from SCN(-) anions, which is converted by salivary peroxidases to hypothiocyanate (OSCN(-)). The correlation between the spectroscopic data with SCN(-) concentration (r > 0.990 for transmission and r = 0.967 for PA mode) was found to be significant (P < 0.01), thus promising to be utilized in future applications. © The Author(s) 2016.

Two dimensional vibrations of the guinea pig apex organ of Corti measured in vivo using phase sensitive Fourier domain optical coherence tomography

Science.gov (United States)

Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Fridberger, Anders; Ren, Tianying; Wang, Ruikang; Jacques, Steven L.; Nuttall, Alfred L.

2015-02-01

In this study, we measure the in vivo apical-turn vibrations of the guinea pig organ of Corti in both axial and radial directions using phase-sensitive Fourier domain optical coherence tomography. The apical turn in guinea pig cochlea has best frequencies around 100 - 500 Hz which are relevant for human speech. Prior measurements of vibrations in the guinea pig apex involved opening the otic capsule, which has been questioned on the basis of the resulting changes to cochlear hydrodynamics. Here this limitation is overcome by measuring the vibrations through bone without opening the otic capsule. Furthermore, we have significantly reduced the surgery needed to access the guinea pig apex in the axial direction by introducing a miniature mirror inside the bulla. The method and preliminary data are discussed in this article.

Fourier transforms in the complex domain

CERN Document Server

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 Münz and Szász 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,

Synthesis and Analysis of Methacryloyl-L-Alanine Methyl Ester using fourier Transform Nuclear Magnetic Resonance

International Nuclear Information System (INIS)

Tri Darwinto

2008-01-01

Methacryloyl-L-alanine methyl ester was synthesized by reacting methacrylic acid with L-alanine methyl ester hydrochloride in triethylamine at temperature of 90 o C. Hydrogel polymer of poly(methacryloyl-L-alanine methyl ester) was much used for diagnosis and therapy of vascular tumor. The molecular structure methacryloyl-L-alanine methyl ester analyzed by fourier transform nuclear magnetic resonance (FT-NMR) for analyzing of carbon atom ( 13 C) using Distortionless Enhancement by Polarization Transfer (DEPT) measurement mode with coupling as well as without coupling from proton atom ( 1 H). Molecular structure analysis result showed that DEPT FT-NMR measurement mode with coupling as well as without coupling from 1 H was very fast, exact and accurate method for molecular analysis of organic compound especially methacryloyl-L-alanine methyl ester. (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)

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 ...

Uncertainty analysis using Monte Carlo method in the measurement of phase by ESPI

International Nuclear Information System (INIS)

Anguiano Morales, Marcelino; Martinez, Amalia; Rayas, J. A.; Cordero, Raul R.

2008-01-01

A method for simultaneously measuring whole field in-plane displacements by using optical fiber and based on the dual-beam illumination principle electronic speckle pattern interferometry (ESPI) is presented in this paper. A set of single mode optical fibers and beamsplitter are employed to split the laser beam into four beams of equal intensity.One pair of fibers is utilized to illuminate the sample in the horizontal plane so it is sensitive only to horizontal in-plane displacement. Another pair of optical fibers is set to be sensitive only to vertical in-plane displacement. Each pair of optical fibers differs in longitude to avoid unwanted interference. By means of a Fourier-transform method of fringe-pattern analysis (Takeda method), we can obtain the quantitative data of whole field displacements. We found the uncertainty associated with the phases by mean of Monte Carlo-based technique

Fourier Series

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 ...

Fourier Transform Infrared Analysis of Urinary Calculi and Metabolic Studies in a Group of Sicilian Children.

Science.gov (United States)

D'Alessandro, Maria Michela; Gennaro, Giuseppe; Tralongo, Pietro; Maringhini, Silvio

2017-05-01

Prevalence of urinary calculi in children has been increasing in the past years. We performed an analysis of the chemical composition of stones formers of the pediatric population in our geographical area over the years 2005 to 2013. Fourier transform infrared spectroscopy was employed for the determination of the calculus composition of a group of Sicilian children, and metabolic studies were performed to formulate the correct diagnosis and establish therapy. The prevalence of stone formation was much higher for boys than for girls, with a sex ratio of 1.9:1. The single most frequent component was found to be calcium oxalate monohydrate, and calcium oxalates (pure or mixed calculi) were the overall most frequent components. Calcium phosphates ranked 2nd for frequency, most often in mixed calculi, while urates ranked 3rd. The metabolic disorder most often associated with pure calcium oxalate monohydrate calculi was hypocitraturia, while hyperoxaluria was predominantly associated with calcium oxalate dihydrate calculi. Mixed calculi had the highest prevalence in our pediatric population. Our data showed that Fourier transform infrared spectroscopy was a useful tool for the determination of the calculi composition.

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

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

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.

Properties of the distributional finite Fourier transform

OpenAIRE

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.

Phase-image-based content-addressable holographic data storage

Science.gov (United States)

John, Renu; Joseph, Joby; Singh, Kehar

2004-03-01

We propose and demonstrate the use of phase images for content-addressable holographic data storage. Use of binary phase-based data pages with 0 and π phase changes, produces uniform spectral distribution at the Fourier plane. The absence of strong DC component at the Fourier plane and more intensity of higher order spatial frequencies facilitate better recording of higher spatial frequencies, and improves the discrimination capability of the content-addressable memory. This improves the results of the associative recall in a holographic memory system, and can give low number of false hits even for small search arguments. The phase-modulated pixels also provide an opportunity of subtraction among data pixels leading to better discrimination between similar data pages.

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....

Optical design and analysis of carbon dioxide laser fusion systems using interferometry and fast Fourier transform techniques

International Nuclear Information System (INIS)

Viswanathan, V.K.

1979-01-01

The optical design and analysis of the LASL carbon dioxide laser fusion systems required the use of techniques that are quite different from the currently used method in conventional optical design problems. The necessity for this is explored and the method that has been successfully used at Los Alamos to understand these systems is discussed with examples. This method involves characterization of the various optical components in their mounts by a Zernike polynomial set and using fast Fourier transform techniques to propagate the beam, taking diffraction and other nonlinear effects that occur in these types of systems into account. The various programs used for analysis are briefly discussed

Imaging vibration of the cochlear partition of an excised guinea pig cochlea using phase-sensitive Fourier domain optical coherence tomography

Science.gov (United States)

Choudhury, Niloy; Zeng, Yaguang; Fridberger, Anders; Chen, Fangyi; Zha, Dingjun; Nuttall, Alfred L.; Wang, Ruikang K.

2011-03-01

Studying the sound stimulated vibrations of various membranes that form the complex structure of the organ of Corti in the cochlea of the inner ear is essential for understanding how the travelling sound wave of the basilar membrane couples its energy to the organ structures. In this paper we report the feasibility of using phase-sensitive Fourier domain optical coherence tomography (FD-OCT) to image the vibration of various micro-structures of the cochlea at the same time. An excised cochlea of a guinea pig was stimulated using sounds at various frequencies and vibration image was obtained. When measuring the apex area, vibration signal from different turns, which have different best response frequencies are obtained in the same image. The method has the potential to measure the response from a much wider region of the cochlea than any other currently used method. The noise floor for vibration image for the system at 200 Hz was ~0.3nm.

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography.

Science.gov (United States)

Yang, Qiang; Vogel, Curtis R; Ellerbroek, Brent L

2006-07-20

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.

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

Science.gov (United States)

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

2015-02-01

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

Mapped Fourier Methods for stiff problems in toroidal geometry

OpenAIRE

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...

Analysis of Index Gases of Coal Spontaneous Combustion Using Fourier Transform Infrared Spectrometer

Directory of Open Access Journals (Sweden)

Xiaojun Tang

2014-01-01

Full Text Available Analysis of the index gases of coal for the prevention of spontaneous combustion is of great importance for the enhancement of coal mine safety. In this work, Fourier Transform Infrared Spectrometer (FTIRS is presented to be used to analyze the index gases of coal in real time to monitor spontaneous combustion conditions. Both the instrument parameters and the analysis method are introduced at first by combining characteristics of the absorption spectra of the target analyte with the analysis requirements. Next, more than ten sets of the gas mixture containing ten components (CH4, C2H6, C3H8, iso-C4H10, n-C4H10, C2H4, C3H6, C2H2, CO, and CO2 are included and analyzed with a Spectrum Two FTIRS made by Perkin Elmer. The testing results show that the detection limit of most analytes is less than 2×10-6. All the detection limits meet the monitoring requirements of coal spontaneous combustion in China, which means that FTIRS may be an ideal instrument and the analysis method used in this paper is sufficient for spontaneous combustion gas monitoring on-line and even in situ, since FTIRS has many advantages such as fast analysis, being maintenance-free, and good safety.

Normal and abnormal electrical activation of the heart. Imaging patterns obtained by phase analysis of equilibrium cardiac studies

International Nuclear Information System (INIS)

Pavel, D.; Byrom, E.; Swiryn, S.; Meyer-Pavel, C.; Rosen, K.

1981-01-01

By using a temporal Fourier analysis of gated equilibrium cardiac studies, phase images were obtained. These functional images were analysed qualitatively and quantitatively to determine if specific patterns can be found for normal versus abnormal electrical activation of the heart. The study included eight subjects with normal cardiac function and 24 patients with abnormal electrical activation: eight with left bundle branch block (LBBB), two with right bundle branch block (RBBB), six with Wolff-Parkinson-White syndrome (WPW), one with junctional rhythm, one with spontaneous sustained ventricular tachycardia (VT) (all with normal wall motion), two with chronic transvenous pacemakers, and four with induced sustained VT (all with regional wall motion abnormalities). The results show that the two ventricals have the same mean phase (within +-9 0 ) in normals, but significantly different mean phases in all patients with bundle branch blocks. Of the six WPW patients, three had a distinctive abnormal pattern. The patient with junctional rhythm, those with transvenous pacemakers, and those with VT all had abnormal patterns on the phase image. The phase image is capable of showing differences between patients with electrical activation and a variety of electrical abnormalities. Within the latter category distinct patterns can be associated with each type of abnormality. (author)

Fourier analysis of Solar atmospheric numerical simulations accelerated with GPUs (CUDA).

Science.gov (United States)

Marur, A.

2015-12-01

Solar dynamics from the convection zone creates a variety of waves that may propagate through the solar atmosphere. These waves are important in facilitating the energy transfer between the sun's surface and the corona as well as propagating energy throughout the solar system. How and where these waves are dissipated remains an open question. Advanced 3D numerical simulations have furthered our understanding of the processes involved. Fourier transforms to understand the nature of the waves by finding the frequency and wavelength of these waves through the simulated atmosphere, as well as the nature of their propagation and where they get dissipated. In order to analyze the different waves produced by the aforementioned simulations and models, Fast Fourier Transform algorithms will be applied. Since the processing of the multitude of different layers of the simulations (of the order of several 100^3 grid points) would be time intensive and inefficient on a CPU, CUDA, a computing architecture that harnesses the power of the GPU, will be used to accelerate the calculations.

Phase-Image Encryption Based on 3D-Lorenz Chaotic System and Double Random Phase Encoding

Science.gov (United States)

Sharma, Neha; Saini, Indu; Yadav, AK; Singh, Phool

2017-12-01

In this paper, an encryption scheme for phase-images based on 3D-Lorenz chaotic system in Fourier domain under the 4f optical system is presented. The encryption scheme uses a random amplitude mask in the spatial domain and a random phase mask in the frequency domain. Its inputs are phase-images, which are relatively more secure as compared to the intensity images because of non-linearity. The proposed scheme further derives its strength from the use of 3D-Lorenz transform in the frequency domain. Although the experimental setup for optical realization of the proposed scheme has been provided, the results presented here are based on simulations on MATLAB. It has been validated for grayscale images, and is found to be sensitive to the encryption parameters of the Lorenz system. The attacks analysis shows that the key-space is large enough to resist brute-force attack, and the scheme is also resistant to the noise and occlusion attacks. Statistical analysis and the analysis based on correlation distribution of adjacent pixels have been performed to test the efficacy of the encryption scheme. The results have indicated that the proposed encryption scheme possesses a high level of security.

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)

Content adaptive illumination for Fourier ptychography.

Science.gov (United States)

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%.

Attenuated total internal reflection Fourier transform infrared spectroscopy: a quantitative approach for kidney stone analysis.

Science.gov (United States)

Gulley-Stahl, Heather J; Haas, Jennifer A; Schmidt, Katherine A; Evan, Andrew P; Sommer, André J

2009-07-01

The impact of kidney stone disease is significant worldwide, yet methods for quantifying stone components remain limited. A new approach requiring minimal sample preparation for the quantitative analysis of kidney stone components has been investigated utilizing attenuated total internal reflection Fourier transform infrared spectroscopy (ATR-FT-IR). Calcium oxalate monohydrate (COM) and hydroxylapatite (HAP), two of the most common constituents of urinary stones, were used for quantitative analysis. Calibration curves were constructed using integrated band intensities of four infrared absorptions versus concentration (weight %). The correlation coefficients of the calibration curves range from 0.997 to 0.93. The limits of detection range from 0.07 +/- 0.02% COM/HAP where COM is the analyte and HAP is the matrix, to 0.26 +/- 0.07% HAP/COM where HAP is the analyte and COM is the matrix. This study shows that linear calibration curves can be generated for the quantitative analysis of stone mixtures provided the system is well understood especially with respect to particle size.

Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform

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)

(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

Spectroscopic analysis of bladder cancer tissues using Fourier transform infrared spectroscopy

Science.gov (United States)

Al-Muslet, Nafie A.; Ali, Essam E.

2012-03-01

Bladder cancer is one of the most common cancers in Africa. It takes several days to reach a diagnosis using histological examinations of specimens obtained by endoscope, which increases the medical expense. Recently, spectroscopic analysis of bladder cancer tissues has received considerable attention as a diagnosis technique due to its sensitivity to biochemical variations in the samples. This study investigated the use of Fourier transform infrared (FTIR) spectroscopy to analyze a number of bladder cancer tissues. Twenty-two samples were collected from 11 patients diagnosed with bladder cancer from different hospitals without any pretreatment. From each patient two samples were collected, one normal and another cancerous. FTIR spectrometer was used to differentiate between normal and cancerous bladder tissues via changes in spectra of these samples. The investigations detected obvious changes in the bands of proteins (1650, 1550 cm-1), lipids (2925, 2850 cm-1), and nucleic acid (1080, 1236 cm-1). The results show that FTIR spectroscopy is promising as a rapid, accurate, nondestructive, and easy to use alternative method for identification and diagnosis of bladder cancer tissues.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

International Nuclear Information System (INIS)

Du, Qiang; Yang, Jiang

2017-01-01

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.

Fourier and non-Fourier bio-heat transfer models to predict ex vivo temperature response to focused ultrasound heating

Science.gov (United States)

Li, Chenghai; Miao, Jiaming; Yang, Kexin; Guo, Xiasheng; Tu, Juan; Huang, Pintong; Zhang, Dong

2018-05-01

Although predicting temperature variation is important for designing treatment plans for thermal therapies, research in this area is yet to investigate the applicability of prevalent thermal conduction models, such as the Pennes equation, the thermal wave model of bio-heat transfer, and the dual phase lag (DPL) model. To address this shortcoming, we heated a tissue phantom and ex vivo bovine liver tissues with focused ultrasound (FU), measured the temperature response, and compared the results with those predicted by these models. The findings show that, for a homogeneous-tissue phantom, the initial temperature increase is accurately predicted by the Pennes equation at the onset of FU irradiation, although the prediction deviates from the measured temperature with increasing FU irradiation time. For heterogeneous liver tissues, the predicted response is closer to the measured temperature for the non-Fourier models, especially the DPL model. Furthermore, the DPL model accurately predicts the temperature response in biological tissues because it increases the phase lag, which characterizes microstructural thermal interactions. These findings should help to establish more precise clinical treatment plans for thermal therapies.

Time Lens based Optical Fourier Transformation for All-Optical Signal Processing of Spectrally-Efficient Data

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Lillieholm, Mads

2017-01-01

We review recent progress in the use of time lens based optical Fourier transformation for advanced all-optical signal processing. A novel time lens based complete optical Fourier transformation (OFT) technique is introduced. This complete OFT is based on two quadratic phase-modulation stages using...... four-wave mixing (FWM), separated by a dispersive medium, which enables time-to-frequency and frequency-to-time conversions simultaneously, thus performing an exchange between the temporal and spectral profiles of the input signal. Using the proposed complete OFT, several advanced all-optical signal......, such as orthogonal frequency division multiplexing (OFDM), Nyquist wavelength-division multiplexing (Nyquist-WDM) and Nyquist optical time division multiplexing (Nyquist-OTDM) signals....

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