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Sample records for fourier mode analysis

  1. 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)

  2. 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

  3. 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

  4. 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

  5. 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.

  6. Anisotropic resonator analysis using the Fourier-Bessel mode solver

    Science.gov (United States)

    Gauthier, Robert C.

    2018-03-01

    A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.

  7. Fourier band-power E/B-mode estimators for cosmic shear

    Energy Technology Data Exchange (ETDEWEB)

    Becker, Matthew R.; Rozo, Eduardo

    2016-01-20

    We introduce new Fourier band-power estimators for cosmic shear data analysis and E/B-mode separation. We consider both the case where one performs E/B-mode separation and the case where one does not. The resulting estimators have several nice properties which make them ideal for cosmic shear data analysis. First, they can be written as linear combinations of the binned cosmic shear correlation functions. Secondly, they account for the survey window function in real-space. Thirdly, they are unbiased by shape noise since they do not use correlation function data at zero separation. Fourthly, the band-power window functions in Fourier space are compact and largely non-oscillatory. Fifthly, they can be used to construct band-power estimators with very efficient data compression properties. In particular, we find that all of the information on the parameters Ωm, σ8 and ns in the shear correlation functions in the range of ~10–400 arcmin for single tomographic bin can be compressed into only three band-power estimates. Finally, we can achieve these rates of data compression while excluding small-scale information where the modelling of the shear correlation functions and power spectra is very difficult. Given these desirable properties, these estimators will be very useful for cosmic shear data analysis.

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

    NARCIS (Netherlands)

    Alieva, T.; Bastiaans, M.J.

    2007-01-01

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

  9. 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.

  10. Research on FBG-based longitudinal-acousto-optic modulator with Fourier mode coupling method.

    Science.gov (United States)

    Li, Zhuoxuan; Pei, Li; Liu, Chao; Ning, Tigang; Yu, Shaowei

    2012-10-20

    Fourier mode coupling model was first applied to achieve the spectra property of a fiber Bragg grating (FBG)-based longitudinal-acousto-optic modulator. Compared with traditional analysis algorithms, such as the transfer matrix method, the Fourier mode coupling model could improve the computing efficiency up to 100 times with a guarantee of accuracy. In this paper, based on the theoretical analysis of this model, the spectra characteristics of the modulator in different frequencies and acoustically induced strains were numerically simulated. In the experiment, a uniform FBG was modulated by acoustic wave (AW) at 12 different frequencies. In particular, the modulator responses at 563 and 885.5 KHz with three different lead zirconate titanate (PZT) loads applied were plotted for illustration, and the linear fitting of experimental data demonstrated a good match with the simulation result. The acoustic excitation of the longitudinal wave is obtained using a conic silica horn attached to the surface of a shear-mode PZT plate paralleled to the fiber axis. This way of generating longitudinal AW with a transversal PZT may shed light on the optimal structural design for the FBG-based longitudinal-acousto-optic modulator.

  11. Analysis of tokamak plasma confinement modes using the fast

    Indian Academy of Sciences (India)

    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 ...

  12. Principles of Fourier analysis

    CERN Document Server

    Howell, Kenneth B

    2001-01-01

    Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...

  13. 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.

  14. Fourier phase in Fourier-domain optical coherence tomography

    Science.gov (United States)

    Uttam, Shikhar; Liu, Yang

    2015-01-01

    Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383

  15. Fourier phase in Fourier-domain optical coherence tomography.

    Science.gov (United States)

    Uttam, Shikhar; Liu, Yang

    2015-12-01

    Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.

  16. 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...

  17. 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

  18. 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.

  19. Calibration and fluctuation of the secular frequency peak amplitude versus initial condition distribution of the ion cloud confined into a three-dimensional quadrupole ion trap using a fourier transform operating mode and a steady ion flow injection mode

    International Nuclear Information System (INIS)

    Janulyte, A.; Andre, J.; Carette, M.; Mercury, M.; Reynard, C; Zerega, Y.

    2009-01-01

    A specific Fourier transform operating mode is applied to a 3-dimensional quadrupolar ion trap for mass analysis (Fourier Transform Quadrupolar Ion Trap (FTQIT) Operating Mode or Mass Spectrometer). With this operating mode, an image signal, which is representative of the collective motion of simultaneously confined ions, is made up from a set of recorded time-of-flight histograms. In an ion trap, the secular frequency of ion motion depends on m/Z ratio of the ion. By Fourier transformation of the image signal, one observes the frequency peak of each confined ionic species. When only one ionic species is confined, the peak amplitude is proportional to the maximal amplitude of the image signal. The maximal amplitude of the image signal is expressed according to the operating parameters, the initial conditions of the ions and the number of ions. Simulation tools lead to fluctuation calculation of the maximal amplitude of the image signal. Two origins are explored: (1) the fluctuation of the numbers of ions according to the steady ion flow injection mode (SIFIM) used with this operating mode and (2) the distribution fluctuation of the initial positions and velocities. Initial confinement conditions, obtained with SIFIM injection mode, lead to optimal detection with small fluctuations of the peak amplitude for Fourier transform operating mode applied to an ion trap. (authors)

  20. 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

  1. Broadband Fourier domain mode-locked laser for optical coherence tomography at 1060 nm

    DEFF Research Database (Denmark)

    Marschall, Sebastian; Klein, Thomas; Wieser, Wolfgang

    2012-01-01

    Optical coherence tomography (OCT) in the 1060nm range is interesting for in vivo imaging of the human posterior eye segment (retina, choroid, sclera) due to low absorption in water and deep penetration into the tissue. Rapidly tunable light sources, such as Fourier domain mode-locked (FDML) lasers...

  2. 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)

  3. Fourier domain mode-locked swept source at 1050 nm based on a tapered amplifier

    DEFF Research Database (Denmark)

    Marschall, Sebastian; Klein, Thomas; Wieser, Wolfgang

    2010-01-01

    While swept source optical coherence tomography (OCT) in the 1050 nm range is promising for retinal imaging, there are certain challenges. Conventional semiconductor gain media have limited output power, and the performance of high-speed Fourier domain mode-locked (FDML) lasers suffers from...

  4. Laser Mode Behavior of the Cassini CIRS Fourier Transform Spectrometer at Saturn

    Science.gov (United States)

    Brasunas, John C.

    2012-01-01

    The CIRS Fourier transform spectrometer aboard the NASA/ESA/ASI Cassini orbiter has been acquiring spectra of the Saturnian system since 2004. The CIRS reference interferometer employs a laser diode to trigger the interferogram sampling. Although the control of laser diode drive current and operating temperature are stringent enough to restrict laser wavelength variation to a small fraction of CIRS finest resolution element, the CIRS instrument does need to be restarted every year or two, at which time it may start in a new laser mode. By monitoring the Mylar absorption features in uncalibrated spectra due to the beam splitter Mylar substrate, it can be shown that these jumps are to adjacent modes and that most of the eight-year operation so far is restricted to three adjacent modes. For a given mode, the wavelength stability appears consistent with the stability of the laser diode drive curren.t and operating temperature.

  5. 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...

  6. 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.

  7. 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...

  8. Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations

    Science.gov (United States)

    Alzahrani, Mohammed A.; Gauthier, Robert C.

    2015-02-01

    For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.

  9. 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.

  10. 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...

  11. 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

  12. 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.

  13. 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)

  14. 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...

  15. 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

  16. 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...

  17. Effect of intravenous drug administration mode on drug distribution in a tumor slab: a finite Fourier transform analysis.

    Science.gov (United States)

    Subramaniam, B; Claudius, J S

    1990-03-08

    Cancer therapy using chemotherapeutic drugs frequently involves injection of the drug into the body through some intravenous mode of administration, viz, continuous (drip) infusion or single/multiple bolus injection(s). An understanding of the effect of the various modes of administration upon tumor penetration of drug is essential to rational design of drug therapy. This paper investigates drug penetration into a model tumor of slab geometry (between two capillaries) in which the overall transport rate of drug is limited by intra-tumor transport characterized by an effective diffusion coefficient. Employing the method of Finite Fourier Transforms (FFT), analytical solutions have been obtained for transient drug distribution in both the plasma and the tumor following three modes of administration, viz, continuous infusion, single bolus injection and equally-spaced equal-dose multiple bolus injections, of a given amount of drug. The qualitative trends exhibited by the plasma drug distribution profiles are consistent with reported experimental studies. Two concepts, viz, the dimensionless decay constant and the plasma/tumor drug concentration trajectories, are found to be particularly useful in the rational design of drug therapy. The dimensionless decay constant provides a measure of the rate of drug decay in the plasma relative to the rate of drug diffusion into the tumor and is thus characteristic of the tumor/drug system. The magnitude of this parameter dictates the choice of drug administration mode for minimizing drug decay in the plasma while simultaneously maximizing drug transport into the tumor. The concentration trajectories provide a measure of the plasma drug concentration relative to the tumor drug concentration at various times following injection. When the tumor drug concentration exceeds the plasma drug concentration, the drug will begin to diffuse out of the tumor. Knowledge of the time at which this diffusion reversal occurs is especially useful

  18. 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.”

  19. 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...

  20. 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.

  1. 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.

  2. High-speed polarization-sensitive OCT at 1060 nm using a Fourier domain mode-locked swept source

    DEFF Research Database (Denmark)

    Marschall, Sebastian; Torzicky, Teresa; Klein, Thomas

    2012-01-01

    sufficiently large datasets. Here, we demonstrate PS-OCT imaging at 350 kHz A-scan rate using a two-channel PS-OCT system in conjunction with a Fourier domain mode-locked laser. The light source spectrum spans up to 100nm around the water absorption minimum at 1060 nm. By modulating the laser pump current, we...

  3. 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)

  4. Analysis of Coherent Phonon Signals by Sparsity-promoting Dynamic Mode Decomposition

    Science.gov (United States)

    Murata, Shin; Aihara, Shingo; Tokuda, Satoru; Iwamitsu, Kazunori; Mizoguchi, Kohji; Akai, Ichiro; Okada, Masato

    2018-05-01

    We propose a method to decompose normal modes in a coherent phonon (CP) signal by sparsity-promoting dynamic mode decomposition. While the CP signals can be modeled as the sum of finite number of damped oscillators, the conventional method such as Fourier transform adopts continuous bases in a frequency domain. Thus, the uncertainty of frequency appears and it is difficult to estimate the initial phase. Moreover, measurement artifacts are imposed on the CP signal and deforms the Fourier spectrum. In contrast, the proposed method can separate the signal from the artifact precisely and can successfully estimate physical properties of the normal modes.

  5. 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)

  6. 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.

  7. 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.

  8. 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.

  9. 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)

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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

    This paper presents the comparison of a reliability technique that employs a Fourier series representation of random axisymmetric and asymmetric imperfections in a cylindrical pressure vessel subjected to an axial end load and external pressure, with evaluations prescribed by the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2 Rules. The ultimate goal of the reliability technique described herein is to predict the critical buckling load associated with the subject cylindrical pressure vessel. Initial geometric imperfections are shown to have a significant effect on the calculated load carrying capacity of the vessel. Fourier decomposition was employed to interpret imperfections as structural features that can be easily related to various other types of defined imperfections. The initial functional description of the imperfections consists of an axisymmetric portion and a deviant portion, which are availed in the form of a double Fourier series. Fifty simulated shells generated by the Monte Carlo technique are employed in the final prediction of the critical buckling load. The representation of initial geometrical imperfections in the cylindrical pressure vessel requires the determination of respective Fourier coefficients. Multi-mode analyses are expanded to evaluate a large number of potential buckling modes for both predefined geometries in combination with asymmetric imperfections as a function of position within the given cylindrical shell. The probability of the ultimate buckling stress exceeding a predefined threshold stress is also calculated. The method and results described herein are in stark contrast to the “knockdown factor” approach as applied to compressive stress evaluations currently utilized in industry. Further effort is needed to improve on the current design rules regarding column buckling of large diameter pressure vessels subjected to an axial end load and external pressure designed in accordance with ASME Boiler and

  15. Spatial stability of jets - the nonaxisymmetric fundamental and reflection modes

    International Nuclear Information System (INIS)

    Hardee, P.E.

    1987-01-01

    A spatial stability analysis of the relativistic dispersion relation governing the growth and propagation of harmonic components comprising a perturbation to the surface of a cylindrical jet is performed. The spatial growth of harmonic components associated with the nonaxisymmetric fundamental solution and reflection solutions of several Fourier modes are analyzed. Approximate analytical expressions describing resonant frequencies and wavelengths, and maximum growth rates at resonance applicable to relativistic jets are found from the dispersion relation, and the nature of the resonances is explored. On transonic jets there is only a fundamental solution for each Fourier mode with no resonance or maximum growth rate. On supersonic jets there is a fundamental solution and reflection solutions for each Fourier mode, and each solution contains a resonance at which the growth rate is a maximum. A numerical analysis of the fundamental and first three reflection solutions of the axisymmetric and first three nonaxisymmetric Fourier modes is performed. The numerical analysis is restricted to nonrelativistic flows but otherwise covers a broad range of Mach numbers and jet densities. The numerical results are used along with the analytical results to obtain accurate expressions for resonant frequencies, wavelengths, and growth rates as a function of Mach numnber and jet density. In all cases the fastest spatial growth rate at a given frequency is of harmonic components associated with the fundamental solution of one of the nonaxisymmetric Fourier modes. The application of these results to jet structure and implication of these results for jet structure in extragalactic radio sources are considered. 23 references

  16. 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)

  17. Wavelength modulation spectroscopy--digital detection of gas absorption harmonics based on Fourier analysis.

    Science.gov (United States)

    Mei, Liang; Svanberg, Sune

    2015-03-20

    This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.

  18. 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.

  19. 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

  20. 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...

  1. 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

  2. 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.

  3. 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.

  4. Efficient formalism for treating tapered structures using the Fourier modal method

    DEFF Research Database (Denmark)

    Østerkryger, Andreas Dyhl; Gregersen, Niels

    2016-01-01

    We investigate the development of the mode occupations in tapered structures using the Fourier modal method. In order to use the Fourier modal method, tapered structures are divided into layers of uniform refractive index in the propagation direction and the optical modes are found within each...... layer. This is not very efficient and in this proceeding we take the first steps towards a more efficient formalism for treating tapered structures using the Fourier modal method. We show that the coupling coefficients through the structure are slowly varying and that only the first few modes...

  5. 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.

  6. 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...

  7. CASTOR: Normal-mode analysis of resistive MHD plasmas

    NARCIS (Netherlands)

    Kerner, W.; Goedbloed, J. P.; Huysmans, G. T. A.; Poedts, S.; Schwarz, E.

    1998-01-01

    The CASTOR (complex Alfven spectrum of toroidal plasmas) code computes the entire spectrum of normal-modes in resistive MHD for general tokamak configurations. The applied Galerkin method, in conjunction with a Fourier finite-element discretisation, leads to a large scale eigenvalue problem A (x)

  8. Fourier analysis in dynamic non periodic phenomena in nuclear medicine

    International Nuclear Information System (INIS)

    Constantinesco, A.; Lallot, C.

    1984-01-01

    The success of Fourier analysis in assessing cardiac function has led us to investigate other possible uses of this technique. We show that phase analysis applied to dynamic non periodic activity changes gives useful parametric functional images. The phase image is comparable to a transit time image, the amplitude image is comparable to the maximum variations of activity and the mean image corresponds to a normalized sum of images. Exemples of this powerful application of Fourier analysis are discussed [fr

  9. 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...

  10. 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

  11. 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.

  12. Motion analysis of optically trapped particles and cells using 2D Fourier analysis

    DEFF Research Database (Denmark)

    Kristensen, Martin Verner; Ahrendt, Peter; Lindballe, Thue Bjerring

    2012-01-01

    Motion analysis of optically trapped objects is demonstrated using a simple 2D Fourier transform technique. The displacements of trapped objects are determined directly from the phase shift between the Fourier transform of subsequent images. Using end-and side-view imaging, the stiffness...... of the trap is determined in three dimensions. The Fourier transform method is simple to implement and applicable in cases where the trapped object changes shape or where the lighting conditions change. This is illustrated by tracking a fluorescent particle and a myoblast cell, with subsequent determination...

  13. 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

  14. 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.

  15. Fourier imaging of non-linear structure formation

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-04-01

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

  16. Fourier imaging of non-linear structure formation

    International Nuclear Information System (INIS)

    Brandbyge, Jacob; Hannestad, Steen

    2017-01-01

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

  17. 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.

  18. Picosecond pulses from wavelength-swept continuous-wave Fourier domain mode-locked lasers.

    Science.gov (United States)

    Eigenwillig, Christoph M; Wieser, Wolfgang; Todor, Sebastian; Biedermann, Benjamin R; Klein, Thomas; Jirauschek, Christian; Huber, Robert

    2013-01-01

    Ultrafast lasers have a crucial function in many fields of science; however, up to now, high-energy pulses directly from compact, efficient and low-power semiconductor lasers are not available. Therefore, we introduce a new approach based on temporal compression of the continuous-wave, wavelength-swept output of Fourier domain mode-locked lasers, where a narrowband optical filter is tuned synchronously to the round-trip time of light in a kilometre-long laser cavity. So far, these rapidly swept lasers enabled orders-of-magnitude speed increase in optical coherence tomography. Here we report on the generation of ~60-70 ps pulses at 390 kHz repetition rate. As energy is stored optically in the long-fibre delay line and not as population inversion in the laser-gain medium, high-energy pulses can now be generated directly from a low-power, compact semiconductor-based oscillator. Our theory predicts subpicosecond pulses with this new technique in the future.

  19. A Fourier analysis for a fast simulation algorithm. [for switching converters

    Science.gov (United States)

    King, Roger J.

    1988-01-01

    This paper presents a derivation of compact expressions for the Fourier series analysis of the steady-state solution of a typical switching converter. The modeling procedure for the simulation and the steady-state solution is described, and some desirable traits for its matrix exponential subroutine are discussed. The Fourier analysis algorithm was tested on a phase-controlled parallel-loaded resonant converter, providing an experimental confirmation.

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

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

    Science.gov (United States)

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

    2007-09-01

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

  6. 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.

  7. 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.

  8. Improved detection of anterior left ventricular aneurysm with multiharmonic fourier analysis

    International Nuclear Information System (INIS)

    Valette, H.B.; Bourguignon, M.H.; Merlet, P.; Gregoire, M.C.; Le Guludec, D.; Pascal, O.; Briandet, P.; Syrota, A.

    1990-01-01

    Single and multiharmonic Fourier analysis of LAO 30-45 degrees gated blood-pool studies were performed in a selected group of 30 patients with a left ventricular anterior aneurysm proven by contrast angiography. The sensitivity of the first harmonic phase image for the diagnosis of ventricular aneurysm was 80%. The clear phase shift (greater than 110 degrees) between the normal and the aneurysmal areas was missing in six patients. Peak acceleration images (negative maximum of the second derivative of the Fourier series) were calculated for each pixel with the analytical Fourier formula using two or three harmonics. A clear phase shift (greater than 126 degrees) than appeared in all the patients. This improvement was related to the increased weight of the second and third harmonics in the aneurysmal area when compared to control patients or to patients with dilative cardiomyopathy. Multiharmonic Fourier analysis clearly improved the sensitivity of the diagnosis of anterior left ventricular aneurysm on LAO 30 degrees-45 degrees gated blood-pool images

  9. Mode-to-mode energy transfers in convective patterns

    Indian Academy of Sciences (India)

    Abstract. We investigate the energy transfer between various Fourier modes in a low- dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical ...

  10. 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.

  11. 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)

  12. 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.

  13. Discrete Fourier Transform Analysis in a Complex Vector Space

    Science.gov (United States)

    Dean, Bruce H.

    2009-01-01

    Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

  14. 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.)

  15. 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)

  16. Exploitation of the Fourier chopper in neutron diffractometry at pulsed sources

    International Nuclear Information System (INIS)

    Hiismaeki, P.; Poeyry, H.; Tiitta, A.

    1988-01-01

    The application of the Fourier chopper in the reverse time-of-flight mode to upgrading the performance of neutron powder diffractometry at pulsed sources is considered. Exploitation of a dual-delay-line binary correlator is suggested and a comprehensive analysis of the necessary data acquisition process is given. The best benefit is shown to be achievable at intensity optimized moderators. (orig.)

  17. 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)

  18. Computation of mode eigenfunctions in graded-index optical fibers by the propagating beam method

    International Nuclear Information System (INIS)

    Feit, M.D.; Fleck, J.A. Jr.

    1980-01-01

    The propagating beam method utilizes discrete Fourier transforms for generating configuration-space solutions to optical waveguide problems without reference to modes. The propagating beam method can also give a complete description of the field in terms of modes by a Fourier analysis with respect to axial distance of the computed fields. Earlier work dealt with the accurate determination of mode propagation constants and group delays. In this paper the method is extended to the computation of mode eigenfunctions. The method is efficient, allowing generation of a large number of eigenfunctions from a single propagation run. Computations for parabolic-index profiles show excellent agreement between analytic and numerically generated eigenfunctions

  19. 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.

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

    International Nuclear Information System (INIS)

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

    2010-01-01

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

  1. Surface Fourier-transform lens using a metasurface

    International Nuclear Information System (INIS)

    Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun

    2015-01-01

    We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)

  2. Minimizing the trend effect on detrended cross-correlation analysis with empirical mode decomposition

    International Nuclear Information System (INIS)

    Zhao Xiaojun; Shang Pengjian; Zhao Chuang; Wang Jing; Tao Rui

    2012-01-01

    Highlights: ► Investigate the effects of linear, exponential and periodic trends on DCCA. ► Apply empirical mode decomposition to extract trend term. ► Strong and monotonic trends are successfully eliminated. ► Get the cross-correlation exponent in a persistent behavior without crossover. - Abstract: Detrended cross-correlation analysis (DCCA) is a scaling method commonly used to estimate long-range power law cross-correlation in non-stationary signals. However, the susceptibility of DCCA to trends makes the scaling results difficult to analyze due to spurious crossovers. We artificially generate long-range cross-correlated signals and systematically investigate the effect of linear, exponential and periodic trends. Specifically to the crossovers raised by trends, we apply empirical mode decomposition method which decomposes underlying signals into several intrinsic mode functions (IMF) and a residual trend. After the removal of residual term, strong and monotonic trends such as linear and exponential trends are successfully eliminated. But periodic trend cannot be separated out according to the criterion of IMF, which can be eliminated by Fourier transform. As a special case of DCCA, detrended fluctuation analysis presents similar results.

  3. 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...

  4. Uniform spacing interrogation of a Fourier domain mode-locked fiber Bragg grating sensor system using a polarization-maintaining fiber Sagnac interferometer

    OpenAIRE

    Lee, Hwi Don; Jung, Eun Joo; Jeong, Myung Yung; Chen, Zhongping; Kim, Chang-Seok

    2013-01-01

    A novel linearized interrogation method is presented for a Fourier domain mode-locked (FDML) fiber Bragg grating (FBG) sensor system. In a high speed regime over several tens of kHz modulations, a sinusoidal wave is available to scan the center wavelength of an FDML wavelength-swept laser, instead of a conventional triangular wave. However, sinusoidal wave modulation suffers from an exaggerated non-uniform wavelength-spacing response in demodulating the time-encoded parameter to the absolute ...

  5. Measurement of nonlinear mode coupling of tearing fluctuations

    International Nuclear Information System (INIS)

    Assadi, S.; Prager, S.C.; Sidikman, K.L.

    1992-03-01

    Three-wave nonlinear coupling of spatial Fourier modes is measured in the MST reversed field pinch by applying bi-spectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 polodial modes and 32 toroidal modes. Comparison to bi-spectra predicted by MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomittant with a broadened (presumably nonlinearly generated) k-spectrum

  6. 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.

  7. 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.)

  8. 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.)

  9. Application of Elliptic Fourier analysis to describe the lamina cribrosa shape with age and intraocular pressure.

    Science.gov (United States)

    Sanfilippo, P G; Grimm, J L; Flanagan, J G; Lathrop, K L; Sigal, I A

    2014-11-01

    The lamina cribrosa (LC) plays an important biomechanical role in the optic nerve head (ONH). We developed a statistical shape model of the LC and tested if the shape varies with age or IOP. The ONHs of 18 donor eyes (47-91 years, mean 76 years) fixed at either 5 or 50 mmHg of IOP were sectioned, stained, and imaged under a microscope. A 3D model of each ONH was reconstructed and the outline of the vertical sagittal section closest to the geometric center of the LC extracted. The outline shape was described using Elliptic Fourier analysis, and principal components analysis (PCA) employed to identify the primary modes of LC shape variation. Linear mixed effect models were used to determine if the shape measurements were associated with age or IOP. The analysis revealed several modes of shape variation: thickness and depth directly (PC 1), or inversely (PC 2) related, and superior-inferior asymmetry (PC 3). Only PC 3 was associated with IOP, with higher IOP correlating with greater curvature of the LC superiorly compared to inferiorly. Our analysis enabled a concise and complete characterization of LC shape, revealing variations without defining them a priori. No association between LC shape and age was found for the relatively old population studied. Superior-inferior asymmetry of LC shape was associated with IOP, with more asymmetry at higher IOP. Increased IOP was not associated with LC thickness or depth. Copyright © 2014 Elsevier Ltd. All rights reserved.

  10. Finite-mode analysis by means of intensity information in fractional optical systems

    NARCIS (Netherlands)

    Alieva, T.; Bastiaans, M.J.

    2002-01-01

    It is shown how a coherent optical signal that contains only a finite number of Hermite-Gauss modes, can be reconstructed from the knowledge of its Radon-Wigner transform -- associated with the intensity distribution in a fractional Fourier transform optical system -- at only two transversal points.

  11. 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.

  12. 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.)

  13. A two-dimensional problem of a mode-I crack in a rotating fibre ...

    Indian Academy of Sciences (India)

    AHMED E ABOUELREGAL

    2018-02-07

    Feb 7, 2018 ... Fibre-reinforced; mode-I crack; dual-phase-lag theory; rotation; normal mode analysis. 1. Introduction ... acki [2, 3] rests upon the hypothesis of the Fourier law of .... forcement and rotation on the variations of different field quantities inside ... The principle of balance of linear momentum leads to the following ...

  14. 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)

  15. Study on MHD instabilities in the CECI plasma device using Fourier probes

    International Nuclear Information System (INIS)

    Rosal, A.C.; Aso, Y.; Ueda, M.

    1991-01-01

    A magnetic diagnostics called Fourier analyser aiming to study MHD instabilities by Fourier series expansion of poloidal magnetic field for m ≤ 3 modes was developed and tested. The diagnostics will be used in the RFP (reversed field pinch) type toroidal plasma device. (M.C.K.)

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. Nonlinear response of dense colloidal suspensions under oscillatory shear: mode-coupling theory and Fourier transform rheology experiments.

    Science.gov (United States)

    Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M

    2010-12-01

    Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

  1. 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...

  2. 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.

  3. Structural characterization of phospholipids by matrix-assisted laser desorption/ionization Fourier transform ion cyclotron resonance mass spectrometry.

    Science.gov (United States)

    Marto, J A; White, F M; Seldomridge, S; Marshall, A G

    1995-11-01

    Matrix-assisted laser desorption/ionization (MALDI) Fourier transform ion cyclotron resonance mass spectrometry provides for structural analysis of the principal biological phospholipids: glycerophosphatidylcholine, -ethanolamine, -serine, and -inositol. Both positive and negative molecular or quasimolecular ions are generated in high abundance. Isolated molecular ions may be collisionally activated in the source side of a dual trap mass analyzer, yielding fragments serving to identify the polar head group (positive ion mode) and fatty acid side chains (negative ion mode). Azimuthal quadrupolar excitation following collisionally activated dissociation refocuses productions close to the solenoid axis; subsequent transfer of product ions to the analyzer ion trap allows for high-resolution mass analysis. Cyro-cooling of the sample probe with liquid nitrogen greatly reduces matrix adduction encountered in the negative ion mode.

  4. A real space calculation of absolutely unstable modes for two-plasmon decay in inhomogeneous plasma

    International Nuclear Information System (INIS)

    Powers, L.V.; Berger, R.L.

    1986-01-01

    Growth rates for absolute modes of two-plasmon decay are obtained by solving for eigenmodes of the coupled mode equations for obliquely scattered Langmuir waves in real space. This analysis establishes a connection both to previous analysis in Fourier transform space and to other parametric instabilities, the analysis of which is commonly done in real space. The essential feature of the instability which admits absolute modes in an inhomogeneous plasma is the strong spatial dependence of the coupling coefficients. Landau damping limits the perpendicular wavenumbers of the most unstable modes and raises the instability thresholds for background plasma temperatures above 1 keV. (author)

  5. Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method

    Directory of Open Access Journals (Sweden)

    WANG Minhao

    2017-08-01

    Full Text Available Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application.

  6. A Fourier Optical Model for the Laser Doppler Velocimeter

    DEFF Research Database (Denmark)

    Lading, Lars

    1972-01-01

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

  7. Vibrational normal modes of diazo-dimedone: A comparative study by Fourier infrared/Raman spectroscopies and conformational analysis by MM/QM

    Science.gov (United States)

    Téllez Soto, C. A.; Ramos, J. M.; Rianelli, R. S.; de Souza, M. C. B. V.; Ferreira, V. F.

    2007-07-01

    The 2-diazo-5,5-dimethyl-cyclohexane-1,3-dione ( 3) was synthesized and the FT-IR/Raman spectra were measured with the purpose of obtain a full assignment of the vibrational modes. Singular aspects concerning the -C dbnd N dbnd N oscillator are discussed in view of two strong bands observed in the region of 2300-2100 cm -1 in both, Infrared and Raman spectra. The density functional theory (DFT) was used to obtain the geometrical structure and for assisting in the vibrational assignment joint to the traditional normal coordinate analysis (NCA). The observed wavenumbers at 2145 (IR), 2144(R) are assigned as the coupled ν(N dbnd N) + ν(C dbnd N) vibrational mode with higher participation of the N dbnd N stretching. A 2188 cm -1 (IR) and at 2186 cm -1 (R) can be assigned as a overtone of one of ν(CC) normal mode or to a combination band of the fundamentals δ(CCH) found at 1169 cm -1 and the δ (CC dbnd N) found at 1017 cm -1 enhanced by Fermi resonance.

  8. 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...

  9. 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)

  10. 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.

  11. 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. 

  12. Higher order mode damping in Kaon factory RF cavities

    International Nuclear Information System (INIS)

    Enegren, T.; Poirier, R.; Griffin, J.; Walling, L.; Thiessen, H.A.; Smythe, W.R.

    1989-05-01

    Proposed designs for Kaon factory accelerators require that the rf cavities support beam currents on the order of several amperes. The beam current has Fourier components at all multiples of the rf frequency. Empty rf buckets produce additional components at all multiples of the revolution frequency. If a Fourier component of the beam coincides with the resonant frequency of a higher order mode of the cavity, which is inevitable if the cavity has a large frequency swing, significant excitation of this mode can occur. The induced voltage may then excite coupled bunch mode instabilities. Effective means are required to damp higher order modes without significantly affecting the fundamental mode. A mode damping scheme based on coupled transmission lines has been investigated and is report

  13. Fourier transform infrared and FT-Raman spectra, assignment, ab initio, DFT and normal co-ordinate analysis of 2-chloro-4-methylaniline and 2-chloro-6-methylaniline.

    Science.gov (United States)

    Arjunan, V; Mohan, S

    2009-03-01

    The Fourier transform infrared (FTIR) and FT-Raman spectra of 2-chloro-4-methylaniline and 2-chloro-6-methylaniline have been measured in the range 4000-400 and 4000-100cm(-1), respectively. Utilising the observed FTIR and FT-Raman data, a complete vibrational assignment and analysis of the fundamental modes of the compounds were carried out. The vibrational frequency which were determined experimentally are compared with those obtained theoretically from ab initio HF and DFT gradient calculations employing the HF/6-31G(d,p) and B3LYP/6-31G(d,p) methods for optimised geometries. The geometries and normal modes of vibration obtained from the HF and DFT methods are in good agreement with the experimental data. The normal co-ordinate analysis was also carried out on the basis of ab initio force fields utilising Wilson's FG matrix method. The manifestations of NH-pi interactions and the influence of bulky chlorine and methyl group on the vibrational modes of the amino group are investigated.

  14. 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...

  15. 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

  16. A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

    Science.gov (United States)

    Debnath, Lokenath

    2012-01-01

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

  17. 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.

  18. On the spectral analysis of iterative solutions of the discretized one-group transport equation

    International Nuclear Information System (INIS)

    Sanchez, Richard

    2004-01-01

    We analyze the Fourier-mode technique used for the spectral analysis of iterative solutions of the one-group discretized transport equation. We introduce a direct spectral analysis for the iterative solution of finite difference approximations for finite slabs composed of identical layers, providing thus a complementary analysis that is more appropriate for reactor applications. Numerical calculations for the method of characteristics and with the diamond difference approximation show the appearance of antisymmetric modes generated by the iteration on boundary data. We have also utilized the discrete Fourier transform to compute the spectrum for a periodic slab containing N identical layers and shown that at the limit N → ∞ one obtains the familiar Fourier-mode solution

  19. Spatial Fourier modes controlling Navier-Stokes flow

    International Nuclear Information System (INIS)

    Treve, Y.M.

    1982-01-01

    As shown by Foias and Prodi in the limit of infinite times the solutions of the two-dimensional Navier-Stokes equations depend only on a finite number of modes, a number for which rigorous estimates can be obtained. A survey of these results is given together with further developments, notably in connection with the numerical approximation to the exact solutions. (Auth.)

  20. 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.)

  1. Absorption Mode FT-ICR Mass Spectrometry Imaging

    Energy Technology Data Exchange (ETDEWEB)

    Smith, Donald F.; Kilgour, David P.; Konijnenburg, Marco; O' Connor, Peter B.; Heeren, Ronald M.

    2013-12-03

    Fourier transform ion cyclotron resonance mass spectrometry offers the highest mass resolving power for molecular imaging experiments. This high mass resolving power ensures that closely spaced peaks at the same nominal mass are resolved for proper image generation. Typically higher magnetic fields are used to increase mass resolving power. However, a gain in mass resolving power can also be realized by phase correction of the data for absorption mode display. In addition to mass resolving power, absorption mode offers higher mass accuracy and signal-to-noise ratio over the conventional magnitude mode. Here we present the first use of absorption mode for Fourier transform ion cyclotron resonance mass spectrometry imaging. The Autophaser algorithm is used to phase correct each spectrum (pixel) in the image and then these parameters are used by the Chameleon work-flow based data processing software to generate absorption mode ?Datacubes? for image and spectral viewing. Absorption mode reveals new mass and spatial features that are not resolved in magnitude mode and results in improved selected ion image contrast.

  2. 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

  3. 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

  4. 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.)

  5. Uniform spacing interrogation of a Fourier domain mode-locked fiber Bragg grating sensor system using a polarization-maintaining fiber Sagnac interferometer

    Science.gov (United States)

    Lee, Hwi Don; Jung, Eun Joo; Jeong, Myung Yung; Chen, Zhongping; Kim, Chang-Seok

    2014-01-01

    A novel linearized interrogation method is presented for a Fourier domain mode-locked (FDML) fiber Bragg grating (FBG) sensor system. In a high speed regime over several tens of kHz modulations, a sinusoidal wave is available to scan the center wavelength of an FDML wavelength-swept laser, instead of a conventional triangular wave. However, sinusoidal wave modulation suffers from an exaggerated non-uniform wavelength-spacing response in demodulating the time-encoded parameter to the absolute wavelength. In this work, the calibration signal from a polarization-maintaining fiber Sagnac interferometer shares the FDML wavelength-swept laser for FBG sensors to convert the time-encoded FBG signal to the wavelength-encoded uniform-spacing signal. PMID:24489440

  6. Uniform spacing interrogation of a Fourier domain mode-locked fiber Bragg grating sensor system using a polarization-maintaining fiber Sagnac interferometer

    International Nuclear Information System (INIS)

    Lee, Hwi Don; Jeong, Myung Yung; Chen, Zhongping; Kim, Chang-Seok; Jung, Eun Joo

    2013-01-01

    A novel linearized interrogation method is presented for a Fourier domain mode-locked (FDML) fiber Bragg grating (FBG) sensor system. In a high speed regime over several tens of kHz modulations, a sinusoidal wave is available to scan the center wavelength of an FDML wavelength-swept laser, instead of a conventional triangular wave. However, sinusoidal wave modulation suffers from an exaggerated non-uniform wavelength-spacing response in demodulating the time-encoded parameter to the absolute wavelength. In this work, the calibration signal from a polarization-maintaining fiber Sagnac interferometer shares the FDML wavelength-swept laser for FBG sensors to convert the time-encoded FBG signal to the wavelength-encoded uniform-spacing signal. (paper)

  7. Uniform spacing interrogation of a Fourier domain mode-locked fiber Bragg grating sensor system using a polarization-maintaining fiber Sagnac interferometer

    Science.gov (United States)

    Lee, Hwi Don; Jung, Eun Joo; Jeong, Myung Yung; Chen, Zhongping; Kim, Chang-Seok

    2013-06-01

    A novel linearized interrogation method is presented for a Fourier domain mode-locked (FDML) fiber Bragg grating (FBG) sensor system. In a high speed regime over several tens of kHz modulations, a sinusoidal wave is available to scan the center wavelength of an FDML wavelength-swept laser, instead of a conventional triangular wave. However, sinusoidal wave modulation suffers from an exaggerated non-uniform wavelength-spacing response in demodulating the time-encoded parameter to the absolute wavelength. In this work, the calibration signal from a polarization-maintaining fiber Sagnac interferometer shares the FDML wavelength-swept laser for FBG sensors to convert the time-encoded FBG signal to the wavelength-encoded uniform-spacing signal.

  8. Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms

    International Nuclear Information System (INIS)

    Chauhan, Kapil; Ng, Henry C H; Marusic, Ivan

    2010-01-01

    Oil-film interferometry is rapidly becoming the preferred method for direct measurement of wall shear stress in studies of wall-bounded turbulent flows. Although being widely accepted as the most accurate technique, it does have inherent measurement uncertainties, one of which is associated with determining the fringe spacing. This is the focus of this paper. Conventional analysis methods involve a certain level of user input and thus some subjectivity. In this paper, we consider empirical mode decomposition (EMD) and the Hilbert transform as an alternative tool for analyzing oil-film interferograms. In contrast to the commonly used Fourier-based techniques, this new method is less subjective and, as it is based on the Hilbert transform, is superior for treating amplitude and frequency modulated data. This makes it particularly robust to wide differences in the quality of interferograms

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

    Science.gov (United States)

    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.

  10. Algorithm, applications and evaluation for protein comparison by Ramanujan Fourier transform.

    Science.gov (United States)

    Zhao, Jian; Wang, Jiasong; Hua, Wei; Ouyang, Pingkai

    2015-12-01

    The amino acid sequence of a protein determines its chemical properties, chain conformation and biological functions. Protein sequence comparison is of great importance to identify similarities of protein structures and infer their functions. Many properties of a protein correspond to the low-frequency signals within the sequence. Low frequency modes in protein sequences are linked to the secondary structures, membrane protein types, and sub-cellular localizations of the proteins. In this paper, we present Ramanujan Fourier transform (RFT) with a fast algorithm to analyze the low-frequency signals of protein sequences. The RFT method is applied to similarity analysis of protein sequences with the Resonant Recognition Model (RRM). The results show that the proposed fast RFT method on protein comparison is more efficient than commonly used discrete Fourier transform (DFT). RFT can detect common frequencies as significant feature for specific protein families, and the RFT spectrum heat-map of protein sequences demonstrates the information conservation in the sequence comparison. The proposed method offers a new tool for pattern recognition, feature extraction and structural analysis on protein sequences. Copyright © 2015 Elsevier Ltd. All rights reserved.

  11. 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

  12. 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.

  13. Time-frequency analysis : mathematical analysis of the empirical mode decomposition.

    Science.gov (United States)

    2009-01-01

    Invented over 10 years ago, empirical mode : decomposition (EMD) provides a nonlinear : time-frequency analysis with the ability to successfully : analyze nonstationary signals. Mathematical : Analysis of the Empirical Mode Decomposition : is a...

  14. Analysis of Energy Transmission Modes of Flyback Converter

    Directory of Open Access Journals (Sweden)

    GONG Shu

    2014-08-01

    Full Text Available It is of significance to investigate energy transmission modes of a flyback converter for its optimum design. In this paper, the ETMs of a flyback converter are divided into three modes, which are continuous conduction mode-complete inductor supply mode, continuous conduction mode- incomplete inductor supply mode and discontinuous conduction mode-incomplete inductor supply mode, respectively. A deep analysis of the operation is made, a reduction of the boundary condition between the modes is conducted and a comparison of current stress, transformer AP and output ripple voltage between the modes is performed. A 30W prototype is developed and its experiment is done. The experiment results are in agreement with the theoretical analysis quite well.

  15. Dioxin analysis by gas chromatography-Fourier transform ion cyclotron resonance mass spectrometry (GC-FTICRMS).

    Science.gov (United States)

    Taguchi, Vince Y; Nieckarz, Robert J; Clement, Ray E; Krolik, Stefan; Williams, Robert

    2010-11-01

    The feasibility of utilizing a gas chromatograph-tandem quadrupole-Fourier transform ion cyclotron resonance mass spectrometer (GC-MS/MS-FTICRMS) to analyze chlorinated-dioxins/furans (CDDs/CDFs) and mixed halogenated dioxins/furans (HDDs/HDFs) was investigated by operating the system in the GC-FTICRMS mode. CDDs/CDFs and mixed HDDs/HDFs could be analyzed at 50,000 to 100,000 resolving power (RP) on the capillary gas chromatographic time scale. Initial experiments demonstrated that 1 pg of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and 5 pg of 2-bromo-3,7,8-trichlorodibenzo-p-dioxin (BTrCDD) could be detected. The feasibility of utilizing an FTICRMS for screening of CDDs/CDFs, HDDs/HDFs and related compounds was also investigated by analyzing an extract from vegetation exposed to fall-out from an industrial fire. CDDs/CDFs, chlorinated pyrenes and chlorinated tetracenes could be detected from a Kendrick plot analysis of the ultrahigh resolution mass spectra. Mass accuracies were of the order of 0.5 ppm on standards with external mass calibration and 1 ppm on a sample with internal mass calibration. Copyright © 2010 American Society for Mass Spectrometry. Published by Elsevier Inc. All rights reserved.

  16. 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

  17. Limitations on continuous variable quantum algorithms with Fourier transforms

    International Nuclear Information System (INIS)

    Adcock, Mark R A; Hoeyer, Peter; Sanders, Barry C

    2009-01-01

    We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.

  18. Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

    Directory of Open Access Journals (Sweden)

    Matthias Saba

    2015-01-01

    Full Text Available We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of Maxwell’s equations, computes the Fourier components of periodic structures composed of distinct homogeneous material domains from a triangulated mesh representation of the inter-material interfaces; this allows substantially more accurate representations of the geometry of complex photonic crystals than the conventional representation by a cubic voxel grid. Our method works for general two-phase composite materials, consisting of bi-anisotropic materials with tensor-valued dielectric and magnetic permittivities ε and μ and coupling matrices ς. We demonstrate for the Bragg mirror and a simple cubic crystal closely related to the Kelvin foam that relatively small numbers of Fourier components are sufficient to yield good convergence of the eigenvalues, making this method viable, despite its computational complexity. As an application, we use the single gyroid crystal to demonstrate that the consideration of both conventional and evanescent Bloch modes is necessary to predict the key features of the reflectance spectrum by analysis of the band structure, in particular for light incident along the cubic [111] direction.

  19. 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

  20. 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

  1. Fourier plane colorimetric sensing using broadband imaging of surface plasmons and application to biosensing

    International Nuclear Information System (INIS)

    Arora, P.; Krishnan, A.

    2015-01-01

    We demonstrate an optical technique for refractive index and thickness sensing of sub-wavelength-thick dielectric analytes. The technique utilizes the broadband, multimode, directional leakage radiation arising from the excitation of hybrid mode surface plasmons (SP) on low aspect ratio periodic plasmonic substrates with period ≈λ. The approach requires relaxed fabrication tolerances compared to extra ordinary transmission-based sensing techniques, wherein minor shifts in the fabricated dimensions result in a very large change from the designed resonant wavelength. We show that refractive index perturbations due to about 10-nm-thick dielectric can be captured optically by the usage of carefully designed plasmonic substrates, a halogen lamp source, free-space optical components, polarizers, and a low-end, consumer-grade charge coupled device camera. The plasmonic substrates were designed for converting the signature of hybrid mode SP excitation into a transmission peak by utilizing a thin homogeneous metal layer sandwiched between the periodic plasmonic structures and the substrate. The resonance is highly sensitive to the refractive index and thickness of the analyte superstrate. The excitation of hybrid mode SP results in a polarization rotation of 90° of the leaked radiation at resonant wavelength. In order to eliminate the problem of image registration (i.e., placing the same feature in the same pixel of the image, for comparison before and after a change in refractive index) for sensing, we perform the color analysis in the Fourier plane. The change in color of the bright emitted spot with highest momentum, corresponding to the leakage of fundamental SP mode, was used to measure the changes in refractive index, whereas the number and color of spots of lower momenta, corresponding to higher-order Fabry Perot modes, was used to measure the variation in thickness. We further show that the Fourier plane analysis can also be used to sense the index of thicker

  2. Fourier plane colorimetric sensing using broadband imaging of surface plasmons and application to biosensing

    Energy Technology Data Exchange (ETDEWEB)

    Arora, P.; Krishnan, A., E-mail: ananthk@iitm.ac.in [Centre for NEMS and Nano Photonics (CNNP), Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai-600036 (India); Experimental Optics Laboratory, Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai-600036 (India)

    2015-12-21

    We demonstrate an optical technique for refractive index and thickness sensing of sub-wavelength-thick dielectric analytes. The technique utilizes the broadband, multimode, directional leakage radiation arising from the excitation of hybrid mode surface plasmons (SP) on low aspect ratio periodic plasmonic substrates with period ≈λ. The approach requires relaxed fabrication tolerances compared to extra ordinary transmission-based sensing techniques, wherein minor shifts in the fabricated dimensions result in a very large change from the designed resonant wavelength. We show that refractive index perturbations due to about 10-nm-thick dielectric can be captured optically by the usage of carefully designed plasmonic substrates, a halogen lamp source, free-space optical components, polarizers, and a low-end, consumer-grade charge coupled device camera. The plasmonic substrates were designed for converting the signature of hybrid mode SP excitation into a transmission peak by utilizing a thin homogeneous metal layer sandwiched between the periodic plasmonic structures and the substrate. The resonance is highly sensitive to the refractive index and thickness of the analyte superstrate. The excitation of hybrid mode SP results in a polarization rotation of 90° of the leaked radiation at resonant wavelength. In order to eliminate the problem of image registration (i.e., placing the same feature in the same pixel of the image, for comparison before and after a change in refractive index) for sensing, we perform the color analysis in the Fourier plane. The change in color of the bright emitted spot with highest momentum, corresponding to the leakage of fundamental SP mode, was used to measure the changes in refractive index, whereas the number and color of spots of lower momenta, corresponding to higher-order Fabry Perot modes, was used to measure the variation in thickness. We further show that the Fourier plane analysis can also be used to sense the index of thicker

  3. Fourier plane colorimetric sensing using broadband imaging of surface plasmons and application to biosensing

    Science.gov (United States)

    Arora, P.; Krishnan, A.

    2015-12-01

    We demonstrate an optical technique for refractive index and thickness sensing of sub-wavelength-thick dielectric analytes. The technique utilizes the broadband, multimode, directional leakage radiation arising from the excitation of hybrid mode surface plasmons (SP) on low aspect ratio periodic plasmonic substrates with period ≈λ. The approach requires relaxed fabrication tolerances compared to extra ordinary transmission-based sensing techniques, wherein minor shifts in the fabricated dimensions result in a very large change from the designed resonant wavelength. We show that refractive index perturbations due to about 10-nm-thick dielectric can be captured optically by the usage of carefully designed plasmonic substrates, a halogen lamp source, free-space optical components, polarizers, and a low-end, consumer-grade charge coupled device camera. The plasmonic substrates were designed for converting the signature of hybrid mode SP excitation into a transmission peak by utilizing a thin homogeneous metal layer sandwiched between the periodic plasmonic structures and the substrate. The resonance is highly sensitive to the refractive index and thickness of the analyte superstrate. The excitation of hybrid mode SP results in a polarization rotation of 90° of the leaked radiation at resonant wavelength. In order to eliminate the problem of image registration (i.e., placing the same feature in the same pixel of the image, for comparison before and after a change in refractive index) for sensing, we perform the color analysis in the Fourier plane. The change in color of the bright emitted spot with highest momentum, corresponding to the leakage of fundamental SP mode, was used to measure the changes in refractive index, whereas the number and color of spots of lower momenta, corresponding to higher-order Fabry Perot modes, was used to measure the variation in thickness. We further show that the Fourier plane analysis can also be used to sense the index of thicker

  4. 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.)

  5. Probing photoelectron multiple interferences via Fourier spectroscopy in energetic photoionization of Xe-C60

    International Nuclear Information System (INIS)

    Potter, Andrea; McCune, Matthew A.; De, Ruma; Chakraborty, Himadri S.; Madjet, Mohamed E.

    2010-01-01

    Considering the photoionization of the Xe-C 60 endohedral compound, we study in detail the ionization cross sections of various levels of the system at energies higher than the plasmon resonance region. Five classes of single-electron levels are identified depending on their spectral character. Each class engenders distinct oscillations in the cross section, emerging from the interference between active ionization modes specific to that class. Analysis of the cross sections based on their Fourier transforms unravels oscillation frequencies that carry unique fingerprints of the emitting level.

  6. Equilibrium calculations and mode analysis

    International Nuclear Information System (INIS)

    Herrnegger, F.

    1987-01-01

    The STEP asymptotic stellarator expansion procedure was used to study the MHD equilibrium and stability properties of stellarator configurations without longitudinal net-current, which also apply to advanced stellarators. The effects of toroidal curvature and magnetic well, and the Shafranov shift were investigated. A classification of unstable modes in toroidal stellarators is given. For WVII-A coil-field configurations having a β value of 1% and a parabolic pressure profile, no free-boundary modes are found. This agrees with the experimental fact that unstable behavior of the plasma column is not observed for this parameter range. So a theoretical β-limit for stability against ideal MHD modes can be estimated by mode analysis for the WVII-A device

  7. 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).

  8. 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)

  9. 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

  10. 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.

  11. Mode shape and natural frequency identification for seismic analysis from background vibration

    International Nuclear Information System (INIS)

    Bhan, S.; Wozniak, Z.

    1986-10-01

    Background vibration in a CANDU plant can be used to determine the dynamic characteristics of major items of equipment, such as calandria, the fuelling machines and the primary heat transport pumps. These dynamic characteristics can then be used to verify the seismic response of the equipment which, at present, is based on theoretical models only. The feasibility and basic theory of this new approach (which uses accelerations measured at several points on a structure and does not require knowledge of the source of excitation) was established in Phase I of the study. This report is based on Phase II in which the methods of analysis developed in Phase I were improved and verified experimentally. A Fast Fourier Transform (FFT) algorithm was incorporated and an interactive curve fitting technique was developed to obtain the dynamic characteristics in the form of natural frequencies, mode shapes and damping ratios. The method is now available for use at a CANDU plant

  12. 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.

  13. 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.

  14. 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

  15. A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Nash, Patrick L.

    2008-01-01

    Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium

  16. 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.)

  17. 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)

  18. Measurement of vibration mode shape by using Hilbert transform

    International Nuclear Information System (INIS)

    Kang, Min Sig

    2001-01-01

    This paper concerns on modal analysis of mechanical structures by using a continuous scanning laser Doppler vibrometer. In modal analysis the Hilbert transform based approach is superior to the Fourier transform based approach because of its fine accuracy and its flexible experimental settings. In this paper the Hilbert transform based approach is extended to measure area mode shape data of a structure by simply modifying the scanning pattern ranging the entire surface of the structure. The effectiveness of this proposed method is illustrated along with results of numerical simulation for a rectangular plate

  19. Interferogram conditioning for improved Fourier analysis and application to X-ray phase imaging by grating interferometry.

    Science.gov (United States)

    Montaux-Lambert, Antoine; Mercère, Pascal; Primot, Jérôme

    2015-11-02

    An interferogram conditioning procedure, for subsequent phase retrieval by Fourier demodulation, is presented here as a fast iterative approach aiming at fulfilling the classical boundary conditions imposed by Fourier transform techniques. Interference fringe patterns with typical edge discontinuities were simulated in order to reveal the edge artifacts that classically appear in traditional Fourier analysis, and were consecutively used to demonstrate the correction efficiency of the proposed conditioning technique. Optimization of the algorithm parameters is also presented and discussed. Finally, the procedure was applied to grating-based interferometric measurements performed in the hard X-ray regime. The proposed algorithm enables nearly edge-artifact-free retrieval of the phase derivatives. A similar enhancement of the retrieved absorption and fringe visibility images is also achieved.

  20. 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

  1. Visualization of hair follicles using high-speed optical coherence tomography based on a Fourier domain mode locking laser

    Science.gov (United States)

    Tsai, M.-T.; Chang, F.-Y.

    2012-04-01

    In this study, a swept-source optical coherence tomography (SS-OCT) system with a Fourier domain mode locking (FDML) laser is proposed for a dermatology study. The homemade FDML laser is one kind of frequency-sweeping light source, which can provide output power of >20 mW and an output spectrum of 65 nm in bandwidth centered at 1300 nm, enabling imaging with an axial resolution of 12 μm in the OCT system. To eliminate the forward scans from the laser output and insert the delayed backward scans, a Mach-Zehnder configuration is implemented. Compared with conventional frequency-sweeping light sources, the FDML laser can achieve much higher scan rates, as high as ˜240 kHz, which can provide a three-dimensional imaging rate of 4 volumes/s. Furthermore, the proposed high-speed SS-OCT system can provide three-dimensional (3D) images with reduced motion artifacts. Finally, a high-speed SS-OCT system is used to visualize hair follicles, demonstrating the potential of this technology as a tool for noninvasive diagnosis of alopecia.

  2. 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.

  3. 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.).

  4. 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.

  5. Suppression law of quantum states in a 3D photonic fast Fourier transform chip

    Science.gov (United States)

    Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio

    2016-01-01

    The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135

  6. 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.

  7. Design Analysis of the Mixed Mode Bending Sandwich Specimen

    DEFF Research Database (Denmark)

    Quispitupa, Amilcar; Berggreen, Christian; Carlsson, Leif A.

    2010-01-01

    A design analysis of the mixed mode bending (MMB) sandwich specimen for face–core interface fracture characterization is presented. An analysis of the competing failure modes in the foam cored sandwich specimens is performed in order to achieve face–core debond fracture prior to other failure modes...... for the chosen geometries and mixed mode loading conditions....

  8. 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

  9. Aqueous contaminant detection via UiO-66 thin film optical fiber sensor platform with fast Fourier transform based spectrum analysis

    Science.gov (United States)

    Nazari, Marziyeh; Rubio-Martinez, Marta; Babarao, Ravichandar; Ayad Younis, Adel; Collins, Stephen F.; Hill, Matthew R.; Duke, Mikel C.

    2018-01-01

    Routine water quality monitoring is required in drinking and waste water management. A particular interest is to measure concentrations of a range of diverse contaminants on-site or remotely in real time. Here we present metal organic framework (MOF) integrated optical fiber sensor that allows for rapid optical measurement based on fast Fourier transform (FFT) spectrum analysis. The end-face of these glass optical fibers was modified with UiO-66(Zr) MOF thin film by in situ hydrothermal synthesis for the detection of the model contaminants, Rhodamine-B and 4-Aminopyridine, in water. The sensing mechanism is based on the change in the optical path length of the thin film induced by the adsorption of chemical molecules by UiO-66. Using FFT analysis, various modes of interaction (physical and chemical) became apparent, showing both irreversible changes upon contact with the contaminant, as well as reversible changes according to actual concentration. This was indicated by the second harmonic elevation to a certain level translating to high sensitivity detection.

  10. 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

  11. 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.

  12. Validation of measurements of Fourier phase and amplitude analysis of technetium99 gated cardiac scans using artificial hearts

    International Nuclear Information System (INIS)

    Yiannikas, J.; Takatani, S.; MacIntyre, W.J.; Underwood, D.A.; Cook, S.A.; Go, R.T.; Napoli, C.; Nose, Y.

    1982-01-01

    The use of artificial hearts, developed for total heart replacement programs, allows assessment of the accuracy of measuring the first Fourier component phase and amplitude when applied to gated cardiac technetium 99 scans. In the extreme example of asynchrony of ventricular contraction in coronary artery disease that of ventricular aneurysms, the first Fourier component measurements of amplitude were highly correlated to volume increases suggesting that the calculated amplitude accurately reflects volume changes. The calculated asynchrony using Fourier analysis of the gated technetium 99 studies of two artificial hearts was highly accurate when compared to the predetermined calculation of phase angle difference and hence degree of asynchrony. The studies suggest that measurement of phase and amplitude using the first Fourier component of time-activity waves of gated cardiac technetium 99 studies accurately measure degree of asynchrony and volume changes respectively

  13. 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.)

  14. 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

  15. Sound radiation modes of cylindrical surfaces and their application to vibro-acoustics analysis of cylindrical shells

    Science.gov (United States)

    Sun, Yao; Yang, Tiejun; Chen, Yuehua

    2018-06-01

    In this paper, sound radiation modes of baffled cylinders have been derived by constructing the radiation resistance matrix analytically. By examining the characteristics of sound radiation modes, it is found that radiation coefficient of each radiation mode increases gradually with the increase of frequency while modal shapes of sound radiation modes of cylindrical shells show a weak dependence upon frequency. Based on understandings on sound radiation modes, vibro-acoustics behaviors of cylindrical shells have been analyzed. The vibration responses of cylindrical shells are described by modified Fourier series expansions and solved by Rayleigh-Ritz method involving Flügge shell theory. Then radiation efficiency of a resonance has been determined by examining whether the vibration pattern is in correspondence with a sound radiation mode possessing great radiation efficiency. Furthermore, effects of thickness and boundary conditions on sound radiation of cylindrical shells have been investigated. It is found that radiation efficiency of thicker shells is greater than thinner shells while shells with a clamped boundary constraint radiate sound more efficiently than simply supported shells under thin shell assumption.

  16. 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

  17. Further Development of Rotating Rake Mode Measurement Data Analysis

    Science.gov (United States)

    Dahl, Milo D.; Hixon, Ray; Sutliff, Daniel L.

    2013-01-01

    The Rotating Rake mode measurement system was designed to measure acoustic duct modes generated by a fan stage. After analysis of the measured data, the mode amplitudes and phases were quantified. For low-speed fans within axisymmetric ducts, mode power levels computed from rotating rake measured data would agree with the far-field power levels on a tone by tone basis. However, this agreement required that the sound from the noise sources within the duct propagated outward from the duct exit without reflection at the exit and previous studies suggested conditions could exist where significant reflections could occur. To directly measure the modes propagating in both directions within a duct, a second rake was mounted to the rotating system with an offset in both the axial and the azimuthal directions. The rotating rake data analysis technique was extended to include the data measured by the second rake. The analysis resulted in a set of circumferential mode levels at each of the two rake microphone locations. Radial basis functions were then least-squares fit to this data to obtain the radial mode amplitudes for the modes propagating in both directions within the duct. The fit equations were also modified to allow evanescent mode amplitudes to be computed. This extension of the rotating rake data analysis technique was tested using simulated data, numerical code produced data, and preliminary in-duct measured data.

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

    Science.gov (United States)

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

    2017-09-01

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

  19. The geometric phase analysis method based on the local high resolution discrete Fourier transform for deformation measurement

    International Nuclear Information System (INIS)

    Dai, Xianglu; Xie, Huimin; Wang, Huaixi; Li, Chuanwei; Wu, Lifu; Liu, Zhanwei

    2014-01-01

    The geometric phase analysis (GPA) method based on the local high resolution discrete Fourier transform (LHR-DFT) for deformation measurement, defined as LHR-DFT GPA, is proposed to improve the measurement accuracy. In the general GPA method, the fundamental frequency of the image plays a crucial role. However, the fast Fourier transform, which is generally employed in the general GPA method, could make it difficult to locate the fundamental frequency accurately when the fundamental frequency is not located at an integer pixel position in the Fourier spectrum. This study focuses on this issue and presents a LHR-DFT algorithm that can locate the fundamental frequency with sub-pixel precision in a specific frequency region for the GPA method. An error analysis is offered and simulation is conducted to verify the effectiveness of the proposed method; both results show that the LHR-DFT algorithm can accurately locate the fundamental frequency and improve the measurement accuracy of the GPA method. Furthermore, typical tensile and bending tests are carried out and the experimental results verify the effectiveness of the proposed method. (paper)

  20. 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.

  1. 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...

  2. 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.

  3. Quasiperiodicity, mode-locking, and universal scaling in Rayleigh-Benard convection

    International Nuclear Information System (INIS)

    Ecke, R.E.

    1990-01-01

    This major review paper describes research on a model nonlinear dynamical system of small-aspect-ratio Rayleigh-Benard convection in 3 He - 4 He mixtures. The nonlinear effects of mode locking and quasiperiodic behavior are described. Analysis techniques for characterizing the state of the dynamical system include Fourier transforms, Poincare sections, phase differences, transients, multifractal f(∝) spectra and scaling function dynamics. Theoretical results such as the fractal staircase of mode-locked intervals and the Arnold tongues are reproduced in experimental data. New techniques for analyzing scaling dynamics are developed and discussed. This is a tutorial article that introduces the major important concepts in nonlinear dynamics and focuses on experimental problems and techniques. 77 refs

  4. 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.

  5. Safety analysis for push-mode and rotary-mode core sampling

    International Nuclear Information System (INIS)

    Milliken, N.J.; Geschke, G.R.

    1995-01-01

    This safety analysis analyzes using the push-mode core sampling truck in the push-mode and the rotary-mode core sampling trucks in both the push- and rotary-modes to retrieve core samples that, once taken and analyzed, will yield waste characterization data for the hazardous waste tanks at the Hanford Site. Operation of the core sampling trucks in both the push- and rotary-modes was reviewed to determine whether the release of radioactive materials could occur during operation. It was concluded that there are three credible scenarios: a sample spill outside of the tank, a steam release event, and an unfiltered release to the environment during continuous exhauster operation. The probability of a sample spill was found to be 10 -4 /event, the probability of a steam release event was determined to fall in the unlikely range (10 -2 /event to 10 -4 /event), and the probability of an unfiltered release was calculated to be 5 x 10 -3 /year. Typically, events with probabilities of 10 -6 /event or less are not considered to be risk significant, and the consequences usually are not analyzed. The three accident scenarios were analyzed to calculate the dose consequences. It was determined that the steam release event is the bounding accident. The onsite and offsite dose consequences for this event are calculated to be 0.24 Sv (24 rem) and 3.2 x 10 -4 Sv (32 mrem), respectively. These consequences are below the risk acceptance guidelines for an unlikely event, as established in WHC-CM-4-46, Nonreactor Facility Safety Analysis Manual. With the design features and the use of the controls presented in Section 8.0, this operation represents a minimal risk

  6. Modeling cavities exhibiting strong lateral confinement using open geometry Fourier modal method

    DEFF Research Database (Denmark)

    Häyrynen, Teppo; Gregersen, Niels

    2016-01-01

    We have developed a computationally efficient Fourier-Bessel expansion based open geometry formalism for modeling the optical properties of rotationally symmetric photonic nanostructures. The lateral computation domain is assumed infinite so that no artificial boundary conditions are needed. Instead,...... around a geometry specific dominant transverse wavenumber region. We will use the developed approach to investigate the Q factor and mode confinement in cavities where top DBR mirror has small rectangular defect confining the modes laterally on the defect region....

  7. Towards the Fourier limit on the super-ACO Storage Ring FEL

    International Nuclear Information System (INIS)

    Couprie, M.E.; De Ninno, G.; Moneron, G.; Nutarelli, D.; Hirsch, M.; Garzella, D.; Renault, E.; Roux, R.; Thomas, C.

    2001-01-01

    Systematic studies on the Free Electron Laser (FEL) line and micropulse have been performed on the Super-ACO storage ring FEL with a monochromator and a double-sweep streak camera under various conditions of operation (detuning, 'CW' and Q-switched mode). From these data, it appears that the FEL is usually operated very close to the Fourier limit

  8. Towards the Fourier limit on the super-ACO Storage Ring FEL

    CERN Document Server

    Couprie, Marie Emmanuelle; Garzella, D; Hirsch, M; Moneron, G; Nutarelli, D; Renault, E; Roux, R; Thomas, C

    2001-01-01

    Systematic studies on the Free Electron Laser (FEL) line and micropulse have been performed on the Super-ACO storage ring FEL with a monochromator and a double-sweep streak camera under various conditions of operation (detuning, 'CW' and Q-switched mode). From these data, it appears that the FEL is usually operated very close to the Fourier limit.

  9. 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....

  10. The propagation of stochastic pixel noise into magnitude and phase values in the Fourier analysis of digital images

    International Nuclear Information System (INIS)

    Holden, J.E.; Halama, J.R.; Hasegawa, B.H.

    1986-01-01

    The use of Fourier analysis in nuclear medicine gated blood ventriculography provides a useful example of the application of Fourier methods to digital medical imaging. In particular, the nuclear medicine experience demonstrates that there is diagnostic significance not only in the pixel averages of temporal Fourier magnitude and phase computed in various image regions, but also in the distributions of the individual pixel values about those averages. However, a region containing pixels that are perfectly synchronous on average would still yield a finite distribution of calculated Fourier coefficients due to the propagation of stochastic pixel noise into the calculated values. The authors have studied this noise component of both the magnitude and phase distributions using phantom studies and computer simulation. In both approaches, several thousand one-pixel 'ventriculograms' were generated, all identical to each other except for stochastic noise. Fourier magnitudes and phases at several frequencies were calculated and histograms generated. A theoretical prediction of the distributions was developed and shown to fit the experimental results well. The authors' formalism can be used to estimate study count requirements or, for fixed study counts, to assess the stochastic noise contribution in the interpretation of measured phase and magnitude distributions. (author)

  11. 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.

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Predicting detection performance with model observers: Fourier domain or spatial domain?

    Science.gov (United States)

    Chen, Baiyu; Yu, Lifeng; Leng, Shuai; Kofler, James; Favazza, Christopher; Vrieze, Thomas; McCollough, Cynthia

    2016-02-27

    The use of Fourier domain model observer is challenged by iterative reconstruction (IR), because IR algorithms are nonlinear and IR images have noise texture different from that of FBP. A modified Fourier domain model observer, which incorporates nonlinear noise and resolution properties, has been proposed for IR and needs to be validated with human detection performance. On the other hand, the spatial domain model observer is theoretically applicable to IR, but more computationally intensive than the Fourier domain method. The purpose of this study is to compare the modified Fourier domain model observer to the spatial domain model observer with both FBP and IR images, using human detection performance as the gold standard. A phantom with inserts of various low contrast levels and sizes was repeatedly scanned 100 times on a third-generation, dual-source CT scanner at 5 dose levels and reconstructed using FBP and IR algorithms. The human detection performance of the inserts was measured via a 2-alternative-forced-choice (2AFC) test. In addition, two model observer performances were calculated, including a Fourier domain non-prewhitening model observer and a spatial domain channelized Hotelling observer. The performance of these two mode observers was compared in terms of how well they correlated with human observer performance. Our results demonstrated that the spatial domain model observer correlated well with human observers across various dose levels, object contrast levels, and object sizes. The Fourier domain observer correlated well with human observers using FBP images, but overestimated the detection performance using IR images.

  19. 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.

  20. 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.

  1. Modeling cavities exhibiting strong lateral confinement using open geometry Fourier modal method

    Science.gov (United States)

    Häyrynen, Teppo; Gregersen, Niels

    2016-04-01

    We have developed a computationally efficient Fourier-Bessel expansion based open geometry formalism for modeling the optical properties of rotationally symmetric photonic nanostructures. The lateral computation domain is assumed infinite so that no artificial boundary conditions are needed. Instead, the leakage of the modes due to an imperfect field confinement is taken into account by using a basis functions that expand the whole infinite space. The computational efficiency is obtained by using a non-uniform discretization in the frequency space in which the lateral expansion modes are more densely sampled around a geometry specific dominant transverse wavenumber region. We will use the developed approach to investigate the Q factor and mode confinement in cavities where top DBR mirror has small rectangular defect confining the modes laterally on the defect region.

  2. A sociological Analysis on the Modes of Science Production

    Directory of Open Access Journals (Sweden)

    Ali Rabbani Khorasgani

    2012-12-01

    Full Text Available The main aim of this article was sociological Analysis on the modes of science, survey of new Approaches in this context, description of available Approaches relevant to Application of Indigenous paradigm in prodvetion of knowledge and conclusion to attain imitated Approaches from Analysis and mentioned discussions for planning in space of science production in society of Iran. After Analysis of propound Approaches in sociology of science concreted that sociology of science three generation transitioned yet : classic sociology of science (OSS [ Theories of Merton ] , New sociology of science ( NSS [Theories of Thomas kuhn and others ] and Third generation sociology of science that consisted of non - Marxist composinal and processive Approaches for example: Actor - Network theory (ANT, Triple Helix Theory life eyeles, mode 2 and Mode 3. On the other hand , because science production is encompass process in social structures and social communications , allowance for Analysis of Recent Development in mode of science production , three paradigm Analysis and critiqued titles mode 1 , 2 , 3 production of knowledge . Also, Application of Indigenous paradigm studied in production of knowledge and introduced two groups: A - External Approaches B - Internal Approaches that each of two groups propounded Ideas relevant to Indigenous knowledge and Indigenization of knowledge. In the final section, mode an efforted to answered this question that what doctrines can be concluded from these discourse in order to improve the conditions in Iran.

  3. 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

  4. High-resolution retinal swept source optical coherence tomography with an ultra-wideband Fourier-domain mode-locked laser at MHz A-scan rates.

    Science.gov (United States)

    Kolb, Jan Philip; Pfeiffer, Tom; Eibl, Matthias; Hakert, Hubertus; Huber, Robert

    2018-01-01

    We present a new 1060 nm Fourier domain mode locked laser (FDML laser) with a record 143 nm sweep bandwidth at 2∙ 417 kHz  =  834 kHz and 120 nm at 1.67 MHz, respectively. We show that not only the bandwidth alone, but also the shape of the spectrum is critical for the resulting axial resolution, because of the specific wavelength-dependent absorption of the vitreous. The theoretical limit of our setup lies at 5.9 µm axial resolution. In vivo MHz-OCT imaging of human retina is performed and the image quality is compared to the previous results acquired with 70 nm sweep range, as well as to existing spectral domain OCT data with 2.1 µm axial resolution from literature. We identify benefits of the higher resolution, for example the improved visualization of small blood vessels in the retina besides several others.

  5. 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.

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

    Directory of Open Access Journals (Sweden)

    Chiu Shen

    2005-01-01

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

  7. Magnetostatic Analysis of a Pinch Mode Magnetorheological Valve

    Directory of Open Access Journals (Sweden)

    Gołdasz Janusz

    2017-09-01

    Full Text Available The study deals with the pinch mode of magnetorheological (MR fluids’ operation and its application in MR valves. By applying the principle in MR valves a highly non-uniform magnetic field can be generated in flow channels in such a way to solidify the portion of the material that is the nearest to the flow channel’s walls. This is in contrary to well-known MR flow mode valves. The authors investigate a basic pinch mode valve in several fundamental configurations, and then examine their magnetic circuits through magnetostatic finite-element (FE analysis. Flux density contour maps are revealed and basic performance figures calculated and analysed. The FE analysis results yield confidence in that the performance of MR pinch mode devices can be effectively controlled through electromagnetic means.

  8. A streamlined failure mode and effects analysis

    International Nuclear Information System (INIS)

    Ford, Eric C.; Smith, Koren; Terezakis, Stephanie; Croog, Victoria; Gollamudi, Smitha; Gage, Irene; Keck, Jordie; DeWeese, Theodore; Sibley, Greg

    2014-01-01

    Purpose: Explore the feasibility and impact of a streamlined failure mode and effects analysis (FMEA) using a structured process that is designed to minimize staff effort. Methods: FMEA for the external beam process was conducted at an affiliate radiation oncology center that treats approximately 60 patients per day. A structured FMEA process was developed which included clearly defined roles and goals for each phase. A core group of seven people was identified and a facilitator was chosen to lead the effort. Failure modes were identified and scored according to the FMEA formalism. A risk priority number,RPN, was calculated and used to rank failure modes. Failure modes with RPN > 150 received safety improvement interventions. Staff effort was carefully tracked throughout the project. Results: Fifty-two failure modes were identified, 22 collected during meetings, and 30 from take-home worksheets. The four top-ranked failure modes were: delay in film check, missing pacemaker protocol/consent, critical structures not contoured, and pregnant patient simulated without the team's knowledge of the pregnancy. These four failure modes hadRPN > 150 and received safety interventions. The FMEA was completed in one month in four 1-h meetings. A total of 55 staff hours were required and, additionally, 20 h by the facilitator. Conclusions: Streamlined FMEA provides a means of accomplishing a relatively large-scale analysis with modest effort. One potential value of FMEA is that it potentially provides a means of measuring the impact of quality improvement efforts through a reduction in risk scores. Future study of this possibility is needed

  9. A streamlined failure mode and effects analysis.

    Science.gov (United States)

    Ford, Eric C; Smith, Koren; Terezakis, Stephanie; Croog, Victoria; Gollamudi, Smitha; Gage, Irene; Keck, Jordie; DeWeese, Theodore; Sibley, Greg

    2014-06-01

    Explore the feasibility and impact of a streamlined failure mode and effects analysis (FMEA) using a structured process that is designed to minimize staff effort. FMEA for the external beam process was conducted at an affiliate radiation oncology center that treats approximately 60 patients per day. A structured FMEA process was developed which included clearly defined roles and goals for each phase. A core group of seven people was identified and a facilitator was chosen to lead the effort. Failure modes were identified and scored according to the FMEA formalism. A risk priority number,RPN, was calculated and used to rank failure modes. Failure modes with RPN > 150 received safety improvement interventions. Staff effort was carefully tracked throughout the project. Fifty-two failure modes were identified, 22 collected during meetings, and 30 from take-home worksheets. The four top-ranked failure modes were: delay in film check, missing pacemaker protocol/consent, critical structures not contoured, and pregnant patient simulated without the team's knowledge of the pregnancy. These four failure modes had RPN > 150 and received safety interventions. The FMEA was completed in one month in four 1-h meetings. A total of 55 staff hours were required and, additionally, 20 h by the facilitator. Streamlined FMEA provides a means of accomplishing a relatively large-scale analysis with modest effort. One potential value of FMEA is that it potentially provides a means of measuring the impact of quality improvement efforts through a reduction in risk scores. Future study of this possibility is needed.

  10. A streamlined failure mode and effects analysis

    Energy Technology Data Exchange (ETDEWEB)

    Ford, Eric C., E-mail: eford@uw.edu; Smith, Koren; Terezakis, Stephanie; Croog, Victoria; Gollamudi, Smitha; Gage, Irene; Keck, Jordie; DeWeese, Theodore; Sibley, Greg [Department of Radiation Oncology and Molecular Radiation Sciences, Johns Hopkins University, Baltimore, MD 21287 (United States)

    2014-06-15

    Purpose: Explore the feasibility and impact of a streamlined failure mode and effects analysis (FMEA) using a structured process that is designed to minimize staff effort. Methods: FMEA for the external beam process was conducted at an affiliate radiation oncology center that treats approximately 60 patients per day. A structured FMEA process was developed which included clearly defined roles and goals for each phase. A core group of seven people was identified and a facilitator was chosen to lead the effort. Failure modes were identified and scored according to the FMEA formalism. A risk priority number,RPN, was calculated and used to rank failure modes. Failure modes with RPN > 150 received safety improvement interventions. Staff effort was carefully tracked throughout the project. Results: Fifty-two failure modes were identified, 22 collected during meetings, and 30 from take-home worksheets. The four top-ranked failure modes were: delay in film check, missing pacemaker protocol/consent, critical structures not contoured, and pregnant patient simulated without the team's knowledge of the pregnancy. These four failure modes hadRPN > 150 and received safety interventions. The FMEA was completed in one month in four 1-h meetings. A total of 55 staff hours were required and, additionally, 20 h by the facilitator. Conclusions: Streamlined FMEA provides a means of accomplishing a relatively large-scale analysis with modest effort. One potential value of FMEA is that it potentially provides a means of measuring the impact of quality improvement efforts through a reduction in risk scores. Future study of this possibility is needed.

  11. Spatial light modulation for mode conditioning

    DEFF Research Database (Denmark)

    Glückstad, Jesper; Palima, Darwin

    We demonstrate patented techniques for generating tuneable complex field distributions for controllable coupling to high-order guided modes of micro-structured fibres. The optical Fourier transform of binary phase-only patterns which are encoded on a computer-controlled spatial light modulator......, generates complex field distributions for selective launching of a desired mode. Both the amplitude and the phase of the programmable fields are modulated by straightforward and fast adjustments of simple pre-defined binary phase-only diffractive patterns. Experiments demonstrate tuneable coupling...

  12. 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

  13. 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)

  14. 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.

  15. 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.

  16. Practical computer analysis of switch mode power supplies

    CERN Document Server

    Bennett, Johnny C

    2006-01-01

    When designing switch-mode power supplies (SMPSs), engineers need much more than simple "recipes" for analysis. Such plug-and-go instructions are not at all helpful for simulating larger and more complex circuits and systems. Offering more than merely a "cookbook," Practical Computer Analysis of Switch Mode Power Supplies provides a thorough understanding of the essential requirements for analyzing SMPS performance characteristics. It demonstrates the power of the circuit averaging technique when used with powerful computer circuit simulation programs. The book begins with SMPS fundamentals and the basics of circuit averaging models, reviewing most basic topologies and explaining all of their various modes of operation and control. The author then discusses the general analysis requirements of power supplies and how to develop the general types of SMPS models, demonstrating the use of SPICE for analysis. He examines the basic first-order analyses generally associated with SMPS performance along with more pra...

  17. Control of 3-D Modes in a Boundary Layer Undergoing Subharmonic Transition.

    Science.gov (United States)

    Corke, T. C.; Peto, J.; Speer, A.; Paroozan, P.; Sciammarella, C.

    1997-11-01

    The effect of alternating standing patterns of wall displacements in the transition region of a Falkner-Skan boundary layer with an adverse pressure gradient is investigated. Transition is controlled by introducing disturbances to excite a pair of oblique modes along with a plane TS mode. The oblique modes are at the TS subharmonic frequency in order to promote subharmonic resonance. Measurements consist of a spanwise rake of hot-wire sensors placed near the wall below the critical layer, and a 2-D (15 x 15) array of optical pressure sensors. The space-time data series are processed using 2-D Fourier analysis to determine the spanwise wave number content of the flow. Of particular interest is the streamwise vortex mode which results from a difference interaction of the subharmonic oblique modes. We examine the effect of different patterns and amplitudes of upstream wall displacements on the development of the travelling and stationary modes in this case leading to transition. Supported by ARO Grant No. DAAH04-93-G-0212

  18. Time-Frequency Analysis of the Dispersion of Lamb Modes

    Science.gov (United States)

    Prosser, W. H.; Seale, Michael D.; Smith, Barry T.

    1999-01-01

    Accurate knowledge of the velocity dispersion of Lamb modes is important for ultrasonic nondestructive evaluation methods used in detecting and locating flaws in thin plates and in determining their elastic stiffness coefficients. Lamb mode dispersion is also important in the acoustic emission technique for accurately triangulating the location of emissions in thin plates. In this research, the ability to characterize Lamb mode dispersion through a time-frequency analysis (the pseudo Wigner-Ville distribution) was demonstrated. A major advantage of time-frequency methods is the ability to analyze acoustic signals containing multiple propagation modes, which overlap and superimpose in the time domain signal. By combining time-frequency analysis with a broadband acoustic excitation source, the dispersion of multiple Lamb modes over a wide frequency range can be determined from as little as a single measurement. In addition, the technique provides a direct measurement of the group velocity dispersion. The technique was first demonstrated in the analysis of a simulated waveform in an aluminum plate in which the Lamb mode dispersion was well known. Portions of the dispersion curves of the A(sub 0), A(sub 1), S(sub 0), and S(sub 2)Lamb modes were obtained from this one waveform. The technique was also applied for the analysis of experimental waveforms from a unidirectional graphite/epoxy composite plate. Measurements were made both along, and perpendicular to the fiber direction. In this case, the signals contained only the lowest order symmetric and antisymmetric modes. A least squares fit of the results from several source to detector distances was used. Theoretical dispersion curves were calculated and are shown to be in good agreement with experimental results.

  19. 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)

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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)

  10. 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.

  11. 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.

  12. Causality analysis of leading singular value decomposition modes identifies rotor as the dominant driving normal mode in fibrillation

    Science.gov (United States)

    Biton, Yaacov; Rabinovitch, Avinoam; Braunstein, Doron; Aviram, Ira; Campbell, Katherine; Mironov, Sergey; Herron, Todd; Jalife, José; Berenfeld, Omer

    2018-01-01

    Cardiac fibrillation is a major clinical and societal burden. Rotors may drive fibrillation in many cases, but their role and patterns are often masked by complex propagation. We used Singular Value Decomposition (SVD), which ranks patterns of activation hierarchically, together with Wiener-Granger causality analysis (WGCA), which analyses direction of information among observations, to investigate the role of rotors in cardiac fibrillation. We hypothesized that combining SVD analysis with WGCA should reveal whether rotor activity is the dominant driving force of fibrillation even in cases of high complexity. Optical mapping experiments were conducted in neonatal rat cardiomyocyte monolayers (diameter, 35 mm), which were genetically modified to overexpress the delayed rectifier K+ channel IKr only in one half of the monolayer. Such monolayers have been shown previously to sustain fast rotors confined to the IKr overexpressing half and driving fibrillatory-like activity in the other half. SVD analysis of the optical mapping movies revealed a hierarchical pattern in which the primary modes corresponded to rotor activity in the IKr overexpressing region and the secondary modes corresponded to fibrillatory activity elsewhere. We then applied WGCA to evaluate the directionality of influence between modes in the entire monolayer using clear and noisy movies of activity. We demonstrated that the rotor modes influence the secondary fibrillatory modes, but influence was detected also in the opposite direction. To more specifically delineate the role of the rotor in fibrillation, we decomposed separately the respective SVD modes of the rotor and fibrillatory domains. In this case, WGCA yielded more information from the rotor to the fibrillatory domains than in the opposite direction. In conclusion, SVD analysis reveals that rotors can be the dominant modes of an experimental model of fibrillation. Wiener-Granger causality on modes of the rotor domains confirms their

  13. Failure mode and effects analysis: an empirical comparison of failure mode scoring procedures.

    Science.gov (United States)

    Ashley, Laura; Armitage, Gerry

    2010-12-01

    To empirically compare 2 different commonly used failure mode and effects analysis (FMEA) scoring procedures with respect to their resultant failure mode scores and prioritization: a mathematical procedure, where scores are assigned independently by FMEA team members and averaged, and a consensus procedure, where scores are agreed on by the FMEA team via discussion. A multidisciplinary team undertook a Healthcare FMEA of chemotherapy administration. This included mapping the chemotherapy process, identifying and scoring failure modes (potential errors) for each process step, and generating remedial strategies to counteract them. Failure modes were scored using both an independent mathematical procedure and a team consensus procedure. Almost three-fifths of the 30 failure modes generated were scored differently by the 2 procedures, and for just more than one-third of cases, the score discrepancy was substantial. Using the Healthcare FMEA prioritization cutoff score, almost twice as many failure modes were prioritized by the consensus procedure than by the mathematical procedure. This is the first study to empirically demonstrate that different FMEA scoring procedures can score and prioritize failure modes differently. It found considerable variability in individual team members' opinions on scores, which highlights the subjective and qualitative nature of failure mode scoring. A consensus scoring procedure may be most appropriate for FMEA as it allows variability in individuals' scores and rationales to become apparent and to be discussed and resolved by the team. It may also yield team learning and communication benefits unlikely to result from a mathematical procedure.

  14. 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.

  15. A sparse-mode spectral method for the simulation of turbulent flows

    International Nuclear Information System (INIS)

    Meneguzzi, M.; Politano, H.; Pouquet, A.; Zolver, M.

    1996-01-01

    We propose a new algorithm belonging to the family of the sparsemode spectral method to simulate turbulent flows. In this method the number of Fourier modes k increases with k more slowly than k D-1 in dimension D, while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burger's equation and two-dimensional incompressible MHD flows

  16. Cascade mode locking: a possible route to chaos in the two-waves hamiltonian system

    International Nuclear Information System (INIS)

    Gell, Y.; Nakach, R.

    1989-06-01

    We present a numerical study of the two-waves Hamiltonian system which reveals the route to large scale stochasticity as a process based on the mode-locking phenomenon. The final chaos is reached after a cascade of lockings, appearing successively for different independent modes of oscillation in the system. Using a Fourier analysis, the different steps in this cascade process are detected by following the change in the frequency of the pronounced modes in the power spectrum; when changing the strength of the pertubation, one observes the locking of the relevant mode to a fixed frequency inherent to the system. It is shown that this mechanism allows for the generation of low frequency oscillations which, due to the nonlinear coupling existing in the system, combine with all the existing peaks into a raised spectrum consisting of broad diffuse patterns, which is the signature of chaotic motion

  17. 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.

  18. 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)

  19. 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)

  20. Electrostatic ion trap and Fourier transform measurements for high-resolution mass spectrometry

    International Nuclear Information System (INIS)

    Bhushan, K. G.; Gadkari, S. C.; Yakhmi, J. V.; Sahni, V. C.

    2007-01-01

    We report on the development of an electrostatic ion trap for high-resolution mass spectrometry. The trap works on purely electrostatic fields and hence trapping and storing of ions is not mass restrictive, unlike other techniques based on Penning, Paul, or radio frequency quadrupole ion traps. It allows simultaneous trapping and studying of multiple mass species over a large mass range. Mass spectra were recorded in ''dispersive'' and ''self-bunching'' modes of ions. Storage lifetimes of about 100 ms and mass resolving power of about 20 000 could be achieved from the fifth harmonic Fourier transform spectrum of Xe ions recorded in the self-bunching mode

  1. Normal mode analysis and applications in biological physics.

    Science.gov (United States)

    Dykeman, Eric C; Sankey, Otto F

    2010-10-27

    Normal mode analysis has become a popular and often used theoretical tool in the study of functional motions in enzymes, viruses, and large protein assemblies. The use of normal modes in the study of these motions is often extremely fruitful since many of the functional motions of large proteins can be described using just a few normal modes which are intimately related to the overall structure of the protein. In this review, we present a broad overview of several popular methods used in the study of normal modes in biological physics including continuum elastic theory, the elastic network model, and a new all-atom method, recently developed, which is capable of computing a subset of the low frequency vibrational modes exactly. After a review of the various methods, we present several examples of applications of normal modes in the study of functional motions, with an emphasis on viral capsids.

  2. A non-radial oscillation mode in an accreting millisecond pulsar?

    Energy Technology Data Exchange (ETDEWEB)

    Strohmayer, Tod [Astrophysics Science Division and Joint Space-Science Institute, NASA' s Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Mahmoodifar, Simin [Department of Physics and Joint Space-Science Institute, University of Maryland College Park, MD 20742 (United States)

    2014-03-20

    We present results of targeted searches for signatures of non-radial oscillation modes (such as r- and g-modes) in neutron stars using RXTE data from several accreting millisecond X-ray pulsars (AMXPs). We search for potentially coherent signals in the neutron star rest frame by first removing the phase delays associated with the star's binary motion and computing fast Fourier transform power spectra of continuous light curves with up to 2{sup 30} time bins. We search a range of frequencies in which both r- and g-modes are theoretically expected to reside. Using data from the discovery outburst of the 435 Hz pulsar XTE J1751–305 we find a single candidate, coherent oscillation with a frequency of 0.5727597 × ν{sub spin} = 249.332609 Hz, and a fractional Fourier amplitude of 7.46 × 10{sup –4}. We estimate the significance of this feature at the 1.6 × 10{sup –3} level, slightly better than a 3σ detection. Based on the observed frequency we argue that possible mode identifications include rotationally modified g-modes associated with either a helium-rich surface layer or a density discontinuity due to electron captures on hydrogen in the accreted ocean. In the latter case the presence of sufficient hydrogen in this ultracompact system with a likely helium-rich donor would present an interesting puzzle. Alternatively, the frequency could be identified with that of an inertial mode or a core r-mode modified by the presence of a solid crust; however, the r-mode amplitude required to account for the observed modulation amplitude would induce a large spin-down rate inconsistent with the observed pulse timing measurements. For the AMXPs XTE J1814–338 and NGC 6440 X–2 we do not find any candidate oscillation signals, and we place upper limits on the fractional Fourier amplitude of any coherent oscillations in our frequency search range of 7.8 × 10{sup –4} and 5.6 × 10{sup –3}, respectively. We briefly discuss the prospects and sensitivity for

  3. Two-dimensional analysis of trapped-ion eigenmodes

    International Nuclear Information System (INIS)

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

    1979-11-01

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

  4. An evaluation of intraoperative and postoperative outcomes of torsional mode versus longitudinal ultrasound mode phacoemulsification: a Meta-analysis

    Directory of Open Access Journals (Sweden)

    Pia Leon

    2016-06-01

    Full Text Available AIM: To evaluate and compare the intraoperative parameters and postoperative outcomes of torsional mode and longitudinal mode of phacoemulsification. METHODS: Pertinent studies were identified by a computerized MEDLINE search from January 2002 to September 2013. The Meta-analysis is composed of two parts. In the first part the intraoperative parameters were considered: ultrasound time (UST and cumulative dissipated energy (CDE. The intraoperative values were also distinctly considered for two categories (moderate and hard cataract group depending on the nuclear opacity grade. In the second part of the study the postoperative outcomes as the best corrected visual acuity (BCVA and the endothelial cell loss (ECL were taken in consideration. RESULTS: The UST and CDE values proved statistically significant in support of torsional mode for both moderate and hard cataract group. The analysis of BCVA did not present statistically significant difference between the two surgical modalities. The ECL count was statistically significant in support of torsional mode (P<0.001. CONCLUSION: The Meta-analysis shows the superiority of the torsional mode for intraoperative parameters (UST, CDE and postoperative ECL outcomes.

  5. An evaluation of intraoperative and postoperative outcomes of torsional mode versus longitudinal ultrasound mode phacoemulsification: a Meta-analysis.

    Science.gov (United States)

    Leon, Pia; Umari, Ingrid; Mangogna, Alessandro; Zanei, Andrea; Tognetto, Daniele

    2016-01-01

    To evaluate and compare the intraoperative parameters and postoperative outcomes of torsional mode and longitudinal mode of phacoemulsification. Pertinent studies were identified by a computerized MEDLINE search from January 2002 to September 2013. The Meta-analysis is composed of two parts. In the first part the intraoperative parameters were considered: ultrasound time (UST) and cumulative dissipated energy (CDE). The intraoperative values were also distinctly considered for two categories (moderate and hard cataract group) depending on the nuclear opacity grade. In the second part of the study the postoperative outcomes as the best corrected visual acuity (BCVA) and the endothelial cell loss (ECL) were taken in consideration. The UST and CDE values proved statistically significant in support of torsional mode for both moderate and hard cataract group. The analysis of BCVA did not present statistically significant difference between the two surgical modalities. The ECL count was statistically significant in support of torsional mode (P<0.001). The Meta-analysis shows the superiority of the torsional mode for intraoperative parameters (UST, CDE) and postoperative ECL outcomes.

  6. Kinetic analysis of MHD ballooning modes in tokamaks

    International Nuclear Information System (INIS)

    Tang, W.M.; Rewoldt, G.; Cheng, C.Z.; Chance, M.S.

    1984-10-01

    A comprehensive analysis of the stability properties of the appropriate kinetically generalized form of MHD ballooning modes together with the usual trapped-particle drift modes is presented. The calculations are fully electromagnetic and include the complete dynamics associated with compressional ion acoustic waves. Trapped-particle effects along with all forms of collisionless dissipation are taken into account without approximations. The influence of collisions is estimated with a model Krook operator. Results from the application of this analysis to realistic tokamak operating conditions indicate that unstable short-wavelength modes with significant growth rates can extend from β = 0 to value above the upper ideal-MHD-critical-beta associated with the so-called second stability regime. Since the strength of the relevant modes appears to vary gradually with β, these results support a soft beta limit picture involving a continuous (rather than abrupt or hard) modification of anomalous transport already present in low-β-tokamaks. However, at higher beta the increasing dominance of the electromagnetic component of the perturbations indicated by these calculations could also imply significantly different transport scaling properties

  7. 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.

  8. 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)

  9. Failure Modes and Effects Analysis (FMEA): A Bibliography

    Science.gov (United States)

    2000-01-01

    Failure modes and effects analysis (FMEA) is a bottom-up analytical process that identifies process hazards, which helps managers understand vulnerabilities of systems, as well as assess and mitigate risk. It is one of several engineering tools and techniques available to program and project managers aimed at increasing the likelihood of safe and successful NASA programs and missions. This bibliography references 465 documents in the NASA STI Database that contain the major concepts, failure modes or failure analysis, in either the basic index of the major subject terms.

  10. 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 ...

  11. Preliminary failure mode and effect analysis

    International Nuclear Information System (INIS)

    Addison, J.V.

    1972-01-01

    A preliminary Failure Mode and Effect Analysis (FMEA) was made on the overall 5 Kwe system. A general discussion of the system and failure effect is given in addition to the tabulated FMEA and a primary block diagram of the system. (U.S.)

  12. 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.

  13. 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.

  14. 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.

  15. On flow reversals in Rayleigh-Bénard convection

    International Nuclear Information System (INIS)

    Chandra, Mani; Verma, Mahendra K

    2011-01-01

    The dynamics of flow reversals are studied numerically using Fourier mode analysis. Our analysis shows that the Fourier modes represent the large-scale flows accurately. We observe that during the reversals, the amplitude of one of the large-scale modes vanishes, while another mode rises sharply, very similar to the cessation-led reversals observed earlier in experiments and numerical simulations. The Fourier coefficients of the RBC equations obey certain symmetries properties, which dictates which modes change sign in flow reversals. Based on our simulation results and symmetry properties of the Fourier modes, we provide a qualitative explanation for the flow reversals.

  16. 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

  17. Multipurpose RTOF Fourier diffractometer at the ET-RR-1 reactor

    International Nuclear Information System (INIS)

    Maayouf, R.M.A.; Tiitta, A.T.

    1993-09-01

    The present work represents a further study of the basic RTOF Fourier multipurpose diffractometer, to start with, at the ET-RR-1 reactor. The functions of the suggested arrangement are thoroughly discussed and the possibilities if its expansion are also assessed. The flexibility of the arrangement allows its further expansion both for stress measurement at 90 deg. scattering angle with two detector banks at opposite sides of the incident beam and for operation in the transmission diffraction mode. (orig.). (19 refs., 10 figs., 1 tab.)

  18. Failure mode and effects analysis of software-based automation systems

    International Nuclear Information System (INIS)

    Haapanen, P.; Helminen, A.

    2002-08-01

    Failure mode and effects analysis (FMEA) is one of the well-known analysis methods having an established position in the traditional reliability analysis. The purpose of FMEA is to identify possible failure modes of the system components, evaluate their influences on system behaviour and propose proper countermeasures to suppress these effects. The generic nature of FMEA has enabled its wide use in various branches of industry reaching from business management to the design of spaceships. The popularity and diverse use of the analysis method has led to multiple interpretations, practices and standards presenting the same analysis method. FMEA is well understood at the systems and hardware levels, where the potential failure modes usually are known and the task is to analyse their effects on system behaviour. Nowadays, more and more system functions are realised on software level, which has aroused the urge to apply the FMEA methodology also on software based systems. Software failure modes generally are unknown - 'software modules do not fail, they only display incorrect behaviour' - and depend on dynamic behaviour of the application. These facts set special requirements on the FMEA of software based systems and make it difficult to realise. In this report the failure mode and effects analysis is studied for the use of reliability analysis of software-based systems. More precisely, the target system of FMEA is defined to be a safety-critical software-based automation application in a nuclear power plant, implemented on an industrial automation system platform. Through a literature study the report tries to clarify the intriguing questions related to the practical use of software failure mode and effects analysis. The study is a part of the research project 'Programmable Automation System Safety Integrity assessment (PASSI)', belonging to the Finnish Nuclear Safety Research Programme (FINNUS, 1999-2002). In the project various safety assessment methods and tools for

  19. 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.

  20. 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...

  1. Risk analysis of geothermal power plants using Failure Modes and Effects Analysis (FMEA) technique

    International Nuclear Information System (INIS)

    Feili, Hamid Reza; Akar, Navid; Lotfizadeh, Hossein; Bairampour, Mohammad; Nasiri, Sina

    2013-01-01

    Highlights: • Using Failure Modes and Effects Analysis (FMEA) to find potential failures in geothermal power plants. • We considered 5 major parts of geothermal power plants for risk analysis. • Risk Priority Number (RPN) is calculated for all failure modes. • Corrective actions are recommended to eliminate or decrease the risk of failure modes. - Abstract: Renewable energy plays a key role in the transition toward a low carbon economy and the provision of a secure supply of energy. Geothermal energy is a versatile source as a form of renewable energy that meets popular demand. Since some Geothermal Power Plants (GPPs) face various failures, the requirement of a technique for team engineering to eliminate or decrease potential failures is considerable. Because no specific published record of considering an FMEA applied to GPPs with common failure modes have been found already, in this paper, the utilization of Failure Modes and Effects Analysis (FMEA) as a convenient technique for determining, classifying and analyzing common failures in typical GPPs is considered. As a result, an appropriate risk scoring of occurrence, detection and severity of failure modes and computing the Risk Priority Number (RPN) for detecting high potential failures is achieved. In order to expedite accuracy and ability to analyze the process, XFMEA software is utilized. Moreover, 5 major parts of a GPP is studied to propose a suitable approach for developing GPPs and increasing reliability by recommending corrective actions for each failure mode

  2. 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

  3. Fast Generation of Ensembles of Cosmological N-Body Simulations via Mode-Resampling

    Energy Technology Data Exchange (ETDEWEB)

    Schneider, M D; Cole, S; Frenk, C S; Szapudi, I

    2011-02-14

    We present an algorithm for quickly generating multiple realizations of N-body simulations to be used, for example, for cosmological parameter estimation from surveys of large-scale structure. Our algorithm uses a new method to resample the large-scale (Gaussian-distributed) Fourier modes in a periodic N-body simulation box in a manner that properly accounts for the nonlinear mode-coupling between large and small scales. We find that our method for adding new large-scale mode realizations recovers the nonlinear power spectrum to sub-percent accuracy on scales larger than about half the Nyquist frequency of the simulation box. Using 20 N-body simulations, we obtain a power spectrum covariance matrix estimate that matches the estimator from Takahashi et al. (from 5000 simulations) with < 20% errors in all matrix elements. Comparing the rates of convergence, we determine that our algorithm requires {approx}8 times fewer simulations to achieve a given error tolerance in estimates of the power spectrum covariance matrix. The degree of success of our algorithm indicates that we understand the main physical processes that give rise to the correlations in the matter power spectrum. Namely, the large-scale Fourier modes modulate both the degree of structure growth through the variation in the effective local matter density and also the spatial frequency of small-scale perturbations through large-scale displacements. We expect our algorithm to be useful for noise modeling when constraining cosmological parameters from weak lensing (cosmic shear) and galaxy surveys, rescaling summary statistics of N-body simulations for new cosmological parameter values, and any applications where the influence of Fourier modes larger than the simulation size must be accounted for.

  4. 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)

  5. CMB in a box: Causal structure and the Fourier-Bessel expansion

    International Nuclear Information System (INIS)

    Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.

    2010-01-01

    This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

  6. 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

  7. A modulation model for mode splitting of magnetic perturbations in the Mega Ampere Spherical Tokamak

    International Nuclear Information System (INIS)

    Hole, M J; Appel, L C

    2009-01-01

    Recent observations of magnetic fluctuation activity in the Mega Ampere Spherical Tokamak (MAST) reveal the presence of plasmas with bands of both low and high frequency magnetic fluctuations. Such plasmas exhibit a spectrum of low frequency modes with adjacent toroidal mode numbers, for which the measured frequency is near the Doppler shifted rotation frequency of the plasma. These are thought to be tearing modes. Also present are a spectrum of high frequency modes (e.g. Alfven, fishbone and/or ICE). The frequency and mode number of the tearing mode and its harmonics is identical to the frequency and mode number splitting of the high frequency MHD activity, strongly suggesting that the high frequency splitting is produced by modulation of the high and low frequency modes. We describe a strong modulation model, in which the nonlinear terms are fitted to produce the amplitude envelope profile of the tearing mode. A bispectral analysis proves that the low frequency modes are indeed in phase with the fundamental, while Fourier-SVD mode analysis confirms the mode numbers are toroidal harmonics. Employing this model, the sideband amplitude profile of the high frequency modes is predicted, and found to be in good agreement with experimental observations. Also, toroidal mode number splitting of the high frequency activity matches the mode number of the tearing mode. Weak evidence is found to indicate the Alfvenic sidebands are in phase with the Alfven eigenmode fundamental. The findings support predictions of a strong modulation model, and suggest a need to further develop nonlinear MHD theory to predict the amplitude of coupled sidebands, and so corroborate the observed nonlinear plasma response.

  8. 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)

  9. Analysis of Few-Mode Multi-Core Fiber Splice Behavior Using an Optical Vector Network Analyzer

    DEFF Research Database (Denmark)

    Rommel, Simon; Mendinueta, Jose Manuel Delgado; Klaus, Werner

    2017-01-01

    The behavior of splices in a 3-mode 36-core fiber is analyzed using optical vector network analysis. Time-domain response analysis confirms splices may cause significant mode-mixing, while frequency-domain analysis shows splices may affect system level mode-dependent loss both positively and negativ......The behavior of splices in a 3-mode 36-core fiber is analyzed using optical vector network analysis. Time-domain response analysis confirms splices may cause significant mode-mixing, while frequency-domain analysis shows splices may affect system level mode-dependent loss both positively...

  10. Deep Borehole Emplacement Mode Hazard Analysis Revision 0

    Energy Technology Data Exchange (ETDEWEB)

    Sevougian, S. David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-08-07

    This letter report outlines a methodology and provides resource information for the Deep Borehole Emplacement Mode Hazard Analysis (DBEMHA). The main purpose is identify the accident hazards and accident event sequences associated with the two emplacement mode options (wireline or drillstring), to outline a methodology for computing accident probabilities and frequencies, and to point to available databases on the nature and frequency of accidents typically associated with standard borehole drilling and nuclear handling operations. Risk mitigation and prevention measures, which have been incorporated into the two emplacement designs (see Cochran and Hardin 2015), are also discussed. A key intent of this report is to provide background information to brief subject matter experts involved in the Emplacement Mode Design Study. [Note: Revision 0 of this report is concentrated more on the wireline emplacement mode. It is expected that Revision 1 will contain further development of the preliminary fault and event trees for the drill string emplacement mode.

  11. Finite mode analysis through harmonic waveguides

    NARCIS (Netherlands)

    Alieva, T.; Wolf, K.B.

    2000-01-01

    The mode analysis of signals in a multimodal shallow harmonic waveguide whose eigenfrequencies are equally spaced and finite can be performed by an optoelectronic device, of which the optical part uses the guide to sample the wave field at a number of sensors along its axis and the electronic part

  12. 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.

  13. 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.

  14. 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.)

  15. 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.

  16. Selection of transverse modes in laser cavities containing waveguides and open parts

    International Nuclear Information System (INIS)

    Gurin, O V; Degtyarev, A V; Maslov, Vyacheslav A; Svich, V A; Tkachenko, V M; Topkov, A N

    2001-01-01

    The transverse modes of a submillimetre laser cavity that contains waveguides and open parts were studied theoretically and experimentally with the purpose of finding methods for mode selection. Two methods based on the filtering of the Fourier spectra of the waveguide modes and the use of their interference were substantiated numerically and realised in experiment. Special attention was paid to the mode selection in tunable lasers. Scaling laws allowing one to use the obtained results in a wide range of the cavity parameters and wavelengths are presented. (laser applications and other topics in quantum electronics)

  17. Fourier transform infrared spectroscopy in physics laboratory courses

    International Nuclear Information System (INIS)

    Möllmann, K-P; Vollmer, M

    2013-01-01

    Infrared spectrometry is one of the most important tools in the field of spectroscopic analysis. This is due to the high information content of spectra in the so-called spectroscopic fingerprint region, which enables measurement not only of gases, but also of liquids and solids. Today, infrared spectroscopy is almost completely dominated by Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy is able to detect minute quantities in the ppm and ppb ranges, and the respective analyses are now standard tools in science as well as industry. Therefore FTIR spectroscopy should be taught within the standard curriculum at university to physicists and engineers. Here we present respective undergraduate laboratory experiments designed for students at the end of their third year. Experiments deal first with understanding the spectrometer and second with recording and analysing spectra. On the one hand, transmission spectra of gases are treated which relate to environmental analytics (being probably the most prominent and well-known examples), and on the other hand, the focus is on the transmission and reflection spectra of solids. In particular, silicon wafers are studied—as is regularly done in the microelectronics industry—in order to characterize their thickness, oxygen content and phonon modes. (paper)

  18. 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)

  19. 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.

  20. Comparative study of various normal mode analysis techniques based on partial Hessians.

    Science.gov (United States)

    Ghysels, An; Van Speybroeck, Veronique; Pauwels, Ewald; Catak, Saron; Brooks, Bernard R; Van Neck, Dimitri; Waroquier, Michel

    2010-04-15

    Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine-stretch, the spectrum of quinine and a bis-cinchona derivative, and the low frequency modes of the LAO binding protein. 2009 Wiley Periodicals, Inc.

  1. Role of Density Gradient Driven Trapped Electron Modes in the H-Mode Inner Core with Electron Heating

    Science.gov (United States)

    Ernst, D.

    2015-11-01

    We present new experiments and nonlinear gyrokinetic simulations showing that density gradient driven TEM (DGTEM) turbulence dominates the inner core of H-Mode plasmas during strong electron heating. Thus α-heating may degrade inner core confinement in H-Mode plasmas with moderate density peaking. These DIII-D low torque quiescent H-mode experiments were designed to study DGTEM turbulence. Gyrokinetic simulations using GYRO (and GENE) closely match not only particle, energy, and momentum fluxes, but also density fluctuation spectra, with and without ECH. Adding 3.4 MW ECH doubles Te /Ti from 0.5 to 1.0, which halves the linear TEM critical density gradient, locally flattening the density profile. Density fluctuations from Doppler backscattering (DBS) intensify near ρ = 0.3 during ECH, displaying a band of coherent fluctuations with adjacent toroidal mode numbers. GYRO closely reproduces the DBS spectrum and its change in shape and intensity with ECH, identifying these as coherent TEMs. Prior to ECH, parallel flow shear lowers the effective nonlinear DGTEM critical density gradient 50%, but is negligible during ECH, when transport displays extreme stiffness in the density gradient. GS2 predictions show the DGTEM can be suppressed, to avoid degradation with electron heating, by broadening the current density profile to attain q0 >qmin > 1 . A related experiment in the same regime varied the electron temperature gradient in the outer half-radius (ρ ~ 0 . 65) using ECH, revealing spatially coherent 2D mode structures in the Te fluctuations measured by ECE imaging. Fourier analysis with modulated ECH finds a threshold in Te profile stiffness. Supported by the US DOE under DE-FC02-08ER54966 and DE-FC02-04ER54698.

  2. Detection of geodesic acoustic mode oscillations, using multiple signal classification analysis of Doppler backscattering signal on Tore Supra

    International Nuclear Information System (INIS)

    Vermare, L.; Hennequin, P.; Gürcan, Ö.D.

    2012-01-01

    This paper presents the first observation of geodesic acoustic modes (GAMs) on Tore Supra plasmas. Using the Doppler backscattering system, the oscillations of the plasma flow velocity, localized between r/a = 0.85 and r/a = 0.95, and with a frequency, typically around 10 kHz, have been observed at the plasma edge in numerous discharges. When the additional heating power is varied, the frequency is found to scale with C s /R. The MUltiple SIgnal Classification (MUSIC) algorithm is employed to access the temporal evolution of the perpendicular velocity of density fluctuations. The method is presented in some detail, and is validated and compared against standard methods, such as the conventional fast Fourier transform method, using a synthetic signal. It stands out as a powerful data analysis method to follow the Doppler frequency with a high temporal resolution, which is important in order to extract the dynamics of GAMs. (paper)

  3. 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.

  4. 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.

  5. 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)

  6. 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.

  7. 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.

  8. 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...

  9. 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

  10. 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.

  11. 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.

  12. Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy*

    OpenAIRE

    Liu, Yan-de; Ying, Yi-bin; Fu, Xia-ping

    2005-01-01

    To develop nondestructive acidity prediction for intact Fuji apples, the potential of Fourier transform near infrared (FT-NIR) method with fiber optics in interactance mode was investigated. Interactance in the 800 nm to 2619 nm region was measured for intact apples, harvested from early to late maturity stages. Spectral data were analyzed by two multivariate calibration techniques including partial least squares (PLS) and principal component regression (PCR) methods. A total of 120 Fuji appl...

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Modeling open nanophotonic systems using the Fourier modal method: generalization to 3D Cartesian coordinates.

    Science.gov (United States)

    Häyrynen, Teppo; Osterkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels

    2017-09-01

    Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform k-space discretization was introduced for rotationally symmetric structures, providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)JOAOD61084-752910.1364/JOSAA.33.001298]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates, allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier k space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence, enabling more accurate and efficient modeling of open 3D nanophotonic structures.

  19. 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.

  20. Simulation and Analysis of the Hybrid Operating Mode in ITER

    International Nuclear Information System (INIS)

    Kessel, C.E.; Budny, R.V.; Indireshkumar, K.

    2005-01-01

    The hybrid operating mode in ITER is examined with 0D systems analysis, 1.5D discharge scenario simulations using TSC and TRANSP, and the ideal MHD stability is discussed. The hybrid mode has the potential to provide very long pulses and significant neutron fluence if the physics regime can be produced in ITER. This paper reports progress in establishing the physics basis and engineering limitation for the hybrid mode in ITER

  1. 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.

  2. The Incorporation of Truncated Fourier Series into Finite Difference Approximations of Structural Stability Equations

    Science.gov (United States)

    Hannah, S. R.; Palazotto, A. N.

    1978-01-01

    A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.

  3. 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

  4. 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.

  5. 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

  6. 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.

  7. 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…

  8. 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

  9. Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs

    Science.gov (United States)

    Roychoudhuri, Chandrasekhar

    2007-09-01

    We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.

  10. 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.

  11. The impact of Mediterranean oscillations on periodicity and trend of temperature in the valley of the Nisava River: A fourier and wavelet approach

    Directory of Open Access Journals (Sweden)

    Martić-Bursać Nataša M.

    2017-01-01

    Full Text Available Periodicity of temperature on three stations in the Nisava River valley in period 1949-2014, has been analyzed by means of Fourier and wavelet transforms. Combined periodogram based on fast Fourier transform shows considerable similarity among individual series and identifies significant periods on 2.2, 2.7, 3.3, 5, 6-7, and 8.2 years in all datasets. Wavelet coherence analysis connects strongest 6-7 years spectral component to Mediterranean oscillation, starting in 1980s. Combined periodogram of Mediterranean oscillation index reveals 6-7 years spectral component as a dominant mode in period 1949-2014. Wavelet power spectra and partial combined periodograms show absence of 6-7 years component before 1975, after which this component becomes dominant in the spectrum. Consistency between alternation in temperature trend in the Nisava River valley and change in periodicity of Mediterranean oscillation was found. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. OI176008

  12. All-sky analysis of the general relativistic galaxy power spectrum

    Science.gov (United States)

    Yoo, Jaiyul; Desjacques, Vincent

    2013-07-01

    We perform an all-sky analysis of the general relativistic galaxy power spectrum using the well-developed spherical Fourier decomposition. Spherical Fourier analysis expresses the observed galaxy fluctuation in terms of the spherical harmonics and spherical Bessel functions that are angular and radial eigenfunctions of the Helmholtz equation, providing a natural orthogonal basis for all-sky analysis of the large-scale mode measurements. Accounting for all the relativistic effects in galaxy clustering, we compute the spherical power spectrum and its covariance matrix and compare it to the standard three-dimensional power spectrum to establish a connection. The spherical power spectrum recovers the three-dimensional power spectrum at each wave number k with its angular dependence μk encoded in angular multipole l, and the contributions of the line-of-sight projection to galaxy clustering such as the gravitational lensing effect can be readily accommodated in the spherical Fourier analysis. A complete list of formulas for computing the relativistic spherical galaxy power spectrum is also presented.

  13. Mode analysis of heuristic behavior of searching for multimodal optimum point

    Energy Technology Data Exchange (ETDEWEB)

    Kamei, K; Araki, Y; Inoue, K

    1982-01-01

    Describes an experimental study of a heuristic behavior of searching for the global optimum (maximum) point of a two-dimensional, multimodal, nonlinear and unknown function. First, the authors define three modes dealing with the trial purposes, called the purpose modes and show the heuristic search behaviors expressed by the purpose modes which the human subjects select in the search experiments. Second, the authors classify the heuristic search behaviors into three types according to the mode transitions and extracts eight states of searches which cause the mode transitions. Third, a model of the heuristic search behavior is composed of the eight mode transitions. The analysis of the heuristic search behaviors by use of the purpose modes plays an important role in the heuristic search techniques. 6 references.

  14. Physicochemical properties determining the detection probability of tryptic peptides in Fourier transform mass spectrometry. A correlation study

    DEFF Research Database (Denmark)

    Nielsen, Michael L; Savitski, Mikhail M; Kjeldsen, Frank

    2004-01-01

    Sequence verification and mapping of posttranslational modifications require nearly 100% sequence coverage in the "bottom-up" protein analysis. Even in favorable cases, routine liquid chromatography-mass spectrometry detects from protein digests peptides covering 50-90% of the sequence. Here we...... investigated the reasons for limited peptide detection, considering various physicochemical aspects of peptide behavior in liquid chromatography-Fourier transform mass spectrometry (LC-FTMS). No overall correlation was found between the detection probability and peptide mass. In agreement with literature data...... between pI and signal response. An explanation of this paradoxal behavior was found through the observation that more acidic tryptic peptide lengths tend to be longer. Longer peptides tend to acquire higher average charge state in positive mode electrospray ionization than more basic but shorter...

  15. Zonal flow excitation by Shukla-Varma modes in a nonuniform dusty magnetoplasma

    International Nuclear Information System (INIS)

    Shukla, P.K.; Stenflo, L.

    2002-01-01

    The nonlinear coupling between the Shukla-Varma (SV) modes and the zonal flows in a nonuniform dusty magnetoplasma is considered. By using a two-fluid model and the guiding center particle drifts, a pair of coupled mode equations is obtained. The latter are Fourier analyzed to obtain a nonlinear dispersion relation, which exhibits the excitation of zonal flows by the ponderomotive force of the SV modes. The increment of the parametrically excited zonal flows is presented. The relevance of our investigation to laboratory and space plasmas is discussed

  16. 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

  17. Robust-mode analysis of hydrodynamic flows

    Science.gov (United States)

    Roy, Sukesh; Gord, James R.; Hua, Jia-Chen; Gunaratne, Gemunu H.

    2017-04-01

    The emergence of techniques to extract high-frequency high-resolution data introduces a new avenue for modal decomposition to assess the underlying dynamics, especially of complex flows. However, this task requires the differentiation of robust, repeatable flow constituents from noise and other irregular features of a flow. Traditional approaches involving low-pass filtering and principle components analysis have shortcomings. The approach outlined here, referred to as robust-mode analysis, is based on Koopman decomposition. Three applications to (a) a counter-rotating cellular flame state, (b) variations in financial markets, and (c) turbulent injector flows are provided.

  18. Comprehensive method of common-mode failure analysis for LMFBR safety systems

    International Nuclear Information System (INIS)

    Unione, A.J.; Ritzman, R.L.; Erdmann, R.C.

    1976-01-01

    A technique is demonstrated which allows the systematic treatment of common-mode failures of safety system performance. The technique uses log analysis in the form of fault and success trees to qualitatively assess the sources of common-mode failure and quantitatively estimate the contribution to the overall risk of system failure. The analysis is applied to the secondary control rod system of an early sized LMFBR

  19. 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.

  20. 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

  1. Molecular dynamics simulation and x-ray structural studies of mode-coupling in monoclinic K2ZnBr4

    International Nuclear Information System (INIS)

    Machida, Mitsuo; Itoh, Hideaki; Koyano, Nobumitsu

    2003-01-01

    The mode-coupling between the rotational and translational motions in the monoclinic K 2 ZnBr 4 was studied by the molecular dynamics simulation and X-ray structure analysis. In the structure analysis, the Fourier analysis indicates that, in the paraelectric phase, electron densities of the bromines Br1 and Br2 on the mirror plane are fairly elongated in the b direction, while the density of the bromine Br3 at the general position spreads more or less in the a direction. In the ferroelectric phase, the elongation is suppressed in particular for Br1 and Br2, and the densities of Br3 and Br4, which are equivalent each other in the paraelectric phase, are nearly isotropic. In addition, Br1 and Br2 displace in the b direction through the rotation of the ZnBr 4 2- ion about the a axis. In the simulation, the ZnBr 4 2- ions are treated as rigid-bodies. The trajectories of the bromines reproduce satisfactorily the characteristic feature of the Fourier maps. This means that the ZnBr 4 2- ions are approximately regarded as rigid-bodies even in the real K 2 ZnBr 4 . The mode-coupling analysis shows that, in the ZnBr 4 2- rigid-bodies, the rotational motion about the a axis and the translational motion in the b direction couple strongly. Moreover, the displacements of rotational and translational motions in the b direction are almost synchronous for Br1 and Br2, and almost asynchronous for Br3 and Br4. (author)

  2. Bayesian soft x-ray tomography and MHD mode analysis on HL-2A

    Science.gov (United States)

    Li, Dong; Liu, Yi; Svensson, J.; Liu, Y. Q.; Song, X. M.; Yu, L. M.; Mao, Rui; Fu, B. Z.; Deng, Wei; Yuan, B. S.; Ji, X. Q.; Xu, Yuan; Chen, Wei; Zhou, Yan; Yang, Q. W.; Duan, X. R.; Liu, Yong; HL-2A Team

    2016-03-01

    A Bayesian based tomography method using so-called Gaussian processes (GPs) for the emission model has been applied to the soft x-ray (SXR) diagnostics on HL-2A tokamak. To improve the accuracy of reconstructions, the standard GP is extended to a non-stationary version so that different smoothness between the plasma center and the edge can be taken into account in the algorithm. The uncertainty in the reconstruction arising from measurement errors and incapability can be fully analyzed by the usage of Bayesian probability theory. In this work, the SXR reconstructions by this non-stationary Gaussian processes tomography (NSGPT) method have been compared with the equilibrium magnetic flux surfaces, generally achieving a satisfactory agreement in terms of both shape and position. In addition, singular-value-decomposition (SVD) and Fast Fourier Transform (FFT) techniques have been applied for the analysis of SXR and magnetic diagnostics, in order to explore the spatial and temporal features of the saturated long-lived magnetohydrodynamics (MHD) instability induced by energetic particles during neutral beam injection (NBI) on HL-2A. The result shows that this ideal internal kink instability has a dominant m/n  =  1/1 mode structure along with a harmonics m/n  =  2/2, which are coupled near the q  =  1 surface with a rotation frequency of 12 kHz.

  3. 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.

  4. 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.

  5. Scaling of mode shapes from operational modal analysis using harmonic forces

    Science.gov (United States)

    Brandt, A.; Berardengo, M.; Manzoni, S.; Cigada, A.

    2017-10-01

    This paper presents a new method for scaling mode shapes obtained by means of operational modal analysis. The method is capable of scaling mode shapes on any structure, also structures with closely coupled modes, and the method can be used in the presence of ambient vibration from traffic or wind loads, etc. Harmonic excitation can be relatively easily accomplished by using general-purpose actuators, also for force levels necessary for driving large structures such as bridges and highrise buildings. The signal processing necessary for mode shape scaling by the proposed method is simple and the method can easily be implemented in most measurement systems capable of generating a sine wave output. The tests necessary to scale the modes are short compared to typical operational modal analysis test time. The proposed method is thus easy to apply and inexpensive relative to some other methods for scaling mode shapes that are available in literature. Although it is not necessary per se, we propose to excite the structure at, or close to, the eigenfrequencies of the modes to be scaled, since this provides better signal-to-noise ratio in the response sensors, thus permitting the use of smaller actuators. An extensive experimental activity on a real structure was carried out and the results reported demonstrate the feasibility and accuracy of the proposed method. Since the method utilizes harmonic excitation for the mode shape scaling, we propose to call the method OMAH.

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

    Energy Technology Data Exchange (ETDEWEB)

    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.

  7. 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)

  8. 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.

  9. 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

  10. 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

  11. Pfaff equation and Fourier analysis to phase extraction from an interferogram with carrier frequency

    International Nuclear Information System (INIS)

    Lara-Cortez, Francisco; Meneses-Fabian, Cruz; Rodriguez-Zurita, Gustavo

    2011-01-01

    In the phase extraction techniques, one of the steps most used is to calculate the phase unwrapping from the wrapped phase, which is generally obtained via the inverse tangent function. With the idea to avoid this process, in the present manuscript a method based in the solution of the Pfaff equations is proposed. It is shown that the Pfaff equation is formed with the phase gradient and an auxiliary vector. The phase gradient is obtained from an interference patron with carrier frequency by applying the Fourier transform method and the partial derivatives. In the present manuscript, mathematical analysis, numerical simulation, and the phase extraction of some experimental interferograms are shown.

  12. 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

  13. 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

  14. Experimental Lamb mode identification in a plate containing a hole using dual signal processing

    International Nuclear Information System (INIS)

    Grondel, Sébastien; Assaad, Jamal; Youbi, Faysal El; Moulin, Emmanuel; Leyla, Najib Abou

    2008-01-01

    The identification of Lamb mode amplitude variation as a function of the damage evolution is still the most difficult step in the process of damage monitoring using embedded Lamb wave-based systems. The aim of this paper is to propose a simple system based on the generation of two different frequencies in order to better identify Lamb mode amplitude and to avoid false data interpretation in plates containing a hole of variable diameter. This identification is based on a simple relation between the short-time Fourier transform and the two-dimensional Fourier transform. Experimentally, a 3 mm thick aluminium plate is used and the two frequencies have been chosen equal to 400 kHz and 600 kHz in order to generate the two first fundamental Lamb waves

  15. 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.

  16. 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

  17. Failure mode and effects analysis and fault tree analysis of surface image guided cranial radiosurgery.

    Science.gov (United States)

    Manger, Ryan P; Paxton, Adam B; Pawlicki, Todd; Kim, Gwe-Ya

    2015-05-01

    Surface image guided, Linac-based radiosurgery (SIG-RS) is a modern approach for delivering radiosurgery that utilizes optical stereoscopic imaging to monitor the surface of the patient during treatment in lieu of using a head frame for patient immobilization. Considering the novelty of the SIG-RS approach and the severity of errors associated with delivery of large doses per fraction, a risk assessment should be conducted to identify potential hazards, determine their causes, and formulate mitigation strategies. The purpose of this work is to investigate SIG-RS using the combined application of failure modes and effects analysis (FMEA) and fault tree analysis (FTA), report on the effort required to complete the analysis, and evaluate the use of FTA in conjunction with FMEA. A multidisciplinary team was assembled to conduct the FMEA on the SIG-RS process. A process map detailing the steps of the SIG-RS was created to guide the FMEA. Failure modes were determined for each step in the SIG-RS process, and risk priority numbers (RPNs) were estimated for each failure mode to facilitate risk stratification. The failure modes were ranked by RPN, and FTA was used to determine the root factors contributing to the riskiest failure modes. Using the FTA, mitigation strategies were formulated to address the root factors and reduce the risk of the process. The RPNs were re-estimated based on the mitigation strategies to determine the margin of risk reduction. The FMEA and FTAs for the top two failure modes required an effort of 36 person-hours (30 person-hours for the FMEA and 6 person-hours for two FTAs). The SIG-RS process consisted of 13 major subprocesses and 91 steps, which amounted to 167 failure modes. Of the 91 steps, 16 were directly related to surface imaging. Twenty-five failure modes resulted in a RPN of 100 or greater. Only one of these top 25 failure modes was specific to surface imaging. The riskiest surface imaging failure mode had an overall RPN-rank of eighth

  18. 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)

  19. Clinical risk analysis with failure mode and effect analysis (FMEA) model in a dialysis unit.

    Science.gov (United States)

    Bonfant, Giovanna; Belfanti, Pietro; Paternoster, Giuseppe; Gabrielli, Danila; Gaiter, Alberto M; Manes, Massimo; Molino, Andrea; Pellu, Valentina; Ponzetti, Clemente; Farina, Massimo; Nebiolo, Pier E

    2010-01-01

    The aim of clinical risk management is to improve the quality of care provided by health care organizations and to assure patients' safety. Failure mode and effect analysis (FMEA) is a tool employed for clinical risk reduction. We applied FMEA to chronic hemodialysis outpatients. FMEA steps: (i) process study: we recorded phases and activities. (ii) Hazard analysis: we listed activity-related failure modes and their effects; described control measures; assigned severity, occurrence and detection scores for each failure mode and calculated the risk priority numbers (RPNs) by multiplying the 3 scores. Total RPN is calculated by adding single failure mode RPN. (iii) Planning: we performed a RPNs prioritization on a priority matrix taking into account the 3 scores, and we analyzed failure modes causes, made recommendations and planned new control measures. (iv) Monitoring: after failure mode elimination or reduction, we compared the resulting RPN with the previous one. Our failure modes with the highest RPN came from communication and organization problems. Two tools have been created to ameliorate information flow: "dialysis agenda" software and nursing datasheets. We scheduled nephrological examinations, and we changed both medical and nursing organization. Total RPN value decreased from 892 to 815 (8.6%) after reorganization. Employing FMEA, we worked on a few critical activities, and we reduced patients' clinical risk. A priority matrix also takes into account the weight of the control measures: we believe this evaluation is quick, because of simple priority selection, and that it decreases action times.

  20. 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)

  1. 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.

  2. 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

  3. 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.

  4. Parametric resonance in neutrino oscillation: A guide to control the effects of inhomogeneous matter density

    International Nuclear Information System (INIS)

    Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe

    2016-01-01

    Effects of the inhomogeneous matter density on the three-generation neutrino oscillation probability are analyzed. Realistic profile of the matter density is expanded into a Fourier series. Taking in the Fourier modes one by one, we demonstrate that each mode has its corresponding target energy. The high Fourier mode selectively modifies the oscillation probability of the low-energy region. This rule is well described by the parametric resonance between the neutrino oscillation and the matter effect. The Fourier analysis gives a simple guideline to systematically control the uncertainty of the oscillation probability caused by the uncertain density of matter. Precise analysis of the oscillation probability down to the low-energy region requires accurate evaluation of the Fourier coefficients of the matter density up to the corresponding high modes.

  5. 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.

  6. Numerical study of the mode selection in response spectrum analysis-condensed version

    International Nuclear Information System (INIS)

    Ng, D.S.

    1986-01-01

    For quality assurance of the dynamic response spectrum analysis, the Nuclear Regulatory Commission (NRC) recommends retaining all modes below the cutoff frequency at which the spectral acceleration (S/sub a/) returns to the peak zero period acceleration (ZPA). It also suggests that modes accounting for at least 90 percent of the structural masses be included in the analysis. A simple frame-type structure is generated as a baseline frame. Then groups of oscillators representing substructure are added onto the frame to study substructure behavior. A base case is established for each frame by including the specific number of modes used. The tests are conducted by incrementing the number of modes in the response spectrum analyses starting with one mode. The structural response of each modal increment is compared with the base case to identify the efficiency of mode selection method. All three methods are then applied to the MFTF-B Axicell Vacuum Vessel. The responses in critical components of the vessel, such as hangers and foundations, will be analyzed to confirm the accuracy of the selected method

  7. 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

  8. 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.

  9. An optical Fourier transform coprocessor with direct phase determination.

    Science.gov (United States)

    Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

    2017-10-20

    The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

  10. 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.

  11. Failure Mode and Effect Analysis for Wind Turbine Systems in China

    DEFF Research Database (Denmark)

    Zhu, Jiangsheng; Ma, Kuichao; N. Soltani, Mohsen

    2017-01-01

    This paper discusses a cost based Failure Mode and Effect Analysis (FMEA) approch for the Wind Turbine (WT) with condition monitoring system in China. Normally, the traditional FMEA uses the Risk Priority Number (RPN) to rank failure modes. But the RPN can be changed with the Condition Monitoring...... Systems (CMS) due to change of the score of detection. The cost of failure mode should also be considered because faults can be detected at an incipient level, and condition-based maintenance can be scheduled. The results show that the proposed failure mode priorities considering their cost consequences...

  12. 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.

  13. 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...

  14. 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...

  15. MHD simulation of high wavenumber ballooning-like modes in LHD

    International Nuclear Information System (INIS)

    Miura, H.; Nakajima, N.

    2008-10-01

    Dynamical growths of high-wavenumber ballooning modes are studied through full-3D nonlinear MHD simulations of the Large Helical Device. The growths of the ballooning modes are identified by studying the growth rates and the radial profiles of the Fourier coefficients of fluctuation variables. The mechanisms to weaken the growth of instability, such as the local fattening of the pressure and the energy release to the parallel kinetic energy, are found being insufficient to suppress the high-wavenumber ballooning modes. Consequently, the mean pressure profile is totally modified when the evolutions of the ballooning modes are saturated. The numerical results reveal that we need some mechanisms which do not originate from an ideal MHD to achieve a mild, saturated behaviors beyond the growths of unstable high ballooning modes in the helical device. The parallel heat conductivity is proposed as one of possible non-ideal mechanisms. (author)

  16. Fractional Fourier transform for confluent hypergeometric beams

    International Nuclear Information System (INIS)

    Tang, Bin; Jiang, Chun; Zhu, Haibin

    2012-01-01

    Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.

  17. 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,

  18. Failure Modes and Effects Analysis (FMEA) Assistant Tool Feasibility Study

    Science.gov (United States)

    Flores, Melissa D.; Malin, Jane T.; Fleming, Land D.

    2013-09-01

    An effort to determine the feasibility of a software tool to assist in Failure Modes and Effects Analysis (FMEA) has been completed. This new and unique approach to FMEA uses model based systems engineering concepts to recommend failure modes, causes, and effects to the user after they have made several selections from pick lists about a component's functions and inputs/outputs. Recommendations are made based on a library using common failure modes identified over the course of several major human spaceflight programs. However, the tool could be adapted for use in a wide range of applications from NASA to the energy industry.

  19. Failure Modes and Effects Analysis (FMEA) Assistant Tool Feasibility Study

    Science.gov (United States)

    Flores, Melissa; Malin, Jane T.

    2013-01-01

    An effort to determine the feasibility of a software tool to assist in Failure Modes and Effects Analysis (FMEA) has been completed. This new and unique approach to FMEA uses model based systems engineering concepts to recommend failure modes, causes, and effects to the user after they have made several selections from pick lists about a component s functions and inputs/outputs. Recommendations are made based on a library using common failure modes identified over the course of several major human spaceflight programs. However, the tool could be adapted for use in a wide range of applications from NASA to the energy industry.

  20. 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)

  1. 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 ...

  2. 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 ...

  3. Modeling and analysis of circular flexural-vibration-mode piezoelectric transformer.

    Science.gov (United States)

    Huang, Yihua; Huang, Wei

    2010-12-01

    We propose a circular flexural-vibration-mode piezoelectric transformer and perform a theoretical analysis of the transformer. An equivalent circuit is derived from the equations of piezoelectricity and the Hamilton's principle. With this equivalent circuit, the voltage gain ratio, input impedance, and the efficiency of the circular flexural-vibration-mode piezoelectric transformer can be determined. The basic behavior of the transformer is shown by numerical results.

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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.

  9. 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....

  10. Analysis and Prediction of Sea Ice Evolution using Koopman Mode Decomposition Techniques

    Science.gov (United States)

    2018-04-30

    Resources: N/A TOTAL: $18,687 2 TECHNICAL STATUS REPORT Abstract The program goal is analysis of sea ice dynamical behavior using Koopman Mode Decompo...Title: Analysis and Prediction of Sea Ice Evolution using Koopman Mode Decomposition Techniques Subject: Monthly Progress Report Period of...Attn: Code 5596 4555 Overlook Avenue, SW Washington, D.C. 20375-5320 E-mail: reports@library.nrl.navy.mil Defense Technical Information Center

  11. 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

  12. [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

  13. 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.

  14. Modal analysis of inter-area oscillations using the theory of normal modes

    Energy Technology Data Exchange (ETDEWEB)

    Betancourt, R.J. [School of Electromechanical Engineering, University of Colima, Manzanillo, Col. 28860 (Mexico); Barocio, E. [CUCEI, University of Guadalajara, Guadalajara, Jal. 44480 (Mexico); Messina, A.R. [Graduate Program in Electrical Engineering, Cinvestav, Guadalajara, Jal. 45015 (Mexico); Martinez, I. [State Autonomous University of Mexico, Toluca, Edo. Mex. 50110 (Mexico)

    2009-04-15

    Based on the notion of normal modes in mechanical systems, a method is proposed for the analysis and characterization of oscillatory processes in power systems. The method is based on the property of invariance of modal subspaces and can be used to represent complex power system modal behavior by a set of decoupled, two-degree-of-freedom nonlinear oscillator equations. Using techniques from nonlinear mechanics, a new approach is outlined, for determining the normal modes (NMs) of motion of a general n-degree-of-freedom nonlinear system. Equations relating the normal modes and the physical velocities and displacements are developed from the linearized system model and numerical issues associated with the application of the technique are discussed. In addition to qualitative insight, this method can be utilized in the study of nonlinear behavior and bifurcation analyses. The application of these procedures is illustrated on a planning model of the Mexican interconnected system using a quadratic nonlinear model. Specifically, the use of normal mode analysis as a basis for identifying modal parameters, including natural frequencies and damping ratios of general, linear systems with n degrees of freedom is discussed. Comparisons to conventional linear analysis techniques demonstrate the ability of the proposed technique to extract the different oscillation modes embedded in the oscillation. (author)

  15. 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.

  16. 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

  17. 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.

  18. 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)

  19. 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%.

  20. A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.

    Science.gov (United States)

    Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei

    2015-09-01

    A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress.

  1. Strong diameter-dependence of nanowire emission coupled to waveguide modes

    Energy Technology Data Exchange (ETDEWEB)

    Dam, Dick van, E-mail: a.d.v.dam@tue.nl; Haverkort, Jos E. M. [Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Abujetas, Diego R.; Sánchez-Gil, José A. [Instituto de Estructura de la Materia (IEM-CSIC), Consejo Superior de Investigaciones Científicas Serrano, 121, 28006 Madrid (Spain); Bakkers, Erik P. A. M. [Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft (Netherlands); Gómez Rivas, Jaime, E-mail: j.gomezrivas@differ.nl [Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Dutch Institute for Fundamental Energy Research DIFFER, P.O. Box 6336, 5600 HH Eindhoven (Netherlands)

    2016-03-21

    The emission from nanowires can couple to waveguide modes supported by the nanowire geometry, thus governing the far-field angular pattern. To investigate the geometry-induced coupling of the emission to waveguide modes, we acquire Fourier microscopy images of the photoluminescence of nanowires with diameters ranging from 143 to 208 nm. From the investigated diameter range, we conclude that a few nanometers difference in diameter can abruptly change the coupling of the emission to a specific mode. Moreover, we observe a diameter-dependent width of the Gaussian-shaped angular pattern in the far-field emission. This dependence is understood in terms of interference of the guided modes, which emit at the end facets of the nanowire. Our results are important for the design of quantum emitters, solid state lighting, and photovoltaic devices based on nanowires.

  2. 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.

  3. Shape descriptors for mode-shape recognition and model updating

    International Nuclear Information System (INIS)

    Wang, W; Mottershead, J E; Mares, C

    2009-01-01

    The most widely used method for comparing mode shapes from finite elements and experimental measurements is the Modal Assurance Criterion (MAC), which returns a single numerical value and carries no explicit information on shape features. New techniques, based on image processing (IP) and pattern recognition (PR) are described in this paper. The Zernike moment descriptor (ZMD), Fourier descriptor (FD), and wavelet descriptor (WD), presented in this article, are the most popular shape descriptors having properties that include efficiency of expression, robustness to noise, invariance to geometric transformation and rotation, separation of local and global shape features and computational efficiency. The comparison of mode shapes is readily achieved by assembling the shape features of each mode shape into multi-dimensional shape feature vectors (SFVs) and determining the distances separating them.

  4. (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

  5. 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

  6. 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.

  7. Robust alignment of chromatograms by statistically analyzing the shifts matrix generated by moving window fast Fourier transform cross-correlation.

    Science.gov (United States)

    Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

    2015-03-01

    Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  8. Integral equation based stability analysis of short wavelength drift modes in tokamaks

    International Nuclear Information System (INIS)

    Hirose, A.; Elia, M.

    2003-01-01

    Linear stability of electron skin-size drift modes in collisionless tokamak discharges has been investigated in terms of electromagnetic, kinetic integral equations in which neither ions nor electrons are assumed to be adiabatic. A slab-like ion temperature gradient mode persists in such a short wavelength regime. However, toroidicity has a strong stabilizing influence on this mode. In the electron branch, the toroidicity induced skin-size drift mode previously predicted in terms of local kinetic analysis has been recovered. The mode is driven by positive magnetic shear and strongly stabilized for negative shear. The corresponding mixing length anomalous thermal diffusivity exhibits favourable isotope dependence. (author)

  9. Robust fault detection in bond graph framework using interval analysis and Fourier-Motzkin elimination technique

    Science.gov (United States)

    Jha, Mayank Shekhar; Chatti, Nizar; Declerck, Philippe

    2017-09-01

    This paper addresses the fault diagnosis problem of uncertain systems in the context of Bond Graph modelling technique. The main objective is to enhance the fault detection step based on Interval valued Analytical Redundancy Relations (named I-ARR) in order to overcome the problems related to false alarms, missed alarms and robustness issues. These I-ARRs are a set of fault indicators that generate the interval bounds called thresholds. A fault is detected once the nominal residuals (point valued part of I-ARRs) exceed the thresholds. However, the existing fault detection method is limited to parametric faults and it presents various limitations with regards to estimation of measurement signal derivatives, to which I-ARRs are sensitive. The novelties and scientific interest of the proposed methodology are: (1) to improve the accuracy of the measurements derivatives estimation by using a dedicated sliding mode differentiator proposed in this work, (2) to suitably integrate the Fourier-Motzkin Elimination (FME) technique within the I-ARRs based diagnosis so that measurements faults can be detected successfully. The latter provides interval bounds over the derivatives which are included in the thresholds. The proposed methodology is studied under various scenarios (parametric and measurement faults) via simulations over a mechatronic torsion bar system.

  10. On the accuracy of mode-superposition analysis of linear systems under stochastic agencies

    International Nuclear Information System (INIS)

    Bellomo, M.; Di Paola, M.; La Mendola, L.; Muscolino, G.

    1987-01-01

    This paper deals with the response of linear structures using modal reduction. The MAM (mode acceleration method) correction is extended to stochastic analysis in the stationary case. In this framework the response of the given structure must be described in a probabilistic sense and the spectral moments of the nodal response must be computed in order to obtain a full description of the vibratory stochastic phenomenon. In the deterministic analysis the response is substantially made up of two terms, one of which accounts for the dynamic response due to the lower modes while the second accounts for the contribution due to the higher modes. In stochastic analysis the nodal spectral moments are made up of three terms; the first accounts for the spectral moments of the dynamic response due to the lower modes, the second accounts for the spectral moments of input and the third accounts for the cross-spectral moments between the input and the nodal output. The analysis is applied to a 35-storey building subjected to wind multivariate environments. (orig./HP)

  11. 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

  12. Analysis of Moisture Content in Beetroot using Fourier Transform Infrared Spectroscopy and by Principal Component Analysis.

    Science.gov (United States)

    Nesakumar, Noel; Baskar, Chanthini; Kesavan, Srinivasan; Rayappan, John Bosco Balaguru; Alwarappan, Subbiah

    2018-05-22

    The moisture content of beetroot varies during long-term cold storage. In this work, we propose a strategy to identify the moisture content and age of beetroot using principal component analysis coupled Fourier transform infrared spectroscopy (FTIR). Frequent FTIR measurements were recorded directly from the beetroot sample surface over a period of 34 days for analysing its moisture content employing attenuated total reflectance in the spectral ranges of 2614-4000 and 1465-1853 cm -1 with a spectral resolution of 8 cm -1 . In order to estimate the transmittance peak height (T p ) and area under the transmittance curve [Formula: see text] over the spectral ranges of 2614-4000 and 1465-1853 cm -1 , Gaussian curve fitting algorithm was performed on FTIR data. Principal component and nonlinear regression analyses were utilized for FTIR data analysis. Score plot over the ranges of 2614-4000 and 1465-1853 cm -1 allowed beetroot quality discrimination. Beetroot quality predictive models were developed by employing biphasic dose response function. Validation experiment results confirmed that the accuracy of the beetroot quality predictive model reached 97.5%. This research work proves that FTIR spectroscopy in combination with principal component analysis and beetroot quality predictive models could serve as an effective tool for discriminating moisture content in fresh, half and completely spoiled stages of beetroot samples and for providing status alerts.

  13. Gas Measurement Using Static Fourier Transform Infrared Spectrometers.

    Science.gov (United States)

    Köhler, Michael H; Schardt, Michael; Rauscher, Markus S; Koch, Alexander W

    2017-11-13

    Online monitoring of gases in industrial processes is an ambitious task due to adverse conditions such as mechanical vibrations and temperature fluctuations. Whereas conventional Fourier transform infrared (FTIR) spectrometers use rather complex optical and mechanical designs to ensure stable operation, static FTIR spectrometers do not require moving parts and thus offer inherent stability at comparatively low costs. Therefore, we present a novel, compact gas measurement system using a static single-mirror Fourier transform spectrometer (sSMFTS). The system works in the mid-infrared range from 650 cm - 1 to 1250 cm - 1 and can be operated with a customized White cell, yielding optical path lengths of up to 120 cm for highly sensitive quantification of gas concentrations. To validate the system, we measure different concentrations of 1,1,1,2-Tetrafluoroethane (R134a) and perform a PLS regression analysis of the acquired infrared spectra. Thereby, the measured absorption spectra show good agreement with reference data. Since the system additionally permits measurement rates of up to 200 Hz and high signal-to-noise ratios, an application in process analysis appears promising.

  14. Empirical mode decomposition and long-range correlation analysis of sunspot time series

    International Nuclear Information System (INIS)

    Zhou, Yu; Leung, Yee

    2010-01-01

    Sunspots, which are the best known and most variable features of the solar surface, affect our planet in many ways. The number of sunspots during a period of time is highly variable and arouses strong research interest. When multifractal detrended fluctuation analysis (MF-DFA) is employed to study the fractal properties and long-range correlation of the sunspot series, some spurious crossover points might appear because of the periodic and quasi-periodic trends in the series. However many cycles of solar activities can be reflected by the sunspot time series. The 11-year cycle is perhaps the most famous cycle of the sunspot activity. These cycles pose problems for the investigation of the scaling behavior of sunspot time series. Using different methods to handle the 11-year cycle generally creates totally different results. Using MF-DFA, Movahed and co-workers employed Fourier truncation to deal with the 11-year cycle and found that the series is long-range anti-correlated with a Hurst exponent, H, of about 0.12. However, Hu and co-workers proposed an adaptive detrending method for the MF-DFA and discovered long-range correlation characterized by H≈0.74. In an attempt to get to the bottom of the problem in the present paper, empirical mode decomposition (EMD), a data-driven adaptive method, is applied to first extract the components with different dominant frequencies. MF-DFA is then employed to study the long-range correlation of the sunspot time series under the influence of these components. On removing the effects of these periods, the natural long-range correlation of the sunspot time series can be revealed. With the removal of the 11-year cycle, a crossover point located at around 60 months is discovered to be a reasonable point separating two different time scale ranges, H≈0.72 and H≈1.49. And on removing all cycles longer than 11 years, we have H≈0.69 and H≈0.28. The three cycle-removing methods—Fourier truncation, adaptive detrending and the

  15. Time–frequency analysis of nonstationary complex magneto-hydro-dynamics in fusion plasma signals using the Choi–Williams distribution

    International Nuclear Information System (INIS)

    Xu, L.Q.; Hu, L.Q.; Chen, K.Y.; Li, E.Z.

    2013-01-01

    Highlights: • Choi–Williams distribution yields excellent time–frequency resolution for discrete signal. • CWD method provides clear time–frequency pictures of EAST and HT-7 fast MHD events. • CWD method has advantages to wavelets transform scalogram and the short-time Fourier transform spectrogram. • We discuss about how to choose the windows and free parameter of CWD method. -- Abstract: The Choi–Williams distribution is applied to the time–frequency analysis of signals describing rapid magneto-hydro-dynamic (MHD) modes and events in tokamak plasmas. A comparison is made with Soft X-ray (SXR) signals as well as Mirnov signal that shows the advantages of the Choi–Williams distribution over both continuous wavelets transform scalogram and the short-time Fourier transform spectrogram. Examples of MHD activities in HT-7 and EAST tokamak are shown, namely the onset of coupling tearing modes, high frequency precursors of sawtooth, and low frequency MHD instabilities in edge localized mode (ELM) free in H mode discharge

  16. Fourier phasing with phase-uncertain mask

    International Nuclear Information System (INIS)

    Fannjiang, Albert; Liao, Wenjing

    2013-01-01

    Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)

  17. Three-dimensional analysis of relationship between relative orientation and motion modes

    Directory of Open Access Journals (Sweden)

    Fan Shijie

    2014-12-01

    Full Text Available Target motion modes have a close relationship with the relative orientation of missile-to-target in three-dimensional highly maneuvering target interception. From the perspective of relationship between the sensor coordinate system and the target body coordinate system, a basic model of sensor is stated and the definition of relative angular velocity between the two coordinate systems is introduced firstly. Then, the three-dimensional analytic expressions of relative angular velocity for different motion modes are derived and simplified by analyzing the influences of target centroid motion, rotation around centroid and relative motion. Finally, the relationships of the relative angular velocity directions and values with motion modes are discussed. Simulation results validate the rationality of the theoretical analysis. It is demonstrated that there are significant differences of the relative orientation in different motion modes which include luxuriant information about motion modes. The conclusions are significant for the research of motion mode identification, maneuver detection, maneuvering target tracking and interception using target signatures.

  18. Fourier and wavelet analysis of skin laser doppler flowmetry signals

    OpenAIRE

    Qi, Wei

    2011-01-01

    ObjectiveThis thesis examines the measurement of skin microvascular blood flows from Laser Doppler Flowmetry (LDF) signals. Both healthy subjects and those with features of the metabolic syndrome are studied using signal processing techniques such as the Fourier and Wavelet transforms. An aim of this study is to investigate whether change in blood flow at rest can be detected from the spectral content of the processed signals in the diferent subject groups. Additionally the effect of insulin ...

  19. The prosaic Laplace and Fourier transform

    International Nuclear Information System (INIS)

    Smith, G.A.

    1995-01-01

    Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics

  20. New predictor of aortic enlargement in uncomplicated type B aortic dissection based on elliptic Fourier analysis.

    Science.gov (United States)

    Sato, Hiroshi; Ito, Toshiro; Kuroda, Yosuke; Uchiyama, Hiroki; Watanabe, Toshitaka; Yasuda, Naomi; Nakazawa, Junji; Harada, Ryo; Kawaharada, Nobuyoshi

    2017-12-01

    This study aimed to re-examine the conventional predictive factors for dissected aortic enlargement, such as the aortic and false lumen diameter and to consider whether the morphological elements of the dissected aorta could be predictors by quantifying the 'shape' of the true lumen based on elliptic Fourier analysis. A total of 80 patients with uncomplicated type B aortic dissection were included. The patients were divided into 'Enlargement group' and 'No Change group.' Between the 2 groups, the mean systolic blood pressure during follow-up, aortic and false lumen maximum diameters, and analysed morphological data were compared using each statistical method. The maximum aortic and false lumen diameters were significantly larger in the Enlargement group than in the No Change group (39.3 vs 35.9 mm; P = 0.0058) (23.5 vs 18.2 mm; P = 0.000095). The principal component 1, which is the data calculated by elliptic Fourier analysis, was significantly lower in the Enlargement group than in the No Change group (0.020 vs - 0.072; P = 0.000049). The mean systolic blood pressure ≥130 mmHg, aortic diameter, false lumen diameter and principal component 1 were included in the Cox proportional hazard model as covariates to determine the significant predictive variable. Principal component 1 demonstrated the only significance with aortic enlargement on multivariate analysis (odds ratio = 0.32; P = 0.048). The analysed and calculated morphological data of the shape of the true lumen can be more effective predictive factors of aortic enlargement of type B dissection than the conventional factors. © The Author 2017. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved.

  1. 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.

  2. Group-invariant finite Fourier transforms

    International Nuclear Information System (INIS)

    Shenefelt, M.H.

    1988-01-01

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

  3. 3-D nonlinear calculations of resistive tearing modes

    International Nuclear Information System (INIS)

    Hicks, H.R.; Holmes, J.A.; Lee, D.K.; Carreras, B.; Waddell, B.V.

    1981-03-01

    Recent numerical calculations of the evolution of resistive tearing modes have been central to the understanding of magnetohydrodynamic activity and disruptions in tokamaks. The nonlinear, 3-D, initial-value computer code RSF has provided many of these results. This code assumes cylindrical geometry with a Fourier series representation in the two periodic coordinates and a finite-difference representation in the radial direction. This choice makes RSF considerably more accurate and efficient than previous codes

  4. On the inverse windowed Fourier transform

    OpenAIRE

    Rebollo Neira, Laura; Fernández Rubio, Juan Antonio

    1999-01-01

    The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed

  5. Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

    Science.gov (United States)

    Zhang, Zhihua

    2014-01-01

    Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

  6. A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

    Science.gov (United States)

    Grimm, C. A.

    This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

  7. Ideal MHD stability analysis of KSTAR target AT mode

    International Nuclear Information System (INIS)

    Yi, S.M.; Kim, J.H.; You, K.I.; Kim, J.Y.

    2009-01-01

    Full text: A main research objective of KSTAR (Korea Superconducting Tokamak Advanced Research) device is to demonstrate the steady-state operation capability of high-performance AT (Advanced Tokamak) mode. To meet this goal, it is critical for KSTAR to have a good MHD stability boundary, particularly against the high-beta ideal instabilities such as the external kink and the ballooning modes. To support this MHD stability KSTAR has been designed to have a strong plasma shape and a close interval between plasma and passive- plate wall. During the conceptual design phase of KSTAR, a preliminary study was performed to estimate the high beta MHD stability limit of KSTAR target AT mode using PEST and VACUUM codes and it was shown that the target AT mode can be stable up to β N ∼ 5 with a well-defined plasma pressure and current profiles. Recently, a new calculation has been performed to estimate the ideal stability limit in various KSTAR operating conditions using DCON code, and it has been observed that there is some difference between the new and old calculation results, particularly in the dependence of the maximum β N value on the toroidal mode number. Here, we thus present a more detailed analysis of the ideal MHD stability limit of KSTAR target AT mode using various codes, which include GATO as well as PEST and DCON, in the comparison of calculation results among the three codes. (author)

  8. Discriminant analysis to predict the occurrence of ELMs in H-mode discharges

    International Nuclear Information System (INIS)

    Kardaun, O.J.W.F.; Itoh, S.; Itoh, K.; Kardaun, J.W.P.F.

    1993-08-01

    After an exposition of its theoretical background, discriminant analysis is applied to the H-mode confinement database to find the region in plasma parameter space in which H-mode with small ELMs (Edge Localized Modes) is likely to occur. The boundary of this region is determined by the condition that the probability of appearance of such a type of H-mode, as a function of the plasma parameters, should be (1) larger than some threshold value and (2) larger than the corresponding probability for other types of H-mode (i.e., H-mode without ELMs or with giant ELMs). In practice, the discrimination has been performed for the ASDEX, JET and JFT-2M tokamaks (a) using four instantaneous plasma parameters (injected power P inj , magnetic field B t , plasma current I p and line averaged electron density (n-bar e ) and (b) taking also memory effects of the plasma and the distance between the plasma and the wall into account, while using variables that are normalised with respect to machine size. Generally speaking, it is found that there is a substantial overlap between the region of H-mode with small ELMs and the region of the two other types of H-mode. However, the ELM-free and the giant ELM H-modes relatively rarely appear in the region, that, according to the analysis, is allocated to small ELMs. A reliable production of H-mode with only small ELMs seems well possible by choosing this regime in parameter space. In the present study, it was not attempted to arrive at a unified discrimination across the machines. So, projection from one machine to another remains difficult, and a reliable determination of the region where small ELMs occur still requires a training sample from the device under consideration. (author) 53 refs

  9. The Navier-Stokes-Fourier system: From weak solutions to numerical analysis

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2015-01-01

    Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml

  10. System reliability analysis using dominant failure modes identified by selective searching technique

    International Nuclear Information System (INIS)

    Kim, Dong-Seok; Ok, Seung-Yong; Song, Junho; Koh, Hyun-Moo

    2013-01-01

    The failure of a redundant structural system is often described by innumerable system failure modes such as combinations or sequences of local failures. An efficient approach is proposed to identify dominant failure modes in the space of random variables, and then perform system reliability analysis to compute the system failure probability. To identify dominant failure modes in the decreasing order of their contributions to the system failure probability, a new simulation-based selective searching technique is developed using a genetic algorithm. The system failure probability is computed by a multi-scale matrix-based system reliability (MSR) method. Lower-scale MSR analyses evaluate the probabilities of the identified failure modes and their statistical dependence. A higher-scale MSR analysis evaluates the system failure probability based on the results of the lower-scale analyses. Three illustrative examples demonstrate the efficiency and accuracy of the approach through comparison with existing methods and Monte Carlo simulations. The results show that the proposed method skillfully identifies the dominant failure modes, including those neglected by existing approaches. The multi-scale MSR method accurately evaluates the system failure probability with statistical dependence fully considered. The decoupling between the failure mode identification and the system reliability evaluation allows for effective applications to larger structural systems

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

    Science.gov (United States)

    Tilley, David G.

    1995-01-01

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

  12. Non-Fourier Vernotte-Cattaneo numerical model for heat conduction in a BWR fuel rod

    Energy Technology Data Exchange (ETDEWEB)

    Espinosa-Martinez, E.G.; Vazquez-Rodriguez, A.; Varela-Ham, J.R.; Espinosa-Paredes, G., E-mail: gepe@xanum.uam.mx [Universidad Autonoma Metropolitana, Area de Ingenieria en Recursos Energeticos, Iztapalapa (Mexico)

    2014-07-01

    A fuel rod mathematical model based on transient heat conduction as constitutive Non-Fourier law for Light Water Reactors (LWRs) transient analysis is presented. The structure of the fuel pellet is affected due to high temperatures and irradiation, which eventually produce fracture or cracks. In principle the fractures are saturated of gas. Then, the Fourier law of the heat conduction is not strictly applicable to describe these phenomena, where the physical properties such as thermal conductivity, heat capacity and density correspond to a heterogeneous material due to gas, and therefore the thermal diffusion process due to molecular transport in the fuel pellet is affected. From the point of view of nuclear reactor safety analysis, the heat transfer from the fuel to the coolant is crucial and superheating of the wall can cause the cladding failure. In the classical theory of diffusion, the Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient assuming that the heat propagation speeds are infinite. The Non-Fourier approach presented in this work eliminates the assumption of an infinite thermal wave speed, therefore time-dependent heat sources were considered in the fuel rod heat transfer model. The numerical experiments in a BWR, show that the Non-Fourier approach is crucial in the pressurization transients such as turbine trip and reactor isolation. (author)

  13. Non-Fourier Vernotte-Cattaneo numerical model for heat conduction in a BWR fuel rod

    International Nuclear Information System (INIS)

    Espinosa-Martinez, E.G.; Vazquez-Rodriguez, A.; Varela-Ham, J.R.; Espinosa-Paredes, G.

    2014-01-01

    A fuel rod mathematical model based on transient heat conduction as constitutive Non-Fourier law for Light Water Reactors (LWRs) transient analysis is presented. The structure of the fuel pellet is affected due to high temperatures and irradiation, which eventually produce fracture or cracks. In principle the fractures are saturated of gas. Then, the Fourier law of the heat conduction is not strictly applicable to describe these phenomena, where the physical properties such as thermal conductivity, heat capacity and density correspond to a heterogeneous material due to gas, and therefore the thermal diffusion process due to molecular transport in the fuel pellet is affected. From the point of view of nuclear reactor safety analysis, the heat transfer from the fuel to the coolant is crucial and superheating of the wall can cause the cladding failure. In the classical theory of diffusion, the Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient assuming that the heat propagation speeds are infinite. The Non-Fourier approach presented in this work eliminates the assumption of an infinite thermal wave speed, therefore time-dependent heat sources were considered in the fuel rod heat transfer model. The numerical experiments in a BWR, show that the Non-Fourier approach is crucial in the pressurization transients such as turbine trip and reactor isolation. (author)

  14. Simple surface structure determination from Fourier transforms of angle-resolved photoemission extended fine structure

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, Y. [Pennsylvania State Univ., University Park, PA (United States)]|[Lawrence Berkeley Lab., CA (United States); Shirley, D.A. [Pennsylvania State Univ., University Park, PA (United States)

    1995-02-01

    The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.

  15. Mode Shape Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

    Directory of Open Access Journals (Sweden)

    Tran Van Lien

    Full Text Available Abstract The present paper addresses free vibration of multiple cracked Timoshenko beams made of Functionally Graded Material (FGM. Cracks are modeled by rotational spring of stiffness calculated from the crack depth and material properties vary according to the power law throughout the beam thickness. Governing equations for free vibration of the beam are formulated with taking into account actual position of the neutral plane. The obtained frequency equation and mode shapes are used for analysis of the beam mode shapes in dependence on the material and crack parameters. Numerical results validate usefulness of the proposed herein theory and show that mode shapes are good indication for detecting multiple cracks in Timoshenko FGM beams.

  16. Bicoherence Analysis of Electrostatic Interchange Mode Coupling in a Turbulent Laboratory Magnetosphere

    Science.gov (United States)

    Abler, M. C.; Mauel, M. E.; Saperstein, A.

    2017-12-01

    Plasmas confined by a strong dipole field exhibit interchange and entropy mode turbulence, which previous experiments have shown respond locally to active feedback [1]. On the Collisionless Terrella Experiment (CTX), this turbulence is characterized by low frequency, low order, quasi-coherent modes with complex spectral dynamics. We apply bicoherence analysis [2] to study nonlinear phase coupling in a variety of scenarios. First, we study the self-interaction of the naturally occurring interchange turbulence; this analysis is then expanded to include the effects of single or multiple driven modes in the frequency range of the background turbulent oscillations. Initial measurements of coupling coefficients are presented in both cases. Driven low frequency interchange modes are observed to generate multiple harmonics which persist throughout the plasma, becoming weaker as they propagate away from the actuator in the direction of the electron magnetic drift. Future work is also discussed, including application of wavelet bicoherence analysis and applications to planetary magnetospheres. [1] Roberts, Mauel, and Worstell, Phys Plasmas (2015). [2] Grierson, Worstell, and Mauel, Phys Plasmas (2009). Supported by NSF-DOE Partnership for Plasma Science Grants DOE-DE-FG02-00ER54585 and NSF-PHY-1201896.

  17. ON THE FOURIER AND WAVELET ANALYSIS OF CORONAL TIME SERIES

    International Nuclear Information System (INIS)

    Auchère, F.; Froment, C.; Bocchialini, K.; Buchlin, E.; Solomon, J.

    2016-01-01

    Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provides a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence and Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence and Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.

  18. ON THE FOURIER AND WAVELET ANALYSIS OF CORONAL TIME SERIES

    Energy Technology Data Exchange (ETDEWEB)

    Auchère, F.; Froment, C.; Bocchialini, K.; Buchlin, E.; Solomon, J., E-mail: frederic.auchere@ias.u-psud.fr [Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, F-91405 Orsay (France)

    2016-07-10

    Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provides a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence and Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence and Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.

  19. A Note on Fourier and the Greenhouse Effect

    OpenAIRE

    Postma, Joseph E.

    2015-01-01

    Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...

  20. Surface analysis by Fourier-transform infrared (FTIR) spectroscopy

    International Nuclear Information System (INIS)

    Powell, G.L.; Smyrl, N.R.; Fuller, E.L.

    1981-01-01

    A diffuse-reflectance capability for the Fourier transform infrared spectrometer at the Y-12 Plant Laboratory has been implemented. A sample cell with a 25 to 400 0 C temperature-controlled sample stage and an ultrahigh-vacuum-to-atmospheric pressure gas-handling capability has been developed. Absorbance of light from the spectrometer beam, resulting from the beam being scattered from a powder sample, can be measured. This capability of detecting molecular species on and in powders is to be used to study chemisorption on actinide and rare-earth metals, alloys, and compounds. Cell design is described along with experiments demonstrating its performance in detecting moisture absorption on uranium oxide, moisture and carbon dioxide absorption on the lithium hydride/hydroxide system, and carbon dioxide absorption on potassium borohydride. 13 figures

  1. Analysis of self-homodyne detection for 6-mode fiber with low-modal crosstalk

    Science.gov (United States)

    Guo, Meng; Hu, Guijun

    2017-12-01

    In this paper, we present an appropriate analysis on self-homodyne coherent system with 56 × 5 × 3 Gb / s WDM-PDM-MDM quadrature phase-shift keying (QPSK) signals using 6-mode weakly coupled few mode fiber. The mode division technology can effectively improve the spectral efficiency (SE) of self-homodyne detection. Of all the LP modes, LP01 mode is used to transmit the pilot tone (PT), while the others for signal channels. The influence of inter-mode crosstalk is analyzed. The proposed frequency domain MMA shows a better BER performance for intra-mode crosstalk elimination. The path-length misalignment's influence caused by mode differential group delay (MDGD) is also investigated. The system tolerance for different laser's line-width is compared as well as the influence of PT filter's bandwidth.

  2. 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

  3. Three dimensional image reconstruction in the Fourier domain

    International Nuclear Information System (INIS)

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

    1987-01-01

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

  4. [Application of Fourier transform attenuated total reflection infrared spectroscopy in analysis of pulp and paper industry].

    Science.gov (United States)

    Zhang, Yong; Cao, Chun-yu; Feng, Wen-ying; Xu, Ming; Su, Zhen-hua; Liu, Xiao-meng; Lü, Wei-jun

    2011-03-01

    As one of the most powerful tools to investigate the compositions of raw materials and the property of pulp and paper, infrared spectroscopy has played an important role in pulp and paper industry. However, the traditional transmission infrared spectroscopy has not met the requirements of the producing processes because of its disadvantages of time consuming and sample destruction. New technique would be needed to be found. Fourier transform attenuated total reflection infrared spectroscopy (ATR-FTIR) is an advanced spectroscopic tool for nondestructive evaluation and could rapidly, accurately estimate the production properties of each process in pulp and paper industry. The present review describes the application of ATR-FTIR in analysis of pulp and paper industry. The analysis processes will include: pulping, papermaking, environmental protecting, special processing and paper identifying.

  5. Fourier Spectroscopy: A Bayesian Way

    Directory of Open Access Journals (Sweden)

    Stefan Schmuck

    2017-01-01

    Full Text Available The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.

  6. Analysis of blowout fractures using cine mode MRI

    International Nuclear Information System (INIS)

    Kawahara, Masaaki; Shiihara, Kumiko; Kimura, Hisashi; Fukai, Sakuko; Tabuchi, Akio; Kojo, Tuyoshi

    1995-01-01

    By observing conventional CT and MRI images, it is difficult to distinguish extension failure from adhesion, bone fracture or damage to the extraocular muscle, any one of which may be the direct cause of the eye movement disturbance accompanying blowout fracture. We therefore carried out dynamic analysis of eye movement disturbance using a cine mode MRI. We put seven fixation points in the gantry of the MRI and filmed eye movement disturbances by the gradient echo method, using a surface coil and holding the vision on each fixation point. We also video recorded the CRT monitor of the MRI to obtain dynamic MRI images. The subjects comprised 5 cases (7-23 years old). In 4 cases, we started orthoptic treatment, saccadic eye movement training, convergence training and fusional amplitude training after surgery, with only orthoptic treatment in the 5 th case. In all cases, fusion area improvement was recognized during training. In 2 cases examined by cine mode MRI before and after surgery, we observed improved eye movement after training, the effectiveness of which was thereby proven. Also, using cine mode MRI we were able to determine the character of incarcerated tissue and the cause of eye movement disturbance. We conclude that it blowout fracture, cine mode MRI may be useful in selecting treatment and observing its effectiveness. (author)

  7. Error analysis in Fourier methods for option pricing for exponential Lévy processes

    KAUST Repository

    Crocce, Fabian; Hä ppö lä , Juho; Keissling, Jonas; Tempone, Raul

    2015-01-01

    We derive an error bound for utilising the discrete Fourier transform method for solving Partial Integro-Differential Equations (PIDE) that describe european option prices for exponential Lévy driven asset prices. We give sufficient conditions

  8. Analysis of a large-break LOCA at lower operational modes

    Energy Technology Data Exchange (ETDEWEB)

    Jeong, H.Y.; Jun, H.Y.; Lee, K. [Korea Electric Power Corporation, Taejon (Korea)

    2000-10-01

    To improve Technical Specifications and Emergency Operating Guidelines (EOGs) applicable at lower operational modes it is required to perform the safety analysis reflecting the operational characteristics in those modes. Because the component availability and system configurations at lower modes are different from those of power mode, the plant safety at lower modes should be confirmed through independent analyses. In the present study, a large-break loss-of-coolant accident is analyzed to evaluate the containment pressure and temperature control function for the preparation of EOGs applicable at lower modes. To reach the required shutdown condition, the plant cool-down is controlled by the secondary steam flow and auxiliary feedwater. The mass and energy releases from primary system are obtained from RELAP5/MOD3.1 calculation and the containment pressure and temperature are evaluated with CONTEMPT-LT code. The reference plant is Korean Next Generation Reactor having 4,000 MW thermal power. Two cases of cold leg LOCA initiated at Mode 3 with and without SIT operation are calculated. At the given plant conditions, all safety injection pumps are still available. The calculation at the condition of maximum mass and energy release shows that the containment pressure and temperature can be controlled within acceptable criteria, which means the operations of 2 or 4 fan coolers are the possible success paths to achieve the containment P/T control safety function. The peak cladding temperature with minimum safety injection flow does not show remarkable excursion, which implies the lower mode LOCA at Mode 3 can be bounded by the results obtained at full power from the viewpoint of ECCS performance. (author)

  9. Tearing mode analysis in tokamaks, revisited

    International Nuclear Information System (INIS)

    Nishimura, Y.; Callen, J.D.; Hegna, C.C.

    1997-12-01

    A new Δ' shooting code has been developed to investigate tokamak plasma tearing mode stability in a cylinder and large aspect ratio (ε ≤ 0.25) toroidal geometries, neglecting toroidal mode coupling. A different computational algorithm is used (shooting out from the singular surface instead of into it) to resolve the strong singularities at the mode rational surface, particularly in the presence of finite pressure term. Numerical results compare favorably with Furth et al. results. The effects of finite pressure, which are shown to decrease Δ', are discussed. It is shown that the distortion of the flux surfaces by the Shafranov shift, which modifies the geometry metric element stabilizes the tearing mode significantly, even in a low β regime before the toroidal magnetic curvature effects come into play. Double tearing modes in toroidal geometries are examined as well. Furthermore, m ≥ 2 tearing mode stability criteria are compared with three dimensional initial value MHD simulation by the FAR code

  10. Comparative Study of Various Normal Mode Analysis Techniques Based on Partial Hessians

    OpenAIRE

    GHYSELS, AN; VAN SPEYBROECK, VERONIQUE; PAUWELS, EWALD; CATAK, SARON; BROOKS, BERNARD R.; VAN NECK, DIMITRI; WAROQUIER, MICHEL

    2010-01-01

    Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and...

  11. A new twist to fourier transforms

    CERN Document Server

    Meikle, Hamish D

    2004-01-01

    Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs

  12. A quantitative method for Failure Mode and Effects Analysis

    NARCIS (Netherlands)

    Braaksma, Anne Johannes Jan; Meesters, A.J.; Klingenberg, W.; Hicks, C.

    2012-01-01

    Failure Mode and Effects Analysis (FMEA) is commonly used for designing maintenance routines by analysing potential failures, predicting their effect and facilitating preventive action. It is used to make decisions on operational and capital expenditure. The literature has reported that despite its

  13. Elliptical Fourier descriptors of outline and morphological analysis in caudal view of foramen magnum of the tropical raccoon (Procyon cancrivorus) (Linnaeus, 1758).

    Science.gov (United States)

    Samuel, O M; Casanova, P M; Olopade, J O

    2018-03-01

    To evaluate sexual-size dimorphism and attempt at categorization of inter-individual shapes of foramen magnum outlines using Fourier descriptors which allow for shape outline evaluations with a resultant specimen character definition. Individual characterization and quantification of foramen magnum shapes in direct caudal view based on elliptical Fourier technique was applied to 46 tropical raccoon skulls (26 females, 20 males). Incremental number of harmonics demonstrates morphological contributions of such descriptors with their relations to specific anatomical constructions established. The initial harmonics (1st to 3rd) described the general foramen shapes while the second (4th to 12th) demonstrated fine morphological details. Sexual-size dimorphism was observed in females (87.1%) and 91.7% in males, normalization of size produces 75% in females and 83% in males. With respect to foramen magnum dimorphism analysis, the result obtained through elliptic Fourier analysis was comparatively better in detail information of outline contours than earlier classical methods. The first four effective principal components defined 70.63% of its shape properties while the rest (22.51%) constituted fine details of morphology. Both size and shape seems important in sexual dimorphisms in this species, this investigation suggest clinical implications, taxonomic and anthropologic perspectives in foramen characterization magnum characterization and further postulates an increased possibility of volume reduction cerebellar protrusion, ontogenic magnum shape irregularities in the sample population with neurologic consequences especially among females. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

  14. Economic analysis of fast reactor fuel cycle with different modes

    International Nuclear Information System (INIS)

    Ding Xiaoming

    2014-01-01

    Because of limitations on the access to technical and economic data and the lack of effective verification, the lack of in-depth study on the economy of fast reactor fuel cycle in China. This paper introduces the analysis and calculation results of the levelized cost of electricity (LCOE) under three different fuel cycle modes including fast reactor fuel cycle carried out by Massachusetts Institute of Technology (MIT). The author used the evaluation method and hypothesis parameters provided by the MIT to carry out the sensitivity analysis for the impact of the overnight cost, the discount rate and changes of uranium price on the LCOE under three fuel cycle modes. Finally, some suggestions are proposed on the study of economy in China's fast reactor fuel cycle. (authors)

  15. Wigner distribution and fractional Fourier transform

    NARCIS (Netherlands)

    Alieva, T.; Bastiaans, M.J.; Boashash, B.

    2003-01-01

    We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

  16. Fourier plane imaging microscopy

    Energy Technology Data Exchange (ETDEWEB)

    Dominguez, Daniel, E-mail: daniel.dominguez@ttu.edu; Peralta, Luis Grave de [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Alharbi, Nouf; Alhusain, Mdhaoui [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Bernussi, Ayrton A. [Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)

    2014-09-14

    We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonic crystals.

  17. Preliminary failure modes and effects analysis on Korean HCCR TBS to be tested in ITER

    International Nuclear Information System (INIS)

    Ahn, Mu-Young; Cho, Seungyon; Jin, Hyung Gon; Lee, Dong Won; Park, Yi-Hyun; Lee, Youngmin

    2015-01-01

    Highlights: • Postulated initiating events are identified through failure modes and effects analysis on the current HCCR TBS design. • A set of postulated initiating events are selected for consideration of deterministic analysis. • Accident evolutions on the selected postualted initiating events are qualitatively described for deterministic analysis. - Abstract: Korean Helium cooled ceramic reflector (HCCR) Test blanket system (TBS), which comprises Test blanket module (TBM) and ancillary systems in various locations of ITER building, is operated at high temperature and pressure with decay heat. Therefore, safety is utmost concern in design process and it is required to demonstrate that the HCCR TBS is designed to comply with the safety requirements and guidelines of ITER. Due to complexity of the system with many interfaces with ITER, a systematic approach is necessary for safety analysis. This paper presents preliminary failure modes and effects analysis (FMEA) study performed for the HCCR TBS. FMEA is a systematic methodology in which failure modes for components in the system and their consequences are studied from the bottom-up. Over eighty failure modes have been investigated on the HCCR TBS. The failure modes that have similar consequences are grouped as postulated initiating events (PIEs) and total seven reference accident scenarios are derived from FMEA study for deterministic accident analysis. Failure modes not covered here due to evolving design of the HCCR TBS and uncertainty in maintenance procedures will be studied further in near future.

  18. Preliminary failure modes and effects analysis on Korean HCCR TBS to be tested in ITER

    Energy Technology Data Exchange (ETDEWEB)

    Ahn, Mu-Young, E-mail: myahn74@nfri.re.kr [National Fusion Research Institute, Daejeon (Korea, Republic of); Cho, Seungyon [National Fusion Research Institute, Daejeon (Korea, Republic of); Jin, Hyung Gon; Lee, Dong Won [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Park, Yi-Hyun; Lee, Youngmin [National Fusion Research Institute, Daejeon (Korea, Republic of)

    2015-10-15

    Highlights: • Postulated initiating events are identified through failure modes and effects analysis on the current HCCR TBS design. • A set of postulated initiating events are selected for consideration of deterministic analysis. • Accident evolutions on the selected postualted initiating events are qualitatively described for deterministic analysis. - Abstract: Korean Helium cooled ceramic reflector (HCCR) Test blanket system (TBS), which comprises Test blanket module (TBM) and ancillary systems in various locations of ITER building, is operated at high temperature and pressure with decay heat. Therefore, safety is utmost concern in design process and it is required to demonstrate that the HCCR TBS is designed to comply with the safety requirements and guidelines of ITER. Due to complexity of the system with many interfaces with ITER, a systematic approach is necessary for safety analysis. This paper presents preliminary failure modes and effects analysis (FMEA) study performed for the HCCR TBS. FMEA is a systematic methodology in which failure modes for components in the system and their consequences are studied from the bottom-up. Over eighty failure modes have been investigated on the HCCR TBS. The failure modes that have similar consequences are grouped as postulated initiating events (PIEs) and total seven reference accident scenarios are derived from FMEA study for deterministic accident analysis. Failure modes not covered here due to evolving design of the HCCR TBS and uncertainty in maintenance procedures will be studied further in near future.

  19. Efficient surrogate models for reliability analysis of systems with multiple failure modes

    International Nuclear Information System (INIS)

    Bichon, Barron J.; McFarland, John M.; Mahadevan, Sankaran

    2011-01-01

    Despite many advances in the field of computational reliability analysis, the efficient estimation of the reliability of a system with multiple failure modes remains a persistent challenge. Various sampling and analytical methods are available, but they typically require accepting a tradeoff between accuracy and computational efficiency. In this work, a surrogate-based approach is presented that simultaneously addresses the issues of accuracy, efficiency, and unimportant failure modes. The method is based on the creation of Gaussian process surrogate models that are required to be locally accurate only in the regions of the component limit states that contribute to system failure. This approach to constructing surrogate models is demonstrated to be both an efficient and accurate method for system-level reliability analysis. - Highlights: → Extends efficient global reliability analysis to systems with multiple failure modes. → Constructs locally accurate Gaussian process models of each response. → Highly efficient and accurate method for assessing system reliability. → Effectiveness is demonstrated on several test problems from the literature.

  20. Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation

    Energy Technology Data Exchange (ETDEWEB)

    Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt (Germany); Martinazzo, Rocco [Dipartimento di Chimica, Universita degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Hughes, Keith H. [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom)

    2012-10-14

    A reduced dynamics representation is introduced which is tailored to a hierarchical, Mori-chain type representation of a bath of harmonic oscillators which are linearly coupled to a subsystem. We consider a spin-boson system where a single effective mode is constructed so as to absorb all system-environment interactions, while the residual bath modes are coupled bilinearly to the primary mode and among each other. Using a cumulant expansion of the memory kernel, correlation functions for the primary mode are obtained, which can be suitably approximated by truncated chains representing the primary-residual mode interactions. A series of reduced-dimensional bath correlation functions is thus obtained, which can be expressed as Fourier-Laplace transforms of spectral densities that are given in truncated continued-fraction form. For a master equation which is second order in the system-bath coupling, the memory kernel is re-expressed in terms of local-in-time equations involving auxiliary densities and auxiliary operators.

  1. Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

    Science.gov (United States)

    Walters, R.A.; Carey, G.F.

    1983-01-01

    The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.

  2. Few-mode fiber, splice and SDM component characterization by spatially-diverse optical vector network analysis.

    Science.gov (United States)

    Rommel, Simon; Mendinueta, José Manuel Delgado; Klaus, Werner; Sakaguchi, Jun; Olmos, Juan José Vegas; Awaji, Yoshinari; Monroy, Idelfonso Tafur; Wada, Naoya

    2017-09-18

    This paper discusses spatially diverse optical vector network analysis for space division multiplexing (SDM) component and system characterization, which is becoming essential as SDM is widely considered to increase the capacity of optical communication systems. Characterization of a 108-channel photonic lantern spatial multiplexer, coupled to a 36-core 3-mode fiber, is experimentally demonstrated, extracting the full impulse response and complex transfer function matrices as well as insertion loss (IL) and mode-dependent loss (MDL) data. Moreover, the mode-mixing behavior of fiber splices in the few-mode multi-core fiber and their impact on system IL and MDL are analyzed, finding splices to cause significant mode-mixing and to be non-negligible in system capacity analysis.

  3. Replica Fourier Transform: Properties and applications

    International Nuclear Information System (INIS)

    Crisanti, A.; De Dominicis, C.

    2015-01-01

    The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically

  4. Numerical Investigation of Vertical Cavity Lasers With High-Contrast Gratings Using the Fourier Modal Method

    DEFF Research Database (Denmark)

    Taghizadeh, Alireza; Mørk, Jesper; Chung, Il-Sug

    2016-01-01

    We explore the use of a modal expansion technique, Fourier modal method (FMM), for investigating the optical properties of vertical cavities employing high-contrast gratings (HCGs). Three techniques for determining the resonance frequency and quality factor (Q-factor) of a cavity mode are compared......, the scattering losses of several HCG-based vertical cavities with inplane heterostructures which have promising prospects for fundamental physics studies and on-chip laser applications, are investigated. This type of parametric study of 3D structures would be numerically very demanding using spatial...

  5. Partial Fourier techniques in single-shot cross-term spatiotemporal encoded MRI.

    Science.gov (United States)

    Zhang, Zhiyong; Frydman, Lucio

    2018-03-01

    Cross-term spatiotemporal encoding (xSPEN) is a single-shot approach with exceptional immunity to field heterogeneities, the images of which faithfully deliver 2D spatial distributions without requiring a priori information or using postacquisition corrections. xSPEN, however, suffers from signal-to-noise ratio penalties due to its non-Fourier nature and due to diffusion losses-especially when seeking high resolution. This study explores partial Fourier transform approaches that, acting along either the readout or the spatiotemporally encoded dimensions, reduce these penalties. xSPEN uses an orthogonal (e.g., z) gradient to read, in direct space, the low-bandwidth (e.g., y) dimension. This substantially changes the nature of partial Fourier acquisitions vis-à-vis conventional imaging counterparts. A suitable theoretical analysis is derived to implement these procedures, along either the spatiotemporally or readout axes. Partial Fourier single-shot xSPEN images were recorded on preclinical and human scanners. Owing to their reduction in the experiments' acquisition times, this approach provided substantial sensitivity gains vis-à-vis previous implementations for a given targeted in-plane resolution. The physical origins of these gains are explained. Partial Fourier approaches, particularly when implemented along the low-bandwidth spatiotemporal dimension, provide several-fold sensitivity advantages at minimal costs to the execution and processing of the single-shot experiments. Magn Reson Med 79:1506-1514, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

  6. Discrete fourier transform (DFT) analysis for applications using iterative transform methods

    Science.gov (United States)

    Dean, Bruce H. (Inventor)

    2012-01-01

    According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

  7. An introduction to Fourier series and integrals

    CERN Document Server

    Seeley, Robert T

    2006-01-01

    This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.

  8. The morphing of geographical features by Fourier transformation.

    Science.gov (United States)

    Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

    2018-01-01

    This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

  9. Fourier Series

    Indian Academy of Sciences (India)

    polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.

  10. Some Applications of Fourier's Great Discovery for Beginners

    Science.gov (United States)

    Kraftmakher, Yaakov

    2012-01-01

    Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…

  11. Numerical design and analysis of parasitic mode oscillations for 95 GHz gyrotron beam tunnel

    Science.gov (United States)

    Kumar, Nitin; Singh, Udaybir; Yadav, Vivek; Kumar, Anil; Sinha, A. K.

    2013-05-01

    The beam tunnel, equipped with the high lossy ceramics, is designed for 95 GHz gyrotron. The geometry of the beam tunnel is optimized considering the maximum RF absorption (ideally 100%) and the suppression of parasitic oscillations. The excitation of parasitic modes is a concerning problem for high frequency, high power gyrotrons. Considering the problem of parasitic mode excitation in beam tunnel, a detail analysis is performed for the suppression of these kinds of modes. Trajectory code EGUN and CST Microwave Studio are used for the simulations of electron beam trajectory and electromagnetic analysis, respectively.

  12. Time-frequency analysis of fusion plasma signals beyond the short-time Fourier transform paradigm: An overview

    International Nuclear Information System (INIS)

    Bizarro, Joao P.S.; Figueiredo, Antonio C.A.

    2008-01-01

    Performing a time-frequency (t-f) analysis on actual magnetic pick-up coil data from the JET tokamak, a comparison is presented between the spectrogram and the Wigner and Choi-Williams distributions. Whereas the former, which stems from the short-time Fourier transform and has been the work-horse for t-f signal processing, implies an unavoidable trade-off between time and frequency resolutions, the latter two belong to a later generation of distributions that yield better, if not optimal joint t-f localization. Topics addressed include signal representation in the t-f plane, frequency identification and evolution, instantaneous-frequency estimation, and amplitude tracking

  13. Discrete frequency identification using the HP 5451B Fourier analyser

    International Nuclear Information System (INIS)

    Holland, L.; Barry, P.

    1977-01-01

    The frequency analysis by the HP5451B discrete frequency Fourier analyser is studied. The advantages of cross correlation analysis to identify discrete frequencies in a background noise are discussed in conjuction with the elimination of aliasing and wraparound error. Discrete frequency identification is illustrated by a series of graphs giving the results of analysing 'electrical' and 'acoustical' white noise and sinusoidal signals [pt

  14. A fractional Fourier transform analysis of the scattering of ultrasonic waves

    Science.gov (United States)

    Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony

    2015-01-01

    Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967

  15. Few-mode fiber, splice and SDM component characterization by spatially-diverse optical vector network analysis

    DEFF Research Database (Denmark)

    Rommel, Simon; Mendinueta, José Manuel Delgado; Klaus, Werner

    2017-01-01

    This paper discusses spatially diverse optical vector network analysis for space division multiplexing (SDM) component and system characterization, which is becoming essential as SDM is widely considered to increase the capacity of optical communication systems. Characterization of a 108-channel ...... in the few-mode multi-core fiber and their impact on system IL and MDL are analyzed, finding splices to cause significant mode-mixing and to be non-negligible in system capacity analysis.......This paper discusses spatially diverse optical vector network analysis for space division multiplexing (SDM) component and system characterization, which is becoming essential as SDM is widely considered to increase the capacity of optical communication systems. Characterization of a 108-channel...... photonic lantern spatial multiplexer, coupled to a 36-core 3-mode fiber, is experimentally demonstrated, extracting the full impulse response and complex transfer function matrices as well as insertion loss (IL) and mode-dependent loss (MDL) data. Moreover, the mode-mixing behavior of fiber splices...

  16. Fourier transform spectroscopy of six stars

    Energy Technology Data Exchange (ETDEWEB)

    Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia

    1981-01-01

    This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.

  17. Linear stability analysis of collective neutrino oscillations without spurious modes

    Science.gov (United States)

    Morinaga, Taiki; Yamada, Shoichi

    2018-01-01

    Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.

  18. Multifrequency spectrum analysis using fully digital G Mode-Kelvin probe force microscopy

    International Nuclear Information System (INIS)

    Collins, Liam; Belianinov, Alex; Somnath, Suhas; Balke, Nina; Kalinin, Sergei V; Jesse, Stephen; Rodriguez, Brian J

    2016-01-01

    Since its inception over two decades ago, Kelvin probe force microscopy (KPFM) has become the standard technique for characterizing electrostatic, electrochemical and electronic properties at the nanoscale. In this work, we present a purely digital, software-based approach to KPFM utilizing big data acquisition and analysis methods. General mode (G-Mode) KPFM works by capturing the entire photodetector data stream, typically at the sampling rate limit, followed by subsequent de-noising, analysis and compression of the cantilever response. We demonstrate that the G-Mode approach allows simultaneous multi-harmonic detection, combined with on-the-fly transfer function correction—required for quantitative CPD mapping. The KPFM approach outlined in this work significantly simplifies the technique by avoiding cumbersome instrumentation optimization steps (i.e. lock in parameters, feedback gains etc), while also retaining the flexibility to be implemented on any atomic force microscopy platform. We demonstrate the added advantages of G-Mode KPFM by allowing simultaneous mapping of CPD and capacitance gradient (C′) channels as well as increased flexibility in data exploration across frequency, time, space, and noise domains. G-Mode KPFM is particularly suitable for characterizing voltage sensitive materials or for operation in conductive electrolytes, and will be useful for probing electrodynamics in photovoltaics, liquids and ionic conductors. (paper)

  19. Finite-Length Diocotron Modes in a Non-neutral Plasma Column

    Science.gov (United States)

    Walsh, Daniel; Dubin, Daniel

    2017-10-01

    Diocotron modes are 2D distortions of a non-neutral plasma column that propagate azimuthally via E × B drifts. While the infinite-length theory of diocotron modes is well-understood for arbitrary azimuthal mode number l, the finite-length mode frequency is less developed (with some exceptions), and is naturally of relevance to experiments. In this poster, we present an approach to address finite length effects, such as temperature dependence of the mode frequency. We use a bounce-averaged solution to the Vlasov Equation, in which the Vlasov Equation is solved using action-angle variables of the unperturbed Hamiltonian. We write the distribution function as a Fourier series in the bounce-angle variable ψ, keeping only the bounce-averaged term. We demonstrate a numerical solution to this equation for a realistic plasma with a finite Debye Length, compare to the existing l = 1 theory, and discuss possible extensions of the existing theory to l ≠ 1 . Supported by NSF/DOE Partnership Grants PHY1414570 and DESC0002451.

  20. Convergence analysis of the rebalance methods in multiplying finite slab having periodic boundary conditions

    International Nuclear Information System (INIS)

    Hong, Ser Gi; Lee, Young Ouk; Song, Jae Seung

    2009-01-01

    This paper analyzes the convergence of the rebalance iteration methods for the discrete ordinates transport equation in the multiplying finite slab problem. The finite slab is assumed to be homogeneous and it has the periodic boundary conditions. A general formulation is used to include three well-known rebalance methods of the linearized form in a unified way. The rebalance iteration methods considered in this paper are the CMR (Coarse-Mesh Rebalance), the CMFD (Coarse-Mesh Finite Difference), and p-CMFD (Partial Current-Based Coarse Mesh Finite Difference) methods which have been popularly used in the reactor physics. The convergence analysis is performed with the well-known Fourier analysis through a linearization. The analyses are applied for one-group problems. The theoretical analysis shows that there are one fundamental mode and N-1 Eigen-modes which determine the convergence if the finite slab is divided into N uniform meshes. The numerical tests show that the Fourier convergence analysis provides the reasonable estimate of the numerical spectral radii for the model problems and the spectral radius for the finite slab approaches the one for the infinite slab as the thickness of the slab increases. (author)

  1. Analysis of event-mode data with Interactive Data Language

    International Nuclear Information System (INIS)

    De Young, P.A.; Hilldore, B.B.; Kiessel, L.M.; Peaslee, G.F.

    2003-01-01

    We have developed an analysis package for event-mode data based on Interactive Data Language (IDL) from Research Systems Inc. This high-level language is high speed, array oriented, object oriented, and has extensive visual (multi-dimensional plotting) and mathematical functions. We have developed a general framework, written in IDL, for the analysis of a variety of experimental data that does not require significant customization for each analysis. Unlike many traditional analysis package, spectra and gates are applied after data are read and are easily changed as analysis proceeds without rereading the data. The events are not sequentially processed into predetermined arrays subject to predetermined gates

  2. Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion.

    Science.gov (United States)

    Siminos, Evangelos; Bénisti, Didier; Gremillet, Laurent

    2011-05-01

    We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed. © 2011 American Physical Society

  3. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    KAUST Repository

    Kabanov, Dmitry I.

    2017-12-08

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  4. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    KAUST Repository

    Kabanov, Dmitry; Kasimov, Aslan R.

    2018-01-01

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  5. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    KAUST Repository

    Kabanov, Dmitry

    2018-03-20

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  6. Anomalous heat transfer modes of nanofluids: a review based on statistical analysis

    Science.gov (United States)

    2011-01-01

    This paper contains the results of a concise statistical review analysis of a large amount of publications regarding the anomalous heat transfer modes of nanofluids. The application of nanofluids as coolants is a novel practise with no established physical foundations explaining the observed anomalous heat transfer. As a consequence, traditional methods of performing a literature review may not be adequate in presenting objectively the results representing the bulk of the available literature. The current literature review analysis aims to resolve the problems faced by researchers in the past by employing an unbiased statistical analysis to present and reveal the current trends and general belief of the scientific community regarding the anomalous heat transfer modes of nanofluids. The thermal performance analysis indicated that statistically there exists a variable enhancement for conduction, convection/mixed heat transfer, pool boiling heat transfer and critical heat flux modes. The most popular proposed mechanisms in the literature to explain heat transfer in nanofluids are revealed, as well as possible trends between nanofluid properties and thermal performance. The review also suggests future experimentation to provide more conclusive answers to the control mechanisms and influential parameters of heat transfer in nanofluids. PMID:21711932

  7. Anomalous heat transfer modes of nanofluids: a review based on statistical analysis

    Science.gov (United States)

    Sergis, Antonis; Hardalupas, Yannis

    2011-05-01

    This paper contains the results of a concise statistical review analysis of a large amount of publications regarding the anomalous heat transfer modes of nanofluids. The application of nanofluids as coolants is a novel practise with no established physical foundations explaining the observed anomalous heat transfer. As a consequence, traditional methods of performing a literature review may not be adequate in presenting objectively the results representing the bulk of the available literature. The current literature review analysis aims to resolve the problems faced by researchers in the past by employing an unbiased statistical analysis to present and reveal the current trends and general belief of the scientific community regarding the anomalous heat transfer modes of nanofluids. The thermal performance analysis indicated that statistically there exists a variable enhancement for conduction, convection/mixed heat transfer, pool boiling heat transfer and critical heat flux modes. The most popular proposed mechanisms in the literature to explain heat transfer in nanofluids are revealed, as well as possible trends between nanofluid properties and thermal performance. The review also suggests future experimentation to provide more conclusive answers to the control mechanisms and influential parameters of heat transfer in nanofluids.

  8. Anomalous heat transfer modes of nanofluids: a review based on statistical analysis

    Directory of Open Access Journals (Sweden)

    Sergis Antonis

    2011-01-01

    Full Text Available Abstract This paper contains the results of a concise statistical review analysis of a large amount of publications regarding the anomalous heat transfer modes of nanofluids. The application of nanofluids as coolants is a novel practise with no established physical foundations explaining the observed anomalous heat transfer. As a consequence, traditional methods of performing a literature review may not be adequate in presenting objectively the results representing the bulk of the available literature. The current literature review analysis aims to resolve the problems faced by researchers in the past by employing an unbiased statistical analysis to present and reveal the current trends and general belief of the scientific community regarding the anomalous heat transfer modes of nanofluids. The thermal performance analysis indicated that statistically there exists a variable enhancement for conduction, convection/mixed heat transfer, pool boiling heat transfer and critical heat flux modes. The most popular proposed mechanisms in the literature to explain heat transfer in nanofluids are revealed, as well as possible trends between nanofluid properties and thermal performance. The review also suggests future experimentation to provide more conclusive answers to the control mechanisms and influential parameters of heat transfer in nanofluids.

  9. Verification of Fourier phase and amplitude values from simulated heart motion using a hydrodynamic cardiac model

    Energy Technology Data Exchange (ETDEWEB)

    Yiannikas, J; Underwood, D A; Takatani, Setsuo; Nose, Yukihiko; MacIntyre, W J; Cook, S A; Go, R T; Golding, L; Loop, F D

    1986-02-01

    Using pusher-plate-type artificial hearts, changes in the degree of synchrony and stroke volume were compared to phase and amplitude calculations from the first Fourier component of individual-pixel time-activity curves generated from gated radionuclide images (RNA) of these hearts. In addition, the ability of Fourier analysis to quantify paradoxical volume shifts was tested using a ventricular aneurysm model by which the Fourier amplitude was correlated to known increments of paradoxical volume. Predetermined phase-angle differences (incremental increases in asynchrony) and the mean phase-angle difference calculated from RNAs showed an agreement of -7/sup 0/ +- 4.4/sup 0/ (mean +- SD). A strong correlation was noted between stroke volume and Fourier amplitude as well as between the paradoxical volume accepted by the 'aneurysm' and the Fourier amplitude. The degree of asynchrony and changes in stroke volume were accurately reflected by the Fourier phase and amplitude values, respectively. In the specific case of ventricular aneurysms, the data demonstrate that using this method, the paradoxically moving areas may be localized, and the expansile volume within these regions can be quantified. (orig.).

  10. Quantitative analysis of red wine tannins using Fourier-transform mid-infrared spectrometry.

    Science.gov (United States)

    Fernandez, Katherina; Agosin, Eduardo

    2007-09-05

    Tannin content and composition are critical quality components of red wines. No spectroscopic method assessing these phenols in wine has been described so far. We report here a new method using Fourier transform mid-infrared (FT-MIR) spectroscopy and chemometric techniques for the quantitative analysis of red wine tannins. Calibration models were developed using protein precipitation and phloroglucinolysis as analytical reference methods. After spectra preprocessing, six different predictive partial least-squares (PLS) models were evaluated, including the use of interval selection procedures such as iPLS and CSMWPLS. PLS regression with full-range (650-4000 cm(-1)), second derivative of the spectra and phloroglucinolysis as the reference method gave the most accurate determination for tannin concentration (RMSEC = 2.6%, RMSEP = 9.4%, r = 0.995). The prediction of the mean degree of polymerization (mDP) of the tannins also gave a reasonable prediction (RMSEC = 6.7%, RMSEP = 10.3%, r = 0.958). These results represent the first step in the development of a spectroscopic methodology for the quantification of several phenolic compounds that are critical for wine quality.

  11. Aliasing modes in the lattice Schwinger model

    International Nuclear Information System (INIS)

    Campos, Rafael G.; Tututi, Eduardo S.

    2007-01-01

    We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considered with boundaries new modes appear due to aliasing effects. In the continuum limit, however, this lattice yields also a Klein-Gordon equation with a reduced mass

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

    Science.gov (United States)

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

    2015-01-01

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

  13. Corrected Fourier series and its application to function approximation

    Directory of Open Access Journals (Sweden)

    Qing-Hua Zhang

    2005-01-01

    Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.

  14. Periodic transonic flow simulation using fourier-based algorithm

    International Nuclear Information System (INIS)

    Mohaghegh, Mohammad Reza; Malekjafarian, Majid

    2014-01-01

    The present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady Euler and Navier-Stokes equations, using time spectral method (TSM) and compares it with the traditional methods like BDF and explicit structured adaptive grid method. The TSM uses a Fourier representation in time and hence solves for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. The TSM has been validated with 2D external aerodynamics test cases. These test cases are NACA 64A010 (CT6) and NACA 0012 (CT1 and CT5) pitching airfoils. Because of turbulent nature of flow, Baldwin-Lomax turbulence model has been used in viscous flow analysis with large oscillation amplitude (CT5 type). The results presented by the TSM are compared with experimental data and the two other methods. By enforcing periodicity and using Fourier representation in time that has a spectral accuracy, tremendous reduction of computational cost has been obtained compared to the conventional time-accurate methods. Results verify the small number of time intervals per pitching cycle (just four time intervals) required to capture the flow physics with small oscillation amplitude (CT6) and large oscillation amplitude (CT5) as compared to the other two methods.

  15. Taylor–Fourier spectra to study fractional order systems

    International Nuclear Information System (INIS)

    Barbé, Kurt; Lauwers, Lieve; Fuentes, Lee Gonzales

    2016-01-01

    In measurement science mathematical models are often used as an indirect measurement of physical properties which are mapped to measurands through the mathematical model. Dynamical systems describing a physical process with a dominant diffusion or dispersion phenomenon requires a large dimensional model due to its long memory. Ignoring a dominant difussion or dispersion component acts as a confounder which may introduce a bias in the estimated quantities of interest. For linear systems it has been observed that fractional order models outperform classical rational forms in terms of the number of parameters for the same fitting error. However it is not straightforward to deal with a fractional order system or long memory effects without prior knowledge. Since the parametric modeling of a fractional system is very involved, we put forward the question whether fractional insight can be gathered in a non-parametric way. In this paper we show that classical Fourier basis leading to the frequency response function lacks fractional insight. To circumvent this problem, we introduce a fractional Taylor–Fourier basis to obtain non-parametric insight in the fractional system. This analysis proposes a novel type of spectrum to visualize the spectral content of a fractional system: Taylor–Fourier spectrum. This spectrum is fully measurement driven which can be used as a first to explore the fractional dynamics of a measured diffusion or dispersion system. (paper)

  16. Secure multi-party quantum summation based on quantum Fourier transform

    Science.gov (United States)

    Yang, Hui-Yi; Ye, Tian-Yu

    2018-06-01

    In this paper, we propose a novel secure multi-party quantum summation protocol based on quantum Fourier transform, where the traveling particles are transmitted in a tree-type mode. The party who prepares the initial quantum states is assumed to be semi-honest, which means that she may misbehave on her own but will not conspire with anyone. The proposed protocol can resist both the outside attacks and the participant attacks. Especially, one party cannot obtain other parties' private integer strings; and it is secure for the colluding attack performed by at most n - 2 parties, where n is the number of parties. In addition, the proposed protocol calculates the addition of modulo d and implements the calculation of addition in a secret-by-secret way rather than a bit-by-bit way.

  17. Analysis of F-Canyon Effluents During the Dissolution Cycle with a Fourier Transform Infrared Spectrometer/Multipath Cell

    International Nuclear Information System (INIS)

    Villa, E.

    1999-01-01

    Air samples from F-Canyon effluents were collected at the F-Canyon stack and transported to a laboratory at the Savannah River Technology Center (SRTC) for analysis using a Fourier transform infrared spectrometer in conjunction with a multipath cell. Air samples were collected during the decladding and acid cuts of the dissolution of the irradiated aluminum-cladded slugs. The FTIR analyses of the air samples show the presence of NO2, NO, HNO2, N2O, SF6, and 85Kr during the dissolution cycle. The concentration time profiles of these effluents corresponded with expected release rates from the F-Canyon operations

  18. Mode dynamics and confinement in the reversed field pinch

    International Nuclear Information System (INIS)

    Brunsell, P.R.; Bergsaker, H.; Brzozowski, J.H.; Cecconello, M.; Drake, J.R.; Malmberg, J.-A.; Scheffel, J.; Schnack, D.D.

    2001-01-01

    Tearing mode dynamics and toroidal plasma flow in the RFP has been experimentally studied in the Extrap T2 device. A toroidally localised, stationary magnetic field perturbation, the 'slinky mode' is formed in nearly all discharges. There is a tendency of increased phase alignment of different toroidal Fourier modes, resulting in higher localised mode amplitudes, with higher magnetic fluctuation level. The fluctuation level increases slightly with increasing plasma current and plasma density. The toroidal plasma flow velocity and the ion temperature has been measured with Doppler spectroscopy. Both the toroidal plasma velocity and the ion temperature clearly increase with I/N. Initial, preliminary experimental results obtained very recently after a complete change of the Extrap T2 front-end system (first wall, shell, TF coil), show that an operational window with mode rotation most likely exists in the rebuilt device, in contrast to the earlier case discussed above. A numerical code DEBSP has been developed to simulate the behaviour of RFP confinement in realistic geometry, including essential transport physics. Resulting scaling laws are presented and compared with results from Extrap T2 and other RFP experiments. (author)

  19. Everywhere divergent Fourier series with respect to the Walsh system and with respect to multiplicative systems

    International Nuclear Information System (INIS)

    Bochkarev, S V

    2004-01-01

    In this paper a new construction of everywhere divergent Fourier-Walsh series is presented. This construction enables one to halve the gap in the Lebesgue-Orlicz classes between the Schipp-Moon lower bound established by using Kolmogorov's construction and the Sjoelin upper bound obtained by using Carleson's method. Fourier series which are everywhere divergent after a rearrangement are constructed with respect to the Walsh system (and to more general systems of characters) with the best lower bound for the Weyl factor. Some results related to an upper bound of the majorant for partial sums of series with respect to rearranged multiplicative systems are established. The results thus obtained show certain merits of harmonic analysis on the dyadic group in clarifying and overcoming fundamental difficulties in the solution of the main problems of Fourier analysis

  20. Noise analysis of the measurement of group delay in Fourier white-light interferometric cross correlation

    International Nuclear Information System (INIS)

    Laude, Vincent

    2002-01-01

    The problem of noise analysis in measuring the group delay introduced by a dispersive optical element by use of white-light interferometric cross correlation is investigated. Two noise types, detection noise and position noise, are specifically analyzed. Detection noise is shown to be highly sensitive to the spectral content of the white-light source at the frequency considered and to the temporal acquisition window. Position noise, which arises from the finite accuracy of the measurement of the scanning mirror's position, can severely damage the estimation of the group delay. Such is shown to be the case for fast Fourier transform-based estimation algorithms. A new algorithm that is insensitive to scanning delay errors is proposed, and subfemtosecond accuracy is obtained without any postprocessing