Generalized Fourier analysis for phase retrieval of fringe pattern.
Zhong, Jingang; Weng, Jiawen
2010-12-20
A generalized Fourier analysis, by use of an adaptive multiscale windowed Fourier transform (AWFT), has been presented for the phase retrieval of fringe patterns. The Fourier transform method can be considered as a special case of AWFT method with a maximum window. The instantaneous frequency of the local signal is introduced to estimate whether the condition for separating the first spectrum component is satisfied for the phase retrieval of fringe patterns. The adaptive window width for this algorithm is determined by the length of the local stationary fringe pattern in order to balance the frequency and space resolution. The local stationary length of fringe pattern is defined as the signal satisfying the condition that whose first spectrum component is separated from all the other spectra within the local spatial area. In comparison with Fourier transform, fixed windowed Fourier transform and wavelet transform in numerical simulation and experiment, the adaptive multiscale windowed Fourier transform can present more accurate results of phase retrieval.
Stade, Eric
2005-01-01
A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of ap
Interpreting the Phase Spectrum in Fourier Analysis of Partial Ranking Data
Directory of Open Access Journals (Sweden)
Ramakrishna Kakarala
2012-01-01
Full Text Available Whenever ranking data are collected, such as in elections, surveys, and database searches, it is frequently the case that partial rankings are available instead of, or sometimes in addition to, full rankings. Statistical methods for partial rankings have been discussed in the literature. However, there has been relatively little published on their Fourier analysis, perhaps because the abstract nature of the transforms involved impede insight. This paper provides as its novel contributions an analysis of the Fourier transform for partial rankings, with particular attention to the first three ranks, while emphasizing on basic signal processing properties of transform magnitude and phase. It shows that the transform and its magnitude satisfy a projection invariance and analyzes the reconstruction of data from either magnitude or phase alone. The analysis is motivated by appealing to corresponding properties of the familiar DFT and by application to two real-world data sets.
Reducing of phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms
Gladic, J; Vucic, Z; Gladic, Jadranko; Lovric, Davorin; Vucic, Zlatko
2006-01-01
In order to measure the radial displacements of facets on surface of a growing spherical Cu_{2-\\delta}Se crystal with sub-nanometer resolution, we have investigated the reliability and accuracy of standard method of Fourier analysis of fringes obtained applying digital laser interferometry method. Guided by the realistic experimental parameters (density and orientation of fringes), starting from 2-dimensional model interferograms and using unconventional custom designed Gaussian filtering window and unwrapping procedure of the retrieved phase, we have demonstrated that for considerable portion of parameter space the non-negligible inherent phase retrieval error is present solely due to non-integer number of fringes within the digitally recorded image (using CCD camera). Our results indicate the range of experimentally adjustable parameters for which the generated error is acceptably small. We also introduce a modification of the (last part) of the usual phase retrieval algorithm which significantly reduces th...
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
Fourier optics analysis of phase-mask-based path-length-multiplexed optical coherence tomography.
Yin, Biwei; Dwelle, Jordan; Wang, Bingqing; Wang, Tianyi; Feldman, Marc D; Rylander, Henry G; Milner, Thomas E
2015-11-01
Optical coherence tomography (OCT) is an imaging technique that constructs a depth-resolved image by measuring the optical path-length difference between broadband light backscattered from a sample and a reference surface. For many OCT sample arm optical configurations, sample illumination and backscattered light detection share a common path. When a phase mask is placed in the sample path, features in the detected signal are observed, which suggests that an analysis of a generic common path OCT imaging system is warranted. In this study, we present a Fourier optics analysis using a Fresnel diffraction approximation of an OCT system with a path-length-multiplexing element (PME) inserted in the sample arm optics. The analysis may be generalized for most phase-mask-based OCT systems. A radial-angle-diverse PME is analyzed in detail, and the point spread function, coherent transfer function, sensitivity of backscattering angular diversity detection, and signal formation in terms of sample spatial frequency are simulated and discussed. The analysis reveals important imaging features and application limitations of OCT imaging systems with a phase mask in the sample path optics.
Fourier analysis an introduction
Stein, Elias M
2003-01-01
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
Montaux-Lambert, Antoine; Mercère, Pascal; Primot, Jérôme
2015-11-01
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.
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
Rudin, Walter
2011-01-01
In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.
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...
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...
Digital Fourier analysis advanced techniques
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to advanced digital Fourier analysis for advanced undergraduate and graduate students. Assuming knowledge of the Fast Fourier Transform, this book covers advanced topics including the Hilbert transform, cepstrum analysis, and the two-dimensional Fourier transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Advanced Techniques" includes practice problems and thorough Appendices. As a central feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. The applet source code in Visual Basic is provided online, enabling advanced students to tweak and change the programs for more sophisticated results. A complete, intuitive guide, "Digital Fourier Analysis - Advanced Techniques" is an essential reference for students in science and engineering.
Energy Technology Data Exchange (ETDEWEB)
Trout, T.K.; Bellama, J.M.; Brinckman, F.E.; Faltynek, R.A.
1989-03-01
Fourier transform infrared spectroscopy (FT-IR) forms the basis for determining the morphological composition of mixtures containing alpha, beta, and amorphous phases of silicon nitride. The analytical technique, involving multiple linear regression treatment of Kubelka-Munk absorbance values from diffuse reflectance measurements, yields specific percent composition data for the amorphous phase as well as the crystalline phases in ternary mixtures of 0--1% by weight Si/sub 3/N/sub 4/ in potassium bromide.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Fourier Analysis of Musical Intervals
LoPresto, Michael C.
2008-01-01
Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace. A recent article in "The Physics Teacher" aptly demonstrated the use of MacScope in just such a manner as a way to teach Fourier analysis. A logical continuation of this project is to…
Fourier analysis for rotating-element ellipsometers.
Cho, Yong Jai; Chegal, Won; Cho, Hyun Mo
2011-01-15
We introduce a Fourier analysis of the waveform of periodic light-irradiance variation to capture Fourier coefficients for multichannel rotating-element ellipsometers. In this analysis, the Fourier coefficients for a sample are obtained using a discrete Fourier transform on the exposures. The analysis gives a generic function that encompasses the discrete Fourier transform or the Hadamard transform, depending on the specific conditions. Unlike the Hadamard transform, a well-known data acquisition method that is used only for conventional multichannel rotating-element ellipsometers with line arrays with specific readout-mode timing, this Fourier analysis is applicable to various line arrays with either nonoverlap or overlap readout-mode timing. To assess the effects of the novel Fourier analysis, the Fourier coefficients for a sample were measured with a custom-built rotating-polarizer ellipsometer, using this Fourier analysis with various numbers of scans, integration times, and rotational speeds of the polarizer.
Directory of Open Access Journals (Sweden)
Eryi Hu
2015-01-01
Full Text Available The phase error caused by the speed mismatch issue is researched in the line-scan images capturing 3D profile measurement. The experimental system is constructed by a line-scan CCD camera, an object moving device, a digital fringe pattern projector, and a personal computer. In the experiment procedure, the detected object is moving relative to the image capturing system by using a motorized translation stage in a stable velocity. The digital fringe pattern is projected onto the detected object, and then the deformed patterns are captured and recorded in the computer. The object surface profile can be calculated by the Fourier transform profilometry. However, the moving speed mismatch error will still exist in most of the engineering application occasion even after an image system calibration. When the moving speed of the detected object is faster than the expected value, the captured image will be compressed in the moving direction of the detected object. In order to overcome this kind of measurement error, an image recovering algorithm is proposed to reconstruct the original compressed image. Thus, the phase values can be extracted much more accurately by the reconstructed images. And then, the phase error distribution caused by the speed mismatch is analyzed by the simulation and experimental methods.
Fourier Analysis of Blazar Variability
Finke, Justin D
2014-01-01
Blazars display strong variability on multiple timescales and in multiple radiation bands. Their variability is often characterized by power spectral densities (PSDs) and time lags plotted as functions of the Fourier frequency. We develop a new theoretical model based on the analysis of the electron transport (continuity) equation, carried out in the Fourier domain. The continuity equation includes electron cooling and escape, and a derivation of the emission properties includes light travel time effects associated with a radiating blob in a relativistic jet. The model successfully reproduces the general shapes of the observed PSDs and predicts specific PSD and time lag behaviors associated with variability in the synchrotron, synchrotron self-Compton (SSC), and external Compton (EC) emission components, from sub-mm to gamma-rays. We discuss applications to BL Lacertae objects and to flat-spectrum radio quasars (FSRQs), where there are hints that some of the predicted features have already been observed. We a...
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Ye, Qiang; Parthasarathy, Ranganathan; Abedin, Farhana; Laurence, Jennifer S; Misra, Anil; Spencer, Paulette
2013-12-01
Water is ubiquitous in the mouths of healthy individuals and is a major interfering factor in the development of a durable seal between the tooth and composite restoration. Water leads to the formation of a variety of defects in dentin adhesives; these defects undermine the tooth-composite bond. Our group recently analyzed phase partitioning of dentin adhesives using high-performance liquid chromatography (HPLC). The concentration measurements provided by HPLC offered a more thorough representation of current adhesive performance and elucidated directions to be taken for further improvement. The sample preparation and instrument analysis using HPLC are, however, time-consuming and labor-intensive. The objective of this work was to develop a methodology for rapid, reliable, and accurate quantitative analysis of near-equilibrium phase partitioning in adhesives exposed to conditions simulating the wet oral environment. Analysis by Fourier transform infrared (FT-IR) spectroscopy in combination with multivariate statistical methods, including partial least squares (PLS) regression and principal component regression (PCR), were used for multivariate calibration to quantify the compositions in separated phases. Excellent predictions were achieved when either the hydrophobic-rich phase or the hydrophilic-rich phase mixtures were analyzed. These results indicate that FT-IR spectroscopy has excellent potential as a rapid method of detection and quantification of dentin adhesives that experience phase separation under conditions that simulate the wet oral environment.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper demonstrates the application of step-scan phase modulation Fourier transform infrared photoacoustic spectroscopy(FTIR-PAS) in non-destructively depth profiling of styrene-butadiene-styrene block copolymer/polyethylene terephthalate(SBS/PET) layered materials.The surface thicknesses of three layered samples were determined to be 1.2,4.3 and 9.4μm by using phase difference analysis,overcoming the spatial detection limits of FTIR.Combined with generalized two-dimensional(G2D) FTIR correlation analysis,the spatial origins of peaks in the SBS/PET spectrum are identified with those having overlapping peaks between different layers are resolved.
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
THE FOURIER SERIES MODEL IN MAP ANALYSIS.
During the past several years the double Fourier Series has been applied to the analysis of contour-type maps as an alternative to the more commonly...used polynomial model. The double Fourier Series has high potential in the study of areal variations, inasmuch as a succession of trend maps based on...and it is shown that the double Fourier Series can be used to summarize the directional properties of areally-distributed data. An Appendix lists
Fourier Phase Domain Steganography: Phase Bin Encoding Via Interpolation
Rivas, Edward
2007-04-01
In recent years there has been an increased interest in audio steganography and watermarking. This is due primarily to two reasons. First, an acute need to improve our national security capabilities in light of terrorist and criminal activity has driven new ideas and experimentation. Secondly, the explosive proliferation of digital media has forced the music industry to rethink how they will protect their intellectual property. Various techniques have been implemented but the phase domain remains a fertile ground for improvement due to the relative robustness to many types of distortion and immunity to the Human Auditory System. A new method for embedding data in the phase domain of the Discrete Fourier Transform of an audio signal is proposed. Focus is given to robustness and low perceptibility, while maintaining a relatively high capacity rate of up to 172 bits/s.
Padilla, Moises; Garnica, Guillermo
2016-01-01
In this paper we apply the frequency transfer function (FTF) formalism to analyze the red, green and blue (RGB) phase-shifting fringe-projection profilometry technique. The phase-shifted fringe patterns in RGB fringe projection are typically corrupted by crosstalk because the sensitivity curves of most projection-recording systems overlap. Crosstalk distortion needs to be compensated in order to obtain high quality measurements. We study phase-demodulation methods for null/mild, moderate, and severe levels of RGB crosstalk. For null/mild crosstalk, we can estimate the searched phase-map using Bruning's 3-step phase-shifting algorithm (PSA). For moderate crosstalk, the RGB recorded data is usually preprocessed before feeding it into Bruning's PSA; alternatively, in this paper we propose a computationally more efficient approach, which combines crosstalk compensation and phase-demodulation into a single process. For severe RGB crosstalk, we expect non-sinusoidal fringes' profiles (distorting harmonics) and sign...
Fully phase encrypted memory using cascaded extended fractional Fourier transform
Nishchal, Naveen K.; Joseph, Joby; Singh, Kehar
2003-11-01
In this paper, we implement a fully phase encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The fully phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, conjugate of encrypted image. The decrypted phase image is converted into an amplitude image by using phase contrast technique. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the phase image, alleviating the need of alignment in the Fourier plane, thereby making the system rugged.
Quantum Fourier Transform and Phase Estimation in Qudit System
Institute of Scientific and Technical Information of China (English)
CAO Ye; PENG Shi-Guo; ZHENG Chao; LONG Gui-Lu
2011-01-01
The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc.In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case.They can be seen as subroutines in a main program run in a qudit quantum computer, and the quantum circuits are given.
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
Numerical analysis of the human nostril by the Fourier series.
Goto, M; Katsuki, T
1990-02-01
Fourier series has been applied in a numerical analysis of the human nostril morphology. The relationship between the nostril form and the Fourier coefficients was examined: the constant affected the size, the first term determined the roundness, and the second term determined the flatness of the morphology. The inclination of the apse line was calculated from the phase of the second term. Ninety-five standardized nostril photographs were analyzed by Fourier series: 48 of adult Japanese females and 47 of German females. The German nostril was larger in size, flatter in shape, and the apse line closer to the sagittal plane than the Japanese counterpart. As a clinical application of nostril digitization, pre- and post-operative cleft lip noses were analyzed. Fourier analysis has proved to be useful in a numerical evaluation of morphological differences of, and post-operative changes made to, the nostril.
Fourier analysis and synthesis tomography.
Energy Technology Data Exchange (ETDEWEB)
Wagner, Kelvin H. (University of Colorado at Boulder, Boulder, CO); Sinclair, Michael B.; Feldkuhn, Daniel (University of Colorado at Boulder, Boulder, CO)
2010-05-01
Most far-field optical imaging systems rely on a lens and spatially-resolved detection to probe distinct locations on the object. We describe and demonstrate a novel high-speed wide-field approach to imaging that instead measures the complex spatial Fourier transform of the object by detecting its spatially-integrated response to dynamic acousto-optically synthesized structured illumination. Tomographic filtered backprojection is applied to reconstruct the object in two or three dimensions. This technique decouples depth-of-field and working-distance from resolution, in contrast to conventional imaging, and can be used to image biological and synthetic structures in fluoresced or scattered light employing coherent or broadband illumination. We discuss the electronically programmable transfer function of the optical system and its implications for imaging dynamic processes. Finally, we present for the first time two-dimensional high-resolution image reconstructions demonstrating a three-orders-of-magnitude improvement in depth-of-field over conventional lens-based microscopy.
Phase retrieval for attacking fractional Fourier transform encryption.
Kong, Dezhao; Shen, Xueju; Cao, Liangcai; Jin, Guofan
2017-04-20
An advanced iterative phase retrieval algorithm is applied to perform a ciphertext-only attack on the fractional Fourier transform-based double random phase encryption system. With the given complex amplitude of ciphertext and definite support of the object image, the original object image can be recovered by estimating the energy of support area in the recovered image. The encryption system can be attacked by analyzing the sensibility of fractional Fourier transform order keys and evaluating the energy of the object image support area. The proposed algorithm can obtain encrypted fractional order and retrieve two random phase keys. Numerical results demonstrate the efficacy of the proposed attacking method.
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
Practical Fourier analysis for multigrid methods
Wienands, Roman
2004-01-01
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions.This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the detai...
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Fourier analysis in several complex variables
Ehrenpreis, Leon
2006-01-01
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations.The three-part treatment begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis. Topics include the geometric structure of ideals and modules, quantitative estimates, and examples in which the theory can be applied. The second part focuses on applications to partial differential equations and covers the solution of homogeneous and inh
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Functional Equations and Fourier Analysis
2010-01-01
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.
Harmonic oscillator: an analysis via Fourier series
de Castro, A S
2013-01-01
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.
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...
Temporal Fourier analysis applied to equilibrium radionuclide cineangiography
Energy Technology Data Exchange (ETDEWEB)
Cardot, J.C.; Verdenet, J.; Bidet, A.; Bidet, R.; Berthout, P.; Faivre, R.; Bassand, J.P.; Maurat, J.P.
1982-08-01
Regional and global left ventricular wall motion was assessed in 120 patients using radionulcide cincangiography (RCA) and contrast angiography. Functional imaging procedures based on a temporal Fourier analysis of dynamic image sequences were applied to the study of cardiac contractility. Two images were constructed by taking the phase and amplitude values of the first harmonic in the Fourier transform for each pixel. These two images aided in determining the perimeter of the left ventricle to calculate the global ejection fraction. Regional left ventricular wall motion was studied by analyzing the phase value and by examining the distribution histogram of these values. The accuracy of global ejection fraction calculation was improved by the Fourier technique. This technique increased the sensitivity of RCA for determining segmental abnormalities especially in the left anterior oblique view (LAO).
Grid-Independent Compressive Imaging and Fourier Phase Retrieval
Liao, Wenjing
2013-01-01
This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem. Many situations in optics, medical imaging and signal processing call…
Energy Technology Data Exchange (ETDEWEB)
Samojlov, A.I.; Ignatova, I.A.; Krivko, A.I.; Kozlova, V.S.; Dodonova, L.P.
1983-01-01
A method is outlined that enables with the use of Fourier-analysis of summary unresolved X-ray diffraction profile of the matrix ..gamma.. and intermetallic ..gamma..' phases of nickel heat resisting alloys of the Ni-Cr-Co-Al-Ti-Nb-W-Mo-V -Hf system, to calculate the location of reflexes of each phase, that is, to determine the periods of their crystal lattices in the alloy (in monolith) directly without electrolytic separation of ..gamma..'-phase. The limits of the method applicability were determined.
Nonlinear Fourier analysis with cnoidal waves
Energy Technology Data Exchange (ETDEWEB)
Osborne, A.R. [Dipt. di Fisica Generale dell`Universita, Torino (Italy)
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
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.
Fourier analysis: from cloaking to imaging
Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping
2016-04-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.
Discrete Fourier Transform Analysis in a Complex Vector Space
Dean, Bruce H.
2009-01-01
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
Institute of Scientific and Technical Information of China (English)
Chujun Zheng; Peng Han; Hongsen Chang
2006-01-01
@@ A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π,and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.
A New Condition for the Uniform Convergence in Fourier Analysis
Institute of Scientific and Technical Information of China (English)
周颂平; 乐瑞君
2004-01-01
@@ In Fourier analysis, since Fourier coefficients are computable and applicable, people have already established many nice results by assuming monotonicty of the coefficients. One famous classical result is done by Chaundy and Jolliffe[1] as follows:
Adaptive Fourier Decomposition Based Time-Frequency Analysis
Institute of Scientific and Technical Information of China (English)
Li-Ming Zhang
2014-01-01
The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition (AFD) offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects: instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.
Grid-Based Fourier Transform Phase Contrast Imaging
Tahir, Sajjad
Low contrast in x-ray attenuation imaging between different materials of low electron density is a limitation of traditional x-ray radiography. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One recently developed phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a technique recently demonstrated by Bennett et al. that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 microm spot Mo source, a CCD with 22 microm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the grid in the Fourier domain. A Matlab code was written to perform the image processing. For the first time, the effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the window function type used to separate the harmonics, and the window widths, were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and new methods investigated to form improved phase contrast images.
Mesh-based phase contrast Fourier transform imaging
Tahir, Sajjad; Bashir, Sajid; MacDonald, C. A.; Petruccelli, Jonathan C.
2017-04-01
Traditional x-ray radiography is limited by low attenuation contrast in materials of low electron density. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a recently developed technique that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 μm spot Mo source, a CCD with 22 μm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the mesh in the Fourier domain. The effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the width of the window function used to separate the harmonics were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and combined to form improved phase contrast images.
Oversampling analysis in fractional Fourier domain
Institute of Scientific and Technical Information of China (English)
ZHANG Feng; TAO Ran; WANG Yue
2009-01-01
Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal Is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.
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...
Experimental robustness of Fourier Ptychography phase retrieval algorithms
Yeh, Li-Hao; Zhong, Jingshan; Tian, Lei; Chen, Michael; Tang, Gongguo; Soltanolkotabi, Mahdi; Waller, Laura
2015-01-01
Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different illumination angles, a nonlinear inverse algorithm can be used to computationally reconstruct the high-resolution complex field. Here, we compare and classify multiple proposed inverse algorithms in terms of experimental robustness. We find that the main sources of error are noise, aberrations and mis-calibration (i.e. model mis-match). Using simulations and experiments, we demonstrate that the choice of cost function plays a critical role, with amplitude-based cost functions performing better than intensity-based ones. The reason for this is that Fourier ptychography datasets consist of images from both brightfield and darkfield illumination, representing a large range of measured intensities. Both noise (e.g. Poisson noise) and model mis-match errors are shown to scale with int...
Single beam Fourier transform digital holographic quantitative phase microscopy
Energy Technology Data Exchange (ETDEWEB)
Anand, A., E-mail: arun-nair-in@yahoo.com; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V. [Optics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390001 (India); Faridian, A.; Pedrini, G.; Osten, W. [Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart (Germany); Dubey, S. K. [Siemens Technology and Services Pvt. Ltd, Corporate Technology—Research and Technology Centre, Bangalore 560100 (India); Javidi, B. [Department of Electrical and Computer Engineering, U-4157, University of Connecticut, Storrs, Connecticut 06269-2157 (United States)
2014-03-10
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
Mathematical principles of signal processing Fourier and wavelet analysis
Brémaud, Pierre
2002-01-01
Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...
Fourier Analysis with Respect to Bilinear Maps
Institute of Scientific and Technical Information of China (English)
O.BLASCO; J.M.CALABUIG
2009-01-01
Several results about convolution and about Fourier coefficients for X-valued functions defined on the torus satisfying the condition sup‖y‖=1∫π-π‖B(f(eiθ),y)‖dθ/2π＜∞ for a bounded bilinear map B:X ×Y →Z are presented and some applications are given.
Double Fourier analysis for Emotion Identification in Voiced Speech
Sierra-Sosa, D.; Bastidas, M.; Ortiz P., D.; Quintero, O. L.
2016-04-01
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.
Fourier spectrum and phases for a signal in a finite interval
Belmont, Gérard; Dorville, Nicolas; Sahraoui, Fouad; Rezeau, Laurence
2015-04-01
When investigating the physics of turbulent media, as the solar wind or the magnetosheath plasmas, obtaining accurate Fourier spectra and phases is a crucial issue. For the different fields, the spectra allow in particular verifying whether one or several power laws can be determined in different frequency ranges. Accurate phases are necessary as well for all the "higher order statistics" studies in Fourier space, the coherence ones and for the polarization studies. Unfortunately, the Fourier analysis is not unique for a finite time interval of duration T: the frequencies lower than 1/T have a large influence on the result, which can hardly be controlled. This unknown "trend" has in particular the effect of introducing jumps at the edges of the interval, for the function under study itself, as well as for all its derivatives. The Fourier transform obtained directly by FFT (Fast Fourier Transform) is generally much influenced by these effects and cannot be used without care for wide band signals. The interference between the jumps and the signal itself provide in particular characteristic "hairs" on the spectrum, which are clearly visible on it with df≈1/T. These fluctuations are usually eliminated by smoothing the spectrum, or by averaging several successive spectra. Nevertheless, such treatments introduce uncertainties on the spectral laws (the phases being anyway completely lost). Windowing is also a method currently used to suppress or decrease the jumps, but it modifies the signal (the windowed trend has a spectrum, which is convolved with the searched one) and the phases are generally much altered. Here, we present a new data processing technique to circumvent these difficulties. It takes advantage of the fact that the signal is generally not unknown out of the interval under study: the complete signal is tapered to this interval of interest thanks to a new window function, sharp but not square. This window function is chosen such that the spectrum obtained
Institute of Scientific and Technical Information of China (English)
Shuang-qing WU; Yin ZHANG; San-yuan ZHANG; Xiu-zi YE
2009-01-01
An integrated and reliable phase unwrapping algorithm is proposed based on residues and blocking-lines detection,closed contour extraction and quality map ordering for the measurement of 3D shapes by Fourier-transform profilometry (FTP).The proposed algorithm first detects the residues on the wrapped phase image, applies wavelet analysis to generate the blockinglines that can just connect the residues of opposite polarity, then carries out the morphology operation to extract the closed contour of the shape, and finally uses the modulation intensity information and the Laplacian of Gaussian operation of the wrapped phase image as the quality map. The unwrapping process is completed from a region of high reliability to that of low reliability and the blocking-lines can prevent the phase error propagation effectively. Furthermore, by using the extracted closed contour to exclude the invalid areas from the phase unwrapping process, the algorithm becomes more efficient. The experiment shows the effectiveness of the new algorithm.
Kim, Tae Hyung; Setsompop, Kawin; Haldar, Justin P
2017-03-01
Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information. The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories. Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches. The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI. Magn Reson Med 77:1021-1035, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
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....
Osherovich, Eliyahu; Zibulevsky, Michael; Yavneh, Irad
2011-10-01
This work evaluates the importance of approximate Fourier phase information in the phase retrieval problem. The main discovery is that a rough phase estimate (up to π/2 rad) allows development of very efficient algorithms whose reconstruction time is an order of magnitude faster than that of the current method of choice--the hybrid input-output (HIO) algorithm. Moreover, a heuristic explanation is provided of why continuous optimization methods like gradient descent or Newton-type algorithms fail when applied to the phase retrieval problem and how the approximate phase information can remedy this situation. Numerical simulations are presented to demonstrate the validity of our analysis and success of our reconstruction method even in cases where the HIO algorithm fails, namely, complex-valued signals without tight support information.
Brief notes in advanced DSP Fourier analysis with Matlab
Grigoryan, Artyom M
2009-01-01
Based on the authors' research in Fourier analysis, Brief Notes in Advanced DSP: Fourier Analysis with MATLAB® addresses many concepts and applications of digital signal processing (DSP). The included MATLAB® codes illustrate how to apply the ideas in practice.The book begins with the basic concept of the discrete Fourier transformation and its properties. It then describes lifting schemes, integer transformations, the discrete cosine transform, and the paired transform method for calculating the discrete Hadamard transform. The text also examines the decomposition of the 1D signal by so-calle
Preliminary Analysis of ULPC Light Curves Using Fourier Decomposition Technique
Ngeow, Chow-Choong; Kanbur, Shashi; Barrett, Brittany; Lin, Bin
2013-01-01
Recent work on Ultra Long Period Cepheids (ULPCs) has suggested their usefulness as a distance indicator, but has not commented on their relationship as compared with other types of variable stars. In this work, we use Fourier analysis to quantify the structure of ULPC light curves and compare them to Classical Cepheids and Mira variables. Our preliminary results suggest that the low order Fourier parameters of ULPCs show a continuous trend defined by Classical Cepheids after the resonance around 10 days. However their Fourier parameters also overlapped with those from Miras, which make the classification of long period variable stars difficult based on the light curves information alone.
2009-01-01
Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently pro...
Comparative analysis of imaging configurations and objectives for Fourier microscopy
Kurvits, Jonathan A; Zia, Rashid
2015-01-01
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, which 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 ide...
Description of shape characteristics through Fourier and wavelet analysis
Directory of Open Access Journals (Sweden)
Yuan Zhanwei
2014-02-01
Full Text Available In this paper, Fourier and Wavelet transformation were adopted to analyze shape characteristics, with twelve simple shapes and two types of second phases from real microstructure morphology. According to the results of Fast Fourier transformation (FFT, the Fourier descriptors can be used to characterize the shape from the aspects of the first eight Normalization amplitudes, the number of the largest amplitudes to inverse reconstruction, similarity of shapes and profile roughness. And the Diepenbroek Roughness was rewritten by Normalization amplitudes of FFT results. Moreover, Sum Square of Relative Errors (SSRE of Wavelet transformation (WT signal sequence, including approximation signals and detail signals, was introduced to evaluate the similarity and relative orientation among shapes. As a complement to FFT results, the WT results can retain more detailed information of shapes including their orientations. Besides, the geometric signatures of the second phases were extracted by image processing and then were analyzed by means of FFT and WT.
Description of shape characteristics through Fourier and wavelet analysis
Institute of Scientific and Technical Information of China (English)
Yuan Zhanwei; Li Fuguo; Zhang Peng; Chen Bo
2014-01-01
In this paper, Fourier and Wavelet transformation were adopted to analyze shape char-acteristics, with twelve simple shapes and two types of second phases from real microstructure mor-phology. According to the results of Fast Fourier transformation (FFT), the Fourier descriptors can be used to characterize the shape from the aspects of the first eight Normalization amplitudes, the number of the largest amplitudes to inverse reconstruction, similarity of shapes and profile roughness. And the Diepenbroek Roughness was rewritten by Normalization amplitudes of FFT results. Moreover, Sum Square of Relative Errors (SSRE) of Wavelet transformation (WT) signal sequence, including approximation signals and detail signals, was introduced to evaluate the simi-larity and relative orientation among shapes. As a complement to FFT results, the WT results can retain more detailed information of shapes including their orientations. Besides, the geometric sig-natures of the second phases were extracted by image processing and then were analyzed by means of FFT and WT.
Fractional Fourier transform-based optical encryption with treble random phase-encoding
Xin, Yi; Tao, Ran; Wang, Yue
2008-03-01
We propose a new architecture of optical encryption technique using the fractional Fourier transform with three statistically independent random phase masks. Compared with the existing double-phase encoding method in the fractional Fourier-domain, the proposed extra phase mask in the last fractional Fourier domain makes the architecture symmetrical, and additive processing to the encrypted image can be turned into complex stationary white noise after decryption, and enlarge the key space without any degradation of its robustness to blind decryption. This property can be utilized to improve the quality of the recover image. Simulation results have verified the validity.
Rajput, Sudheesh K.; Nishchal, Naveen K.
2017-04-01
We propose a novel security scheme based on the double random phase fractional domain encoding (DRPE) and modified Gerchberg-Saxton (G-S) phase retrieval algorithm for securing two images simultaneously. Any one of the images to be encrypted is converted into a phase-only image using modified G-S algorithm and this function is used as a key for encrypting another image. The original images are retrieved employing the concept of known-plaintext attack and following the DRPE decryption steps with all correct keys. The proposed scheme is also used for encryption of two color images with the help of convolution theorem and phase-truncated fractional Fourier transform. With some modification, the scheme is extended for simultaneous encryption of gray-scale and color images. As a proof-of-concept, simulation results have been presented for securing two gray-scale images, two color images, and simultaneous gray-scale and color images.
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian;
2015-01-01
We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time.......We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time....
DEFF Research Database (Denmark)
Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads
2016-01-01
We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude......We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...
Institute of Scientific and Technical Information of China (English)
Ding Lu; Weimin Jin
2011-01-01
A novel fully phase color image encryption/decryption scheme based on joint fractional Fourier transform correlator (JFRTC) and phase retrieval algorithm (PRA) is proposed. The security of the system is enhanced by the fractional order as a new added key. This method takes full advantage of the parallel processing features of the optical system and could optically realize single-channel color image encryption.The system and operation procedures are simplified. The simulation results of a color image indicate that the new method provides efficient solutions with a strong sense of security.%@@ A novel fully phase color image encryption/decryption scheme based on joint fractional Fourier transform correlator (JFRTC) and phase retrieval algorithm (PRA) is proposed. The security of the system is enhanced by the fractional order as a new added key. This method takes full advantage of the parallel processing features of the optical system and could optically realize single-channel color image encryption. The system and operation procedures are simplified. The simulation results of a color image indicate that the new method provides efficient solutions with a strong sense of security.
Fourier analysis of time series an introduction
Bloomfield, Peter
2000-01-01
A new, revised edition of a yet unrivaled work on frequency domain analysis Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample
Comparative analysis of imaging configurations and objectives for Fourier microscopy.
Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid
2015-11-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.
Fully phase-encrypted memory using cascaded extended fractional Fourier transform
Nishchal, Naveen Kumar; Joseph, Joby; Singh, Kehar
2004-08-01
In this paper, we implement a fully phase-encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The full phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, the conjugate of the encrypted image. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the decrypted phase image, alleviating the need of alignment in the Fourier plane making the system rugged.
DEFF Research Database (Denmark)
Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads
2016-01-01
We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...
Luo, David; Kudenov, Michael W
2016-05-16
Systematic phase errors in Fourier transform spectroscopy can severely degrade the calculated spectra. Compensation of these errors is typically accomplished using post-processing techniques, such as Fourier deconvolution, linear unmixing, or iterative solvers. This results in increased computational complexity when reconstructing and calibrating many parallel interference patterns. In this paper, we describe a new method of calibrating a Fourier transform spectrometer based on the use of artificial neural networks (ANNs). In this way, it is demonstrated that a simpler and more straightforward reconstruction process can be achieved at the cost of additional calibration equipment. To this end, we provide a theoretical model for general systematic phase errors in a polarization birefringent interferometer. This is followed by a discussion of our experimental setup and a demonstration of our technique, as applied to data with and without phase error. The technique's utility is then supported by comparison to alternative reconstruction techniques using fast Fourier transforms (FFTs) and linear unmixing.
The Fourier decomposition method for nonlinear and non-stationary time series analysis.
Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik
2017-03-01
for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
Rotation-invariant texture analysis using Radon and Fourier transforms
Institute of Scientific and Technical Information of China (English)
Songshan Xiao; Yongxing Wu
2007-01-01
@@ Texture analysis is a basic issue in image processing and computer vision, and how to attain the rotationinvariant texture characterization is a key problem. This paper proposes a rotation-invariant texture analysis technique using Radon and Fourier transforms. This method uses Radon transform to convert rotation to translation, then utilizes Fourier transform and takes the moduli of the Fourier transform of these functions to make the translation invariant. A k-nearest-neighbor rule is employed to classify texture images. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. Experiment results show the feasibility of the proposed method and its robustness to additive white noise.
Optical Fourier techniques for medical image processing and phase contrast imaging.
Yelleswarapu, Chandra S; Kothapalli, Sri-Rajasekhar; Rao, D V G L N
2008-04-01
This paper briefly reviews the basics of optical Fourier techniques (OFT) and applications for medical image processing as well as phase contrast imaging of live biological specimens. Enhancement of microcalcifications in a mammogram for early diagnosis of breast cancer is the main focus. Various spatial filtering techniques such as conventional 4f filtering using a spatial mask, photoinduced polarization rotation in photosensitive materials, Fourier holography, and nonlinear transmission characteristics of optical materials are discussed for processing mammograms. We also reviewed how the intensity dependent refractive index can be exploited as a phase filter for phase contrast imaging with a coherent source. This novel approach represents a significant advance in phase contrast microscopy.
The Pegg-Barnett phase operator and the discrete Fourier transform
Perez-Leija, Armando; Andrade-Morales, Luis A.; Soto-Eguibar, Francisco; Szameit, Alexander; Moya-Cessa, Héctor M.
2016-04-01
In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg-Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London-Susskind-Glogower phase operator, whose natural logarithm gives rise to the Pegg-Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties.
Thibos, L N; Wheeler, W; Horner, D
1997-06-01
The description of sphero-cylinder lenses is approached from the viewpoint of Fourier analysis of the power profile. It is shown that the familiar sine-squared law leads naturally to a Fourier series representation with exactly three Fourier coefficients, representing the natural parameters of a thin lens. The constant term corresponds to the mean spherical equivalent (MSE) power, whereas the amplitude and phase of the harmonic correspond to the power and axis of a Jackson cross-cylinder (JCC) lens, respectively. Expressing the Fourier series in rectangular form leads to the representation of an arbitrary sphero-cylinder lens as the sum of a spherical lens and two cross-cylinders, one at axis 0 degree and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vector representation of the power profile. Advantages of this power vector representation of a sphero-cylinder lens for numerical and graphical analysis of optometric data are described for problems involving lens combinations, comparison of different lenses, and the statistical distribution of refractive errors.
360-degrees profilometry using strip-light projection coupled to Fourier phase-demodulation.
Servin, Manuel; Padilla, Moises; Garnica, Guillermo
2016-01-11
360 degrees (360°) digitalization of three dimensional (3D) solids using a projected light-strip is a well-established technique in academic and commercial profilometers. These profilometers project a light-strip over the digitizing solid while the solid is rotated a full revolution or 360-degrees. Then, a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based light-strip centroid estimation, we propose to use Fourier phase-demodulation for 360° solid digitalization. The advantage of Fourier demodulation over strip-centroid estimation is that the accuracy of phase-demodulation linearly-increases with the fringe density, while in strip-light the centroid-estimation errors are independent. Here we proposed first to construct a carrier-frequency fringe-pattern by closely adding the individual light-strip images recorded while the solid is being rotated. Next, this high-density fringe-pattern is phase-demodulated using the standard Fourier technique. To test the feasibility of this Fourier demodulation approach, we have digitized two solids with increasing topographic complexity: a Rubik's cube and a plastic model of a human-skull. According to our results, phase demodulation based on the Fourier technique is less noisy than triangulation based on centroid light-strip estimation. Moreover, Fourier demodulation also provides the amplitude of the analytic signal which is a valuable information for the visualization of surface details.
Fourier analysis on local fields (MN-15)
Taibleson, M H
2015-01-01
This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (rea
Fourier analysis of the aerodynamic behavior of cup anemometers
Pindado, Santiago; Pérez, Imanol; Aguado, Maite
2013-06-01
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.
Teaching Fourier Analysis and Wave Physics with the Bass Guitar
Courtney, M; Courtney, Michael; Althausen, Norm
2006-01-01
This article describes a laboratory or demonstration technique employing the bass guitar and a Vernier LabPro (or a PC soundcard) for teaching wave physics and introducing Fourier analysis. The Fourier transform of an open string provides a demonstration of oscillatory modes out to the 20th harmonic consistent with expectations containing a fundamental frequency and harmonics. The playing of "harmonics" (suppressing resonant modes by lightly touching the string to enforce nodes at desired locations) demonstrates oscillations made up (mostly) of individual modes. Students see that the complete set of Fourier components (fundamental and harmonics) present on the open string can be explicitly connected with individual resonant frequencies as described in typical textbook discussions of natural frequencies of waves on a string. The use of a bass guitar rather than the six string electric guitar allows higher harmonics to be individually excited, and it is also easier for students to play the harmonics themselves.
Multiple-image encryption based on phase mask multiplexing in fractional Fourier transform domain.
Liansheng, Sui; Meiting, Xin; Ailing, Tian
2013-06-01
A multiple-image encryption scheme is proposed based on the phase retrieval process and phase mask multiplexing in the fractional Fourier transform domain. First, each original gray-scale image is encoded into a phase only function by using the proposed phase retrieval process. Second, all the obtained phase functions are modulated into an interim, which is encrypted into the final ciphertext by using the fractional Fourier transform. From a plaintext image, a group of phase masks is generated in the encryption process. The corresponding decrypted image can be recovered from the ciphertext only with the correct phase mask group in the decryption process. Simulation results show that the proposed phase retrieval process has high convergence speed, and the encryption algorithm can avoid cross-talk; in addition, its encrypted capacity is considerably enhanced.
Huang, Yulin; Wu, Junjie; Li, Zhongyu; Yang, Haiguang; Yang, Jianyu
2016-01-01
Raw data generation for synthetic aperture radar (SAR) is very powerful for designing systems and testing imaging algorithms. In this paper, a raw data generation method based on Fourier analysis for one-stationary bistatic SAR is presented. In this mode, two-dimensional (2-D) spatial variation is the major problem faced by the fast Fourier transform-based raw data generation. To deal with this problem, a 2-D linearization followed by a 2-D frequency transformation is employed in this method. This frequency transformation can reflect the 2-D spatial variation. Residual phase compensation is also discussed. Numerical simulation verifies the method.
Fourier analysis for discontinuous Galerkin and related methods
Institute of Scientific and Technical Information of China (English)
ZHANG MengPing; SHU Chi-Wang
2009-01-01
In this paper we review a series of recent work on using a Fourier analysis technique to study the sta-bility and error estimates for the discontinuous Galerkin method and other related schemes. The ad-vantage of this approach is that it can reveal instability of certain "bad"' schemes; it can verify stability for certain good schemes which are not easily amendable to standard finite element stability analysis techniques; it can provide quantitative error comparisons among different schemes; and it can be used to study superconvergence and time evolution of errors for the discontinuous Galerkin method. We will briefly describe this Fourier analysis technique, summarize its usage in stability and error estimates for various schemes, and indicate the advantages and disadvantages of this technique in comparison with other finite element techniques.
Institute of Scientific and Technical Information of China (English)
潘卫清; 朱勇建; 王建中
2009-01-01
在维格纳相空间中,通过将一阶光学系统的传输矩阵分解为坐标旋转、比例缩放和啁啾矩阵的组合,得到了一阶光学系统在空域的分数傅里叶表示.结果表明:任意一阶光学系统均可表示为经过比例缩放和二次相位调制的分数傅里叶变换.通过将输入输出光场在相空间中作π/2角旋转,得到了一阶光学系统在频域的传输矩阵和衍射积分公式,进而得到了一阶光学系统在频域的分数傅里叶表示.比较空域和频域一阶光学系统的相空间变换矩阵,说明2个系统本质上属同一变换在不同基坐标下的表示,并推导出了光学系统在空域和频域具有相同分数傅里叶变换的条件.%The fractional Fourier express of the first-order optical system was derived by decomposing the transfer matrices of firstorder optical system into coordinate rotation matrix, scale matrix and chirp matrix in Wigner phase space. The results show that an arbitrary first-order optical system can be expressed as the scaled and chirp modulation fractional Fourier transform. The transfer matrix and diffractive integral formula in frequency domain were acquired by rotating the input and output optical field π/2 in the phase space. Accordingly the fractional Fourier transforms of a first-order optical system in frequency domain were also obtained. By comparing the transfer matrices of two first-order optical systems in space and frequency domains respectively, it is found that the two first-order optical systems in different domain can be expressed as two different expressions of one and the same transfer based on different coordinates. At last the condition is derived for an optical system to implement the fractional Fourier transform in space and frequency domains with the same order.
Fractional Fourier domain analysis of decimation and interpolation
Institute of Scientific and Technical Information of China (English)
MENG XiangYi; TAO Ran; WANG Yue
2007-01-01
The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal.Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security.Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital frequency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sampling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.
On One Application of Fourier Analysis in Plastic Surgery
Rakhimov, Abdumalik; Zainuddin, Hishamuddin
In present paper, we discuss the spectral methods of measurement of the degree of speech and/or quality of sound by comparing the coefficient of performance indicators depending on energy distributions, ratio of energy of the fundamental tone and energy of overtones. Such a method is very efficient for string oscillation with different initial conditions and it is useful for justification of applications of Fourier analysis in plastic surgery in treatment of some medical diseases.
Fourier analysis of the aerodynamic behavior of cup anemometers
Pindado Carrion, Santiago; Pérez Sarasola, Imanol; Aguado Roca, 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 r...
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.)
Fourier Transform Infrared Spectroscopic Analysis of Protein Secondary Structures
Institute of Scientific and Technical Information of China (English)
Jilie KONG; Shaoning YU
2007-01-01
Infrared spectroscopy is one of the oldest and well established experimental techniques for the analysis of secondary structure of polypeptides and proteins. It is convenient, non-destructive, requires less sample preparation, and can be used under a wide variety of conditions. This review introduces the recent developments in Fourier transform infrared (FTIR) spectroscopy technique and its applications to protein structural studies. The experimental skills, data analysis, and correlations between the FTIR spectroscopic bands and protein secondary structure components are discussed. The applications of FTIR to the secondary structure analysis, conformational changes, structural dynamics and stability studies of proteins are also discussed.
Lo, Men-Tzung; Novak, Vera; Peng, C-K; Liu, Yanhui; Hu, Kun
2009-06-01
Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently proposed multimodal pressure flow (MMPF) analysis that is based on Hilbert-Huang transform (HHT)-an advanced nonlinear decomposition algorithm. We considered three types of nonstationarities that are often presented in physical and physiological signals: (i) missing segments of data, (ii) linear and step-function trends embedded in data, and (iii) multiple chaotic oscillatory components at different frequencies in data. By generating two coupled oscillatory signals with an assigned phase shift, we quantify the change in the estimated phase shift after imposing artificial nonstationarities into the oscillatory signals. We found that all three types of nonstationarities affect the performances of the Fourier-based and the HHT-based phase analyses, introducing bias and random errors in the estimation of the phase shift between two oscillatory signals. We also provided examples of nonstationarities in real physiological data (cerebral blood flow and blood pressure) and showed how nonstationarities can complicate result interpretation. Furthermore, we propose certain strategies that can be implemented in the TFA and the MMPF methods to reduce the effects of nonstationarities, thus improving the performances of the two methods.
Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography.
Wang, Yimin; Huang, David; Su, Ya; Yao, X Steve
2016-11-14
For phase-related imaging modalities using interferometric techniques, it is important to develop effective method to recover phase information that is mathematically wrapped. In this paper, we propose and demonstrate a two-dimensional (2D) method to achieve effective phase unwrapping in Doppler Fourier-domain (FD) optical coherence tomography (OCT), and recover the discontinuous phase distribution in retinal blood flow successfully for the first time in Doppler OCT studies. The proposed method is based on phase gradient approach in the axial dimension, with phase denoising performed through 2D window moving average in the sampled phase image using complex Doppler OCT data. The 2D unwrapping is carried out to correct phase discontinuities in the wrapped Doppler phase map, and the abrupt phase changes can be identified and corrected accurately. The proposed algorithm is computationally efficient and easy to be implemented.
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.
Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.
Caple, Jodi; Byrd, John; Stephan, Carl N
2017-02-17
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.
Vortex metrology using Fourier analysis techniques: vortex networks correlation fringes.
Angel-Toro, Luciano; Sierra-Sosa, Daniel; Tebaldi, Myrian; Bolognini, Néstor
2012-10-20
In this work, we introduce an alternative method of analysis in vortex metrology based on the application of the Fourier optics techniques. The first part of the procedure is conducted as is usual in vortex metrology for uniform in-plane displacement determination. On the basis of two recorded intensity speckled distributions, corresponding to two states of a diffuser coherently illuminated, we numerically generate an analytical signal from each recorded intensity pattern by using a version of the Riesz integral transform. Then, from each analytical signal, a two-dimensional pseudophase map is generated in which the vortices are located and characterized in terms of their topological charges and their core's structural properties. The second part of the procedure allows obtaining Young's interference fringes when Fourier transforming the light passing through a diffracting mask with multiple apertures at the locations of the homologous vortices. In fact, we use the Fourier transform as a mathematical operation to compute the far-field diffraction intensity pattern corresponding to the multiaperture set. Each aperture from the set is associated with a rectangular hole that coincides both in shape and size with a pixel from recorded images. We show that the fringe analysis can be conducted as in speckle photography in an extended range of displacement measurements. Effects related with speckled decorrelation are also considered. Our experimental results agree with those of speckle photography in the range in which both techniques are applicable.
Servin, Manuel; Garnica, Guillermo
2015-01-01
360-degrees digitalization of three-dimensional (3D) solids using a projected light-strip is a well established technique. These profilometers project a light-strip over the solid under analysis while the solid is rotated a full revolution. Then a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based strip centroid estimation, we propose to use Fourier phase-demodulation. This 360-degrees profilometer first constructs a carrier-frequency fringe-pattern by closely adding individual light-strip images. Secondly this high-density fringe-pattern is phase-demodulated using the standard Fourier technique.
Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy
Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks
2016-06-01
Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described.
Error Analysis for Fourier Methods for Option Pricing
Häppölä, Juho
2016-01-06
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.
Institute of Scientific and Technical Information of China (English)
吴春旺; 韩阳; 邓志姣; 李虹轶; 陈平形; 李承祖
2011-01-01
We propose a theoretical scheme for realizing the general conditional phase shift gate of charge qubits situated in a high-Q superconducting transmission line resonator. The phase shifting angle can be tuned from 0 to 27r by simply adjusting the qubit-resonator detuning and the interaction time. Based on this gate proposal, we give a detailed procedure to implement the three-qubit quantum Fourier transform with circuit quantum eleetrodynamics （QED）. A careful analysis of the decoherence sources shows that the algorithm can be achieved with a high fidelity using current circuit QED techniques.
Li, Beiwen; Liu, Ziping; Zhang, Song
2016-10-03
We propose a hybrid computational framework to reduce motion-induced measurement error by combining the Fourier transform profilometry (FTP) and phase-shifting profilometry (PSP). The proposed method is composed of three major steps: Step 1 is to extract continuous relative phase maps for each isolated object with single-shot FTP method and spatial phase unwrapping; Step 2 is to obtain an absolute phase map of the entire scene using PSP method, albeit motion-induced errors exist on the extracted absolute phase map; and Step 3 is to shift the continuous relative phase maps from Step 1 to generate final absolute phase maps for each isolated object by referring to the absolute phase map with error from Step 2. Experiments demonstrate the success of the proposed computational framework for measuring multiple isolated rapidly moving objects.
[A phase error correction method for the new Fourier transforms spectrometer].
Wang, Ning; Gong, Tian-Cheng; Chen, Jian-Jun; Li, Yang; Yang, Yi-Ning; Zhu, Yong; Zhang, Jie; Chen, Wei-Min
2014-11-01
To decrease the distortion of the recovered spectrum, improve the quantity of the recovered spectrum and decrease the influence of the phase error of the new spectrum detection system based on MEMS (micro-electro-mechanical systems) micro-mirrors, a new phase error correction method for this system is proposed in the present paper. The source of phase error of the spectrum detection system based on MEMS micro-mirrors is analyzed firstly. The analyzed result indicated that the phase error of the new spectral Fourier transform detection system is the zero drift of the optical path difference, and the phase error can be corrected by Zero-crossing sampling which is realized by improving the structure of the interferometer system and Mertz product The spectrum detection system is set up and the phase error correction method is verified by this system. The experiment result is show that the quantity of the recovered spectrum of the spectrum detection is improved obviously by using the improved interferometer system and Mertz product, and the recovered spectrum has no negative peaks and the side lobes is suppressed markedly. This correction method can reduce the influence caused by phase error to the system performance well and improve the spectral detection performance effectively. In this paper, the origin of the system phase error based on the new MEMS micromirror Fourier transform spectroscopy detection system is analyzed, and the phase error correction method is proposed. This method can improve the performance of the spectrum detection system.
Discrete Fourier Analysis and Chebyshev Polynomials with G2 Group
Directory of Open Access Journals (Sweden)
Huiyuan Li
2012-10-01
Full Text Available The discrete Fourier analysis on the 30°-60°-90° triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G2, which leads to the definition of four families generalized Chebyshev polynomials. The study of these polynomials leads to a Sturm-Liouville eigenvalue problem that contains two parameters, whose solutions are analogues of the Jacobi polynomials. Under a concept of m-degree and by introducing a new ordering among monomials, these polynomials are shown to share properties of the ordinary orthogonal polynomials. In particular, their common zeros generate cubature rules of Gauss type.
Particle field holography data reduction by Fourier transform analysis
Hess, Cecil F.; Trolinger, James D.
1987-01-01
The size distribution of a particle field hologram is obtained with a Fourier transformation of the Fraunhofer diffraction pattern of the reconstructed hologram. Off-axis absorption holograms of particle fields with known characteristics were obtained and analyzed with a commercially available instrument. The mean particle size of the reconstructed hologram was measured with an error of + or - 5 percent, while the distribution broadening was estimated within + or - 15 percent. Small sections of a pulsed laser hologram of a synthetic fuel spray were analyzed with this method thus yielding a spatially resolved size distribution. The method yields fast and accurate automated analysis of particle field holograms.
Some Topics in Fourier Analysis and Approximation Theory
Trigub, R M
1996-01-01
This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are given. These results are published in serious scientific journals and reported at various conferences, including international ones at Moscow,ICM66; Kaluga,1975; Kiev,1983; Haifa,1994; Zürich,ICM94; Moscow,1995. The area of investigation is the Fourier analysis and the theory of approximation of functions. Used are methods of classical analysis including special functions, Banach spaces, etc., of harmonic analysis in finitedimensional Euclidean space, of Diophantine analysis, of random choice, etc. The results due to the author and active participants of the seminar, namely E. S. Belinskii, O. I. Kuznetsova, E. R. Liflyand, Yu. L. Nosenko, V. A. Glukhov, V. P. Zastavny, Val. V. Volchkov, V. O. Leontyev, and others, are given. Besides the participants of the seminar and other ma...
Motion artifact reduction using hybrid Fourier transform with phase-shifting methods
Li, Beiwen; Liu, Ziping; Zhang, Song
2016-08-01
We propose to combine the Fourier transform profilometry (FTP) and phase-shifting profilometry (PSP) to reduce motion induced artifacts. The proposed method can be divided into three steps: Step 1 is to obtain a temporarily unwrapped absolute phase map of the entire scene using the FTP method, albeit the absolute phase map has motion introduced artifacts; Step 2 is to generate continuous relative phase maps without motion artifacts for each isolated object by spatially unwrapping each isolated phase map retrieved from the FTP method; and Step 3 is to determine the absolute phase map for each isolate region by referring to the temporally unwrapped phase using PSP method. Experimental results demonstrated success of the proposed method for measuring rapidly moving multiple isolated objects.
Fourier and fractal analysis of cytoskeletal morphology altered by xenobiotics
Crosta, Giovanni F.; Urani, Chiara; Fumarola, Laura
2003-06-01
The cytoskeletal microtubules (MTs) of rat hepatocytes treated by Benomyl (a fungicide) were imaged by means of immunofluorescent staining and optical microscopy. Images of untreated, or control (C), and of treated (T) cells were processed both by fractal and Fourier analysis. The C-MTs had contour fractal dimensions higher (>= 1.4) than those of T-MTs (enhancement," which corresponds to the application of a (pseudo)differential operator to the image. Enhanced spectra were interpolated by a polynomial, q, of degree 39, from which morphological descriptors were extracted. Descriptors from Fourier analysis made image classification possible. Principal components analysis was applied to the descriptors. In the plane of the first two components, {z1,z2}, the minimum spanning tree was drawn. Images of T-MTs formed a single cluster, whereas images of C-MTs formed two clusters, C1 and C2. The component z1 correlated positively with the local maxima and minima of q, which reflected differences between T and C in power spectral density in the 1 to 2000 cycles/mm spatial frequency band. The difference between C1 and C2 was ascribed to anisotropy of the MT bundles. The implemented image classifier is capable of telling differences in cytoskeletal organization. As a consequence the method can become a tool for testing cytotoxicity and for extracting quantitative information about intracellular alterations of various origin.
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.
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.
Fractional Fourier domain analysis of cyclic multirate signal processing
Institute of Scientific and Technical Information of China (English)
2008-01-01
The cyclic filter banks, which are used widely in the image subband coding, refer to signal processing on the finite field. This study investigates the fractional Fourier domain (FRFD) analysis of cyclic multirate systems based on the fractional circular convolution and chirp period. The proposed theorems include the fractional Fourier domain analysis of cyclic decimation and cyclic interpolation, the noble identities of cyclic decimation and cyclic interpolation in the FRFD, the polyphase represen-tation of cyclic signal in the FRFD, and the perfect reconstruction condition for the cyclic filter banks in the FRFD. Furthermore, this paper proposes the design methods for perfect reconstruction cyclic filter bank and cyclic filter bank with chirp modulation in the FRFD. The proposed theorems extend the multirate signal processing in the FRFD, which also advance the applications of the theorems of filter bank in the FRFD on the finite signal field, such as digital image processing. At last, the proposed design methods for the cyclic filter banks in the FRFD are validated by simulations.
Walde, Marie; Jost, Aurélie; Wicker, Kai; Heintzmann, Rainer
2017-01-01
Bessel illumination is an established method in optical imaging and manipulation to achieve an extended depth of field without compromising the lateral resolution. When broadband or multicolour imaging is required, wavelength-dependent changes in the radial profile of the Bessel illumination can complicate further image processing and analysis. We present a solution for engineering a multicolour Bessel beam that is easy to implement and promises to be particularly useful for broadband imaging applications. A phase-only spatial light modulator (SLM) in the image plane and an iterative Fourier Transformation algorithm (IFTA) are used to create an annular light distribution in the back focal plane of a lens. The 2D Fourier transformation of such a light ring yields a Bessel beam with a constant radial profile for different wavelength.
Phase Retrieval From Multiple-Window Short-Time Fourier Measurements
Li, Lan; Cheng, Cheng; Han, Deguang; Sun, Qiyu; Shi, Guangming
2017-04-01
In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal from magnitude measurements of its multiple-window short-time Fourier transform. Also we propose an algebraic reconstruction algorithm, and provide an error estimate to our algorithm when magnitude measurements are corrupted by deterministic/random noises.
Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.
2017-01-01
We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.
Underwood, Kenneth J; Jones, Andrew M; Gopinath, Juliet T
2015-06-20
We present a new application of the stochastic parallel gradient descent (SPGD) algorithm to fast active phase control in a Fourier synthesis system. Pulses (4.9 ns) with an 80 MHz repetition rate are generated by feedback from a single phase-sensitive metric. Phase control is applied via fast current modulation of a tapered amplifier using an SPGD algorithm realized on a field-programmable gate array (FPGA). The waveforms are maintained by constant active feedback from the FPGA. We also discuss the extension of this technique to many more semiconductor laser emitters in a diode laser array.
Natural majorization of the Quantum Fourier Transformation in phase-estimation algorithms
Orus, R; Martín-Delgado, M A; Orus, Roman; Latorre, Jose I.; Martin-Delgado, Miguel A.
2002-01-01
We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms considered in the canonical decomposition. Our result relies on the fact that states which are mixed by Hadamard operators at any stage of the computation only differ by a phase. This property is a consequence of the structure of the initial state and of the QFT, based on controlled-phase operators and a single action of a Hadamard gate per qubit. As a consequence, Hadamard gates order the probability distribution associated to the quantum state, whereas controlled-phase operators carry all the entanglement but are immaterial to majorization. We also prove that majorization in phase-estimation algorithms follows in a most natural way from unitary evolution, unlike its counterpart in Grover's algorithm.
Calculation of Fresnel diffraction from 1D phase step by discrete Fourier transform
Aalipour, Rasoul
2017-01-01
When a part of an optical wave-front experiences a sharp change in its phase, Fresnel diffraction becomes appreciable. Sharp change in phase occurs as a wave-front strikes with a phase step. The intensity distributions of diffraction patterns of the phase step is formulated by applying Fresnel-Kirchhoff integral. For while the incident light on the step is coherent, the Fresnel-Kirchhoff integral can be solved by using familiar Fresnel integrals. But, when the incident light is partially coherent, one can not express the diffraction integral as the Fresnel integrals and the problem is summarized in solving some unusual integrals. In this report, we propose Fourier transform method for solving the Fresnel-Kirchhoff integral. In this regard we use discrete Fourier transform method and calculate Fresnel diffraction from the 1D phase step by FFT-based algorithms. This method does not have any restriction on the coherence and profile shape of the incident light. We show that the method have appropriate solutions for coherent and partially coherent lights. For the case of the coherent light illumination of the step, the obtained results are in good agreement with the calculated results by using the Fresnel integrals in reported literatures.
On The Fourier And Wavelet Analysis Of Coronal Time Series
Auchère, F; 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 provies 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 & 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 & 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 c...
Measurement of absolute optical thickness of mask glass by wavelength-tuning Fourier analysis.
Kim, Yangjin; Hbino, Kenichi; Sugita, Naohiko; Mitsuishi, Mamoru
2015-07-01
Optical thickness is a fundamental characteristic of an optical component. A measurement method combining discrete Fourier-transform (DFT) analysis and a phase-shifting technique gives an appropriate value for the absolute optical thickness of a transparent plate. However, there is a systematic error caused by the nonlinearity of the phase-shifting technique. In this research the absolute optical-thickness distribution of mask blank glass was measured using DFT and wavelength-tuning Fizeau interferometry without using sensitive phase-shifting techniques. The error occurring during the DFT analysis was compensated for by using the unwrapping correlation. The experimental results indicated that the absolute optical thickness of mask glass was measured with an accuracy of 5 nm.
Fourier transform based iterative method for x-ray differential phase-contrast computed tomography
Cong, Wenxiang; Wang, Ge
2011-01-01
Biological soft tissues encountered in clinical and pre-clinical imaging mainly consist of light element atoms, and their composition is nearly uniform with little density variation. Thus, x-ray attenuation imaging suffers from low image contrast resolution. By contrast, x-ray phase shift of soft tissues is about a thousand times greater than x-ray absorption over the diagnostic energy range, thereby a significantly higher sensitivity can be achieved in terms of phase shift. In this paper, we propose a novel Fourier transform based iterative method to perform x-ray tomographic imaging of the refractive index directly from differential phase shift data. This approach offers distinct advantages in cases of incomplete and noisy data than analytic reconstruction, and especially suitable for phase-contrast interior tomography by incorporating prior knowledge in a region of interest (ROI). Biological experiments demonstrate the merits of the proposed approach.
Partial differential equation transform - Variational formulation and Fourier analysis.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-12-01
Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform's controllable frequency localization obtained by adjusting the order of PDEs. The
Xia, Shaoyan; Huang, Yong; Peng, Shizhao; Wu, Yanfeng; Tan, Xiaodi
2016-08-01
Phase image in Fourier domain Doppler optical coherence tomography offers additional flow information of investigated samples, which provides valuable evidence towards accurate medical diagnosis. High quality phase images are thus desirable. We propose a noise reduction method for phase images by combining a synthetic noise estimation criteria based on local noise estimator (LNE) and distance median value (DMV) with anisotropic diffusion model. By identifying noise and signal pixels accurately and diffusing them with different coefficients respectively and adaptive iteration steps, we demonstrated the effectiveness of our proposed method in both phantom and mouse artery images. Comparison with other methods such as filtering method (mean, median filtering), wavelet method, probabilistic method and partial differential equation based methods in terms of peak signal-to-noise ratio (PSNR), equivalent number of looks (ENL) and contrast-to-noise ratio (CNR) showed the advantages of our method in reserving image energy and removing noise.
Bai, Jianying; Dong, Xue; He, Sheng; Bao, Min
2017-06-03
Ocular dominance has been extensively studied, often with the goal to understand neuroplasticity, which is a key characteristic within the critical period. Recent work on monocular deprivation, however, demonstrates residual neuroplasticity in the adult visual cortex. After deprivation of patterned inputs by monocular patching, the patched eye becomes more dominant. Since patching blocks both the Fourier amplitude and phase information of the input image, it remains unclear whether deprivation of the Fourier phase information alone is able to reshape eye dominance. Here, for the first time, we show that removing of the phase regularity without changing the amplitude spectra of the input image induced a shift of eye dominance toward the deprived eye, but only if the eye dominance was measured with a binocular rivalry task rather than an interocular phase combination task. These different results indicate that the two measurements are supported by different mechanisms. Phase integration requires the fusion of monocular images. The fused percept highly relies on the weights of the phase-sensitive monocular neurons that respond to the two monocular images. However, binocular rivalry reflects the result of direct interocular competition that strongly weights the contour information transmitted along each monocular pathway. Monocular phase deprivation may not change the weights in the integration (fusion) mechanism much, but alters the balance in the rivalry (competition) mechanism. Our work suggests that ocular dominance plasticity may occur at different stages of visual processing, and that homeostatic compensation also occurs for the lack of phase regularity in natural scenes. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.
Universal and special keys based on phase-truncated Fourier transform
Qin, Wan; Peng, Xiang; Meng, Xiangfeng; Gao, Bruce
2011-08-01
We propose a novel optical asymmetric cryptosystem based on a phase-truncated Fourier transform. Two decryption keys independent of each other are generated. They are referred to as universal key and special key, respectively. Each of them can be used for decryption independently in absence of the other. The universal key is applicable to decrypt any ciphertext encoded by the same encryption key, but with poor legibility. On the contrary, the special key is adequate for legible decryption, but only valid for one ciphertext corresponding to the specified plaintext. A set of simulation results show the interesting performance of two types of decryption keys.
Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.
Mikkonen, Jopi J W; Raittila, Jussi; Rieppo, Lassi; Lappalainen, Reijo; Kullaa, Arja M; Myllymaa, Sami
2016-09-01
Saliva provides a valuable tool for assessing oral and systemic diseases, but concentrations of salivary components are very small, calling the need for precise analysis methods. In this work, Fourier transform infrared (FT-IR) spectroscopy using transmission and photoacoustic (PA) modes were compared for quantitative analysis of saliva. The performance of these techniques was compared with a calibration series. The linearity of spectrum output was verified by using albumin-thiocyanate (SCN(-)) solution at different SCN(-) concentrations. Saliva samples used as a comparison were obtained from healthy subjects. Saliva droplets of 15 µL were applied on the silicon sample substrate, 6 drops for each specimen, and dried at 37 ℃ overnight. The measurements were carried out using an FT-IR spectrometer in conjunction with an accessory unit for PA measurements. The findings with both transmission and PA modes mirror each other. The major bands presented were 1500-1750 cm(-1) for proteins and 1050-1200 cm(-1) for carbohydrates. In addition, the distinct spectral band at 2050 cm(-1) derives from SCN(-) anions, which is converted by salivary peroxidases to hypothiocyanate (OSCN(-)). The correlation between the spectroscopic data with SCN(-) concentration (r > 0.990 for transmission and r = 0.967 for PA mode) was found to be significant (P < 0.01), thus promising to be utilized in future applications.
Imaging Analysis by Means of Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Starting from the diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.
Fourier analysis of multi-tracer cosmological surveys
Abramo, L Raul; Loureiro, Arthur
2015-01-01
We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure. Our estimators can be used to simultaneously fit the matter power spectrum and the biases of the tracers - as well as redshift-space distortions (RSDs), non-Gaussianities (NGs), or any other effects that are manifested through differences between the clusterings of distinct species of tracers. Our estimators reduce to the one by Feldman, Kaiser & Peacock (ApJ 1994, FKP) in the case of a survey consisting of a single species of tracer. We show that the multi-tracer estimators are unbiased, and that their covariance is given by the inverse of the multi-tracer Fisher matrix (Abramo, MNRAS 2013; Abramo & Leonard, MNRAS 2013). When the biases, RSDs and NGs are fixed to their fiducial values, and one is only interested in measuring the underlying power spectrum, our estimators are projected into the estimator found by Percival, Verde & Peacock ...
On the Fourier and Wavelet Analysis of Coronal Time Series
Auchère, F.; Froment, C.; Bocchialini, K.; Buchlin, E.; Solomon, J.
2016-07-01
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 & 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 & 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.
Fourier Analysis and Structure Determination. Part II: Pulse NMR and NMR Imaging.
Chesick, John P.
1989-01-01
Uses simple pulse NMR experiments to discuss Fourier transforms. Studies the generation of spin echoes used in the imaging procedure. Shows that pulse NMR experiments give signals that are additions of sinusoids of differing amplitudes, frequencies, and phases. (MVL)
Fourier domain image fusion for differential X-ray phase-contrast breast imaging.
Coello, Eduardo; Sperl, Jonathan I; Bequé, Dirk; Benz, Tobias; Scherer, Kai; Herzen, Julia; Sztrókay-Gaul, Anikó; Hellerhoff, Karin; Pfeiffer, Franz; Cozzini, Cristina; Grandl, Susanne
2017-04-01
X-Ray Phase-Contrast (XPC) imaging is a novel technology with a great potential for applications in clinical practice, with breast imaging being of special interest. This work introduces an intuitive methodology to combine and visualize relevant diagnostic features, present in the X-ray attenuation, phase shift and scattering information retrieved in XPC imaging, using a Fourier domain fusion algorithm. The method allows to present complementary information from the three acquired signals in one single image, minimizing the noise component and maintaining visual similarity to a conventional X-ray image, but with noticeable enhancement in diagnostic features, details and resolution. Radiologists experienced in mammography applied the image fusion method to XPC measurements of mastectomy samples and evaluated the feature content of each input and the fused image. This assessment validated that the combination of all the relevant diagnostic features, contained in the XPC images, was present in the fused image as well.
[Analysis of cell arrangements in Biota orientalis using Fourier transformation].
Duo, Hua-Qiong; Wang, Xi-Ming
2009-10-01
Fourier transform image-processing technology is applied for determining the cross section cell arrangement of early-wood in Biota orientalis. In this method, the disc-convoluted dot map from each cell radius with 10 pixels is transformed by Fourier transform, generating the angle distribution function in the power spectral pattern. The maximum value is the arrangement of the cell. The results of Fourier transform image-processing technology indicated that the arrangements of the cell of Biota orientalis are 15 degrees in oblique direction, respectively. This method provides a new basis for the digitized identification of the wood, and also the new theoretical research direction for the digitized identification and examination of the wood species.
Yuan, Lin; Ran, Qiwen; Zhao, Tieyu
2017-02-01
In this paper an image authentication scheme is proposed based on double-image encryption and partial phase decryption in nonseparable Fractional Fourier transform domain. Two original images are combined and transformed into the nonseparable fractional Fourier domain. Only part of the phase information of the encrypted result is kept for decryption while the rest part of phase and all the amplitude information are discarded. The two recovered images are hardly recognized by visual inspection but can be authenticated by the nonlinear correlation algorithm. The numerical simulations demonstrate the viability and validity of the proposed image authentication scheme.
Yang, J; Chan, E H W; Wang, X; Feng, X; Guan, B
2015-05-04
An all-optical photonic microwave phase shifter that can realize a continuous 360° phase shift over a wide frequency range is presented. It is based on the new concept of controlling the amplitude and phase of the two RF modulation sidebands via a Fourier-domain optical processor. The operating frequency range of the phase shifter is largely increased compared to the previously reported Fourier-domain optical processor based phase shifter that uses only one RF modulation sideband. This is due to the extension of the lower RF operating frequency by designing the amplitude and phase of one of the RF modulation sidebands while the other sideband is designed to realize the required RF signal phase shift. The two-sideband amplitude-and-phase-control based photonic microwave phase shifter has a simple structure as it only requires a single laser source, a phase modulator, a Fourier-domain optical processor and a single photodetector. Investigation on the bandwidth limitation problem in the conventional Fourier-domain optical processor based phase shifter is presented. Comparisons between the measured phase shifter output RF amplitude and phase responses with theory, which show excellent agreement, are also presented for the first time. Experimental results demonstrate the full -180° to + 180° phase shift with little RF signal amplitude variation of less than 3 dB and with a phase deviation of less than 4° over a 7.5 GHz to 26.5 GHz frequency range, and the phase shifter exhibits a long term stable performance.
Scarfone, A. M.
2017-08-01
We present a new formulation of Fourier transform in the picture of the κ-algebra derived in the framework of the κ-generalized statistical mechanics. The κ-Fourier transform is obtained from a κ-Fourier series recently introduced by Scarfone (2013). The kernel of this transform, that reduces to the usual exponential phase in the κ → 0 limit, is composed by a κ-deformed phase and a damping factor that gives a wavelet-like behaviour. We show that the κ-Fourier transform is isomorph to the standard Fourier transform through a changing of time and frequency variables. Nevertheless, the new formalism is useful to study, according to Fourier analysis, those functions defined in the realm of the κ-algebra. As a relevant application, we discuss the central limit theorem for the κ-sum of n-iterate statistically independent random variables.
Makey, Ghaith; El-Daher, Moustafa Sayem; Al-Shufi, Kanj
2012-11-10
This paper introduces a new modification for the well-known binary detour phase method, which is largely used to represent Fourier holograms; the modification utilizes gray scale level control provided by a liquid crystal spatial light modulator to improve the traditional binary detour phase. Results are shown by both simulation and experiment.
Directory of Open Access Journals (Sweden)
Sohel Rana
2014-01-01
Full Text Available Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE and finite element method (FEM. The non-Fourier heat conduction has been investigated where the maximum likelihood (ML and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response. To reduce the increased computational time by Tikhonov WCAWE using ML (TWCAWE-ML, another well-conditioned scheme, called mass effect (ME T-WCAWE, is introduced. TWCAWE with ME (TWCAWE-ME showed more stable and accurate temperature spectrum in comparison to asymptotic wave evaluation (AWE and also partial Pade AWE without sacrificing the computational time. However, the TWCAWE-ML remains as the most stable and hence accurate model to analyze the fast transient thermal analysis of non-Fourier heat conduction model.
Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis
LoPresto, Michael C.
2013-01-01
What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.
Superresolution imaging method using phase-shifting digital lensless Fourier holography.
Granero, Luis; Micó, Vicente; Zalevsky, Zeev; García, Javier
2009-08-17
A method which is useful for obtaining superresolved imaging in a digital lensless Fourier holographic configuration is presented. By placing a diffraction grating between the input object and the CCD recording device, additional high-order spatial-frequency content of the object spectrum is directed towards the CCD. Unlike other similar methods, the recovery of the different band pass images is performed by inserting a reference beam in on-axis mode and using phase-shifting method. This strategy provides advantages concerning the usage of the whole frequency plane as imaging plane. Thus, the method is no longer limited by the zero order term and the twin image. Finally, the whole process results in a synthetic aperture generation that expands up the system cutoff frequency and yields a superresolution effect. Experimental results validate our concepts for a resolution improvement factor of 3.
Energy Technology Data Exchange (ETDEWEB)
Lebensohn, Ricardo A [Los Alamos National Laboratory; Lee, Sukbin [CMU; Rollett, Anthony D [CMU
2009-01-01
A viscoplastic approach using the Fast Fourier Transform (FFT) method for obtaining local mechanical response is utilized to study microstructure-property relationships in composite materials. Specifically, three-dimensional, two-phase digital materials containing isotropically coarsened particles surrounded by a matrix phase, generated through a Kinetic Monte Carlo Potts model for Ostwald ripening, are used as instantiations in order to calculate the stress and strain rate fields under uniaxial tension. The effects of the morphology of the matrix phase, the volume fraction and the contiguity of particles, and the polycrystallinity of matrix phase, on the stress and strain rate fields under uniaxial tension are examined. It is found that the first moments of the stress and strain rate fields have a different dependence on the particle volume fraction and the particle contiguity from their second moments. The average stresses and average strain rates of both phases and of the overall composite have rather simple relationships with the particle volume fraction whereas their standard deviations vary strongly, especially when the particle volume fraction is high, and the contiguity of particles has a noticeable effect on the mechanical response. It is also found that the shape of stress distribution in the BCC hard particle phase evolves as the volume fraction of particles in the composite varies, such that it agrees with the stress field in the BCC polycrystal as the volume of particles approaches unity. Finally, it is observed that the stress and strain rate fields in the microstructures with a polycrystalline matrix are less sensitive to changes in volume fraction and contiguity of particles.
Vatine, J J; Shochina, M; Mahler, Y; Gonen, B; Magora, A
1991-08-01
Real time computer analysis of the electrophysiological development of muscular fatigue after small doses of d-tubocurarine (TC), has been examined in anesthetized human beings. As compared to a decrease of frequency in the control measurements, previous studies have shown an increase of the frequency of spikes after TC administration. The present experiments were carried out on the biceps brachii of 8 healthy human volunteers maintained in isometric contraction against a constant counter load until complete fatigue occurred. The Fourier spectrum analysis showed a statistically significant shift to lower frequencies before, and a milder statistically non significant shift after TC. These results may indicate that under mild curarization the early phase of muscular contraction requires a higher number of large motor units and thus, at a later stage of the contraction the pool of available large motor units becomes smaller. This conclusion supports the hypothesis that mild curarization causes a state of initial muscular fatigue.
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.
DPL Model Analysis of Non-Fourier Heat Conduction Restricted by Continuous Boundary Interface
Institute of Scientific and Technical Information of China (English)
Jiang Fangming; Liu Dengying
2001-01-01
Dual-phase lag (DPL) model is used to describe the non-Fourier heat conduction in a finite medium where the boundary at x=-0 is heated by a rectangular pulsed energy source and the other boundary is tightly contacted with another medium and satisfies the continuous boundary condition. Numerical solution of this kind of. non-Fourier heat conduction is presented in this paper. The results are compared with those predicted by the hyperbolic heat conduction (HHC) equation.
Numerical Analysis of Inhomogeneous Dielectric Waveguide Using Periodic Fourier Transform
Directory of Open Access Journals (Sweden)
M. Moradian
2007-01-01
Full Text Available A general method is introduced to obtain the propagation constants of the inhomogeneous dielectric waveguide. The periodic Fourier transform is applied to the normalized Maxwell's equations and makes the field components periodic. Then they are expanded in Fourier series. Finally, the trapezoidal rule is applied to approximate the convolution integral which leads to a set of coupled second-order differential equations that can be solved as an eigenvalue-eigenvector problem. The normalized propagation constant can be obtained as the square roots of the eigenvalues of the coefficient matrices. The proposed method is applied to the dielectric waveguide with a two-layered dielectric profile in the transverse direction, and the first four-confined TE modes are obtained. The propagation constants for the mentioned dielectric waveguide are also derived analytically and are then compared with those derived by the proposed method. Comparison of results shows the efficacy of the proposed method.
Du, Lin; Kjaergaard, Henrik G
2011-11-10
Dimethylamine (DMA) has been studied by gas-phase Fourier transform infrared (FTIR) spectroscopy. We have identified a spectral transition that is assigned to the DMA dimer. The IR spectra of the dimer in the gas phase are obtained by spectral subtraction of spectra recorded at different pressures. The enthalpy of hydrogen bond formation was obtained for the DMA dimer by temperature-dependence measurements. We complement the experimental results with ab initio and anharmonic local mode model calculations of monomer and dimer. Compared to the monomer, our calculations show that in the dimer the N-H bond is elongated, and the NH-stretching fundamental shifts to a lower wavenumber. More importantly, the weak NH-stretching fundamental transition has a pronounced intensity increase upon complexation. However, the first NH-stretching overtone transition is not favored by the same intensity enhancement, and we do not observe the first NH-stretching overtone of the dimer. On the basis of the measured and calculated intensity of the NH-stretching transition of the dimer, the equilibrium constant for dimerization at room temperature was determined.
A sapphire fibre thermal probe based on fast Fourier transform and phase-lock loop
Institute of Scientific and Technical Information of China (English)
Wang Yu-Tian; Wang Dong-Sheng; Ge Wen-Qian; Cui Li-Chao
2006-01-01
A sapphire fibre thermal probe with Cra+ ion-doped end is developed by using the laser heated pedestal growth method. The fluorescence thermal probe offers advantages of compact structure, high performance and ability to withstand high temperature in a detection range from room temperature to 450℃. Based on the fast Fourier transform(FFT), the fluorescence lifetime is obtained from the tangent function of phase angle of the non-zeroth terms in the FFT result. This method has advantages such as quick calculation, high accuracy and immunity to the background noise. This FFT method is compared with other traditional fitting methods, indicating that the standard deviation of the FFT method is about half of that of the Prony method and about 1/6 of that of the log-fit method. And the FFT method is immune to the background noise involved in a signal. So, the FFT method is an excellent way of processing signals. In addition, a phase-lock amplifier can effectively suppress the noise.
Energy Technology Data Exchange (ETDEWEB)
Shirafuji, T [International Innovation Center, Kyoto University, Sakyo-ku, Kyoto 606-8501 (Japan); Motomura, H [Department of Electronics, Kyoto University, Nishikyo-ku, Katsura 615-8510 (Japan); Tachibana, K [Department of Electronics, Kyoto University, Nishikyo-ku, Katsura 615-8510 (Japan)
2004-03-21
Applicability of Fourier transform infrared (FTIR) spectroscopy to an in situ diagnostics tool of plasma-surface interactions is described. After a brief review of conventional reflection absorption spectroscopy (RAS) and phase-modulated RAS (PMRAS), our FTIR phase-modulated spectroscopic ellipsometry (PMSE) is described in detail. The FTIR PMSE is constructed by insertion of a grid polarizer as an analyser in front of an infrared detector in addition to the conventional set-up of PMRAS. This simple change brings about a higher sensitivity than that of conventional PMRAS, which enables us to detect chemical species generated on (or removed from) the top surface layer during plasma processing. This feature is demonstrated by the fact that our FTIR PMSE can be applied to surface diagnostics during reactive ion etching processes such as for Si, SiO{sub 2}/Si, SiO{sub 2}/Si{sub 3}N{sub 4}, SiO{sub 2}/photo-resist and low-dielectric-constant films. (topical review)
Wang, Xiaogang; Zhao, Daomu
2013-09-01
A nonlinear color and grayscale images cryptosystem based on phase-truncated fractional Fourier transform and optical superposition principle is proposed. In order to realize simultaneous encryption of color and grayscale images, each grayscale image is first converted into two phase masks by using an optical coherent superposition, one of which is treated as a part of input information that will be fractional Fourier transformed while the other in the form of a chaotic random phase mask (CRPM) is used as a decryption key. For the purpose of optical performance, all the processes are performed through three channels, i.e., red, green, and blue. Different from most asymmetric encryption methods, the decryption process is designed to be linear for the sake of effective decryption. The encryption level of a double random phase encryption based on phase-truncated Fourier transform is enhanced by extending it into fractional Fourier domain and the load of the keys management and transmission is lightened by using CRPMs. The security of the proposed cryptosystem is discussed and computer simulation results are presented to verify the validity of the proposed method.
Precise and fast spatial-frequency analysis using the iterative local Fourier transform.
Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook
2016-09-19
The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.
Mode analysis of structures using the Fourier p-element method
Institute of Scientific and Technical Information of China (English)
吴国荣; 钟伟芳
2003-01-01
The Fourier p-element method is an improvement to the finite element method, and is particularly suitable for vibration analysis due to the well-behaved Fourier series. In this paper, an iteration procedure is presented for solving the resulting nonlinear eigenvalue problem. Three types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration, the plate in-plane vibration and annular plate flexural vibration modes, respectively.The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation, especially for higher mode analysis.
Spatial Fourier Analysis of a Free-Free Beam for Structural Damage Detection
Bhagat, Mihir; Ganguli, Ranjan
2014-07-01
Free-free beams (FFB) are used to model many structures, such as missiles, rockets, MEMS (Micro Electro Mechanical Systems), etc. This paper aims to illustrate a novel structural health monitoring method-Fourier analysis of mode shapes of damaged beams-and extend it to the case of FFB. The damaged mode shapes of FFB are obtained by a finite element model and then studied using spatial Fourier analysis. The effect of noise in the mode shape data is considered and it is found that the Fourier coefficients provide a useful indication about the location and size of damage.
Sideroudi, Haris; Labiris, Georgios; Georgatzoglou, Kimon; Ditzel, Fienke; Siganos, Charalambos; Kozobolis, Vassilios
PURPOSE: To evaluate the contribution of Fourier analysis of videokeratographic data in the diagnosis of subclinical keratoconus and keratoconus. SETTING: Eye Institute of Thrace, Democritus University, Alexandroupolis, Greece. DESIGN: Observational case series. METHODS: The following
Sideroudi, Haris; Labiris, Georgios; Georgatzoglou, Kimon; Ditzel, Fienke; Siganos, Charalambos; Kozobolis, Vassilios
2016-01-01
PURPOSE: To evaluate the contribution of Fourier analysis of videokeratographic data in the diagnosis of subclinical keratoconus and keratoconus. SETTING: Eye Institute of Thrace, Democritus University, Alexandroupolis, Greece. DESIGN: Observational case series. METHODS: The following Pentacam-deriv
Dantas, José L; Camata, Thiago V; Brunetto, Maria A C; Moraes, Antonio C; Abrão, Taufik; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in isometric and dynamic exercise. The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in isometric and dynamic exercise (P>0.05). However, the results of the variance was lower for both types of exercise in CWT compared to STFT (P signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Analysis of a thioether lubricant by infrared Fourier microemission spectrophotometry
Jones, W. R., Jr.; Morales, W.; Lauer, J. L.
1986-01-01
An infrared Fourier microemission spectrophotometer is used to obtain spectra (wavenumber range, 630 to 1230 0.1 cm) from microgram quantities of thioether lubricant samples deposited on aluminum foil. Infrared bands in the spectra are reproducible and could be identified as originating from aromatic species (1,3-disubstituted benzenes). Spectra from all samples (neat and formulated, used and unused) are very similar. Additives (an acid and a phosphinate) present in low concentration (0.10 percent) in the formulated fluid are not detected. This instrument appears to be a viable tool in helping to identify lubricant components separated by liquid chromatography.
Fourier optics for polymeric substrates and coating textures analysis
Sparavigna, Amelia
2008-01-01
Several devices for substrate texture detection based on diffractive optics, for paper, textiles and non-wovens have been proposed in the past for direct inspection during the production processes. In spite of the presence of devices totally based on image processing, the use of diffractive optics cannot be considered surpassed for many reasons. Compared with image processing procedures, it is less sensitive to vibrations and does not suffer from the presence of ambient light. Based on transmitted light, it can give information on changes in refractive indexes, thickness variation and surface conditions. We study the use of optical Fourier spectrum to identify textures of polymer films. As the power spectrum reveals, the texture is seldom homogeneous. Here we report investigation on several substrates and on thin ink coatings on substrate. Role of bulk and surface conditions is analysed.
Fourier optics analysis of grating sensors with tilt errors.
Ferhanoglu, Onur; Toy, M Fatih; Urey, Hakan
2011-06-15
Dynamic diffraction gratings can be microfabricated with precision and offer extremely sensitive displacement measurements and light intensity modulation. The effect of pure translation of the moving part of the grating on diffracted order intensities is well known. This study focuses on the parameters that limit the intensity and the contrast of the interference. The effects of grating duty cycle, mirror reflectivities, sensor tilt and detector size are investigated using Fourier optics theory and Gaussian beam optics. Analytical findings reveal that fringe visibility becomes <0.3 when the optical path variation exceeds half the wavelength within the grating interferometer. The fringe visibility can be compensated by monitoring the interfering portion of the diffracted order light only through detector size reduction in the expense of optical power. Experiments were conducted with a grating interferometer that resulted in an eightfold increase in fringe visibility with reduced detector size, which is in agreement with theory. Findings show that diffraction grating readout principle is not limited to translating sensors but also can be used for sensors with tilt or other deflection modes.
Analysis of ovarian tumor pathology by Fourier Transform Infrared Spectroscopy
Directory of Open Access Journals (Sweden)
Mehrotra Ranjana
2010-12-01
Full Text Available Abstract Background Ovarian cancer is the second most common cancer among women and the leading cause of death among gynecologic malignancies. In recent years, infrared (IR spectroscopy has gained attention as a simple and inexpensive method for the biomedical study of several diseases. In the present study infrared spectra of normal and malignant ovarian tissues were recorded in the 650 cm-1 to 4000 cm-1 region. Methods Post surgical tissue samples were taken from the normal and tumor sections of the tissue. Fourier Transform Infrared (FTIR data on twelve cases of ovarian cancer with different grades of malignancy from patients of different age groups were analyzed. Results Significant spectral differences between the normal and the ovarian cancerous tissues were observed. In particular changes in frequency and intensity in the spectral region of protein, nucleic acid and lipid vibrational modes were observed. It was evident that the sample-to-sample or patient-to-patient variations were small and the spectral differences between normal and diseased tissues were reproducible. Conclusion The measured spectroscopic features, which are the spectroscopic fingerprints of the tissues, provided the important differentiating information about the malignant and normal tissues. The findings of this study demonstrate the possible use of infrared spectroscopy in differentiating normal and malignant ovarian tissues.
On zero-curvature condition and Fourier analysis
Energy Technology Data Exchange (ETDEWEB)
Saksida, Pavle, E-mail: Pavle.Saksida@fmf.uni-lj.si [Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana (Slovenia)
2011-02-25
We study a system of conserved quantities of the periodic Klein-Gordon equation. We obtain these quantities by means of a perturbation construction from a Lax pair of the periodic sine-Gordon equation. We show that for a suitable choice of values of the spectral parameter, our conserved quantities have simple expressions in terms of the Fourier coefficients of the initial data. Moreover, they turn out to be the action variables. This provides an interesting illustration of the role of the spectral parameter. Our perturbation construction also provides a new Lax pair for the Klein-Gordon equation, and our action variables arise from this Lax pair. This turns out to be a special case (k = 2) of a more general Lax pair for a certain k-jet system of the sine-Gordon equation. The structure algebra of this Lax pair is the algebra T A{sub k} of upper triangular k x k block Toeplitz matrices whose blocks are elements of su(2). The Ad-invariant functions on the Lie group T G{sub k} corresponding to the Lie algebra T A{sub k} are needed for the construction of the integrals. These functions are not given by the spectra of the matrices. They have to be constructed by other means.
2014-10-16
1 Extracting micro-Doppler radar signatures from rotating targets using Fourier- Bessel Transform and Time-Frequency analysis P. Suresh1,T...kvenkataramanaiah@sssihl.edu.in Abstract In this paper, we report the efficiency of Fourier Bessel transform and time-frequency based method in conjunction with...decomposed into stationary and non-stationary components using Fourier Bessel transform in conjunction with the fractional Fourier transform. The
Samlan, C T; Naik, Dinesh N; Viswanathan, Nirmal K
2016-09-14
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-01-01
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena. PMID:27625210
Williams, Anthony; Chung, Jaebum; Ou, Xiaoze; Zheng, Guoan; Rawal, Siddarth; Ao, Zheng; Datar, Ram; Yang, Changhuei; Cote, Richard
2014-06-01
Circulating tumor cells (CTCs) are recognized as a candidate biomarker with strong prognostic and predictive potential in metastatic disease. Filtration-based enrichment technologies have been used for CTC characterization, and our group has previously developed a membrane microfilter device that demonstrates efficacy in model systems and clinical blood samples. However, uneven filtration surfaces make the use of standard microscopic techniques a difficult task, limiting the performance of automated imaging using commercially available technologies. Here, we report the use of Fourier ptychographic microscopy (FPM) to tackle this challenge. Employing this method, we were able to obtain high-resolution color images, including amplitude and phase, of the microfilter samples over large areas. FPM's ability to perform digital refocusing on complex images is particularly useful in this setting as, in contrast to other imaging platforms, we can focus samples on multiple focal planes within the same frame despite surface unevenness. In model systems, FPM demonstrates high image quality, efficiency, and consistency in detection of tumor cells when comparing corresponding microfilter samples to standard microscopy with high correlation (R2=0.99932). Based on these results, we believe that FPM will have important implications for improved, high throughput, filtration-based CTC analysis, and, more generally, image analysis of uneven surfaces.
Fourier Analysis for Demand Forecasting in a Fashion Company
Directory of Open Access Journals (Sweden)
Andrea Fumi
2013-08-01
sectors. The entire analysis was performed on a common spreadsheet, in order to demonstrate that accurate results exploiting advanced numerical computation techniques can be carried out without necessarily using expensive software.
On the Fourier Spectra of Distributions in Clifford Analysis
Institute of Scientific and Technical Information of China (English)
Fred BRACKX; Bram De KNOCK; Hennie De SCHEPPER
2006-01-01
In recent papers by Brackx, Delanghe and Sommen, some fundamental higher dimensional distributions have been reconsidered in the framework of Clifford analysis,eventually leading to the introduction of four broad classes of new distributions in Euclidean space. In the current paper we continue the in-depth study of these distributions, more specifically the study of their behaviour in frequency space, thus extending classical results of harmonic analysis.
A COMPARISION BETWEEN WALSHHADAMARD AND FOURIER ANALYSIS OF THE EEG SIGNALS
Directory of Open Access Journals (Sweden)
AZADEH BASTANI
2011-07-01
Full Text Available Electroencephalography (EEG is one of the most important diagnostic tools in neurology and getting information about the brain activity. One of this is real-time and quantified study of brain activities to measure the stage of unconsciousness due to injection drug in operation room. EEG signal is a stochastic non-stationary process. Regarding the complexity of brain activities on EEG process, studies are based on time-frequency features analysis of EEG signals. Most of these analyses are based on Fourier Transform and the most significant are classic and parametric estimation of power spectral density analysis. Considering the origins of EEG in the brain, it seems that Walsh-Hadamard transform is more effective than Fourier transform in feature extracting of these signals. In this paper the efficiency of Walsh-Hadamard transform features were comparedwith extracted features from Fourier transform. To evaluate these features, three different classifying algorithms are used. The results showed that Walsh-Hadamard extracted features are suitable tools for recognition of difference between different stages of EEG signals. Simplicity and speed of Walsh-Hadamard transform calculation made it preferable then Fourier spectral features. The fast Walsh-Hadamard transform is an attractive alternative to the fast fourier transform because it is computationally more efficient, and thus faster to perform on a digital computer.
Subpixel translation of MEMS measured by discrete fourier transform analysis of CCD images
Yamahata, C.; Sarajlic, Edin; Stranczl, M.; Krijnen, Gijsbertus J.M.; Gijs, M.A.M.
2011-01-01
We present a straightforward method for measuring in-plane linear displacements of microelectromechanical systems (MEMS) with subnanometer resolution. The technique is based on Fourier transform analysis of a video recorded with a Charge-Coupled Device (CCD) camera attached to an optical microscope
Subpixel translation of MEMS measured by discrete fourier transform analysis of CCD images
Yamahata, C.; Sarajlic, E.; Stranczl, M.; Krijnen, G.J.M.; Gijs, M.A.M.
2011-01-01
We present a straightforward method for measuring in-plane linear displacements of microelectromechanical systems (MEMS) with subnanometer resolution. The technique is based on Fourier transform analysis of a video recorded with a Charge-Coupled Device (CCD) camera attached to an optical microscope
Characterization of multilayers by Fourier analysis of x-ray reflectivity
Voorma, H. J.; E. Louis,; Koster, N. B.; F. Bijkerk,; Spiller, E.
1997-01-01
We discuss a new method to characterize multilayer structures with grazing-incidence reflectivity measurements using hard x-ray radiation, such as Cu-K-alpha or Mo-K-alpha radiation. The method is based on the analysis of the reverse Fourier transforms of the reflectivity at the Bragg peaks in
Fourier and wavelet spectral analysis of EMG signals in supramaximal constant load dynamic exercise.
Camata, Thiago V; Dantas, Jose L; Abrao, Taufik; Brunetto, Maria A C; Moraes, Antonio C; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in supramaximal constant load dynamic exercise (110% VO(2peak)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in supramaximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Fourier and wavelet spectral analysis of EMG signals in maximal constant load dynamic exercise.
Costa, Marcelo V; Pereira, Lucas A; Oliveira, Ricardo S; Pedro, Rafael E; Camata, Thiago V; Abrao, Taufik; Brunetto, Maria A C; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in maximal constant load dynamic exercise (100% W(max)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in maximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P〈0.05) indicating more variability in the EMG signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Program for the analysis of time series. [by means of fast Fourier transform algorithm
Brown, T. J.; Brown, C. G.; Hardin, J. C.
1974-01-01
A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.
Munoz, R. M. (Inventor)
1974-01-01
An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. The original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications.
Fractals and spectra related to fourier analysis and function spaces
Triebel, Hans
1997-01-01
Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...
Laplace-Fourier analysis and instabilities of a gainy slab
Hågenvik, Hans Olaf
2015-01-01
The idealization of monochromatic plane waves leads to considerable simplifications in the analysis of electromagnetic systems. However, for active systems this idealization may be dangerous due to the presence of growing waves. Here we consider a gainy slab, and use a realistic incident beam, which is both causal and has finite width. This clarifies some apparent paradoxes arising from earlier analyses of this setup. In general it turns out to be necessary to involve complex frequencies $\\omega$ and/or complex transversal wavenumbers $k_x$. Simultaneously real $\\omega$ and $k_x$ cannot describe amplified waves in a slab which is infinite in the transversal direction. We also show that the only possibility to have an absolute instability for a finite width beam, is if a normally incident plane wave would experience an instability.
Wang, Xiaogang; Zhao, Daomu
2013-09-15
We propose a simple amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier-transform-based encryption using a random amplitude mask (RAM). The RAM that is not saved during the encryption provides extremely high security for the two private keys, and no iterative calculations are involved in the nonlinear encryption process. Lack of enough constraints makes the specific attack based on iterative amplitude-phase retrieval algorithms unusable. Numerical simulation results are given for testing the validity and security of the proposed approach.
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.
Takasago, K; Takekawa, M; Shirakawa, A; Kannari, F
2000-05-10
A new, to our knowledge, space-variant optical interconnection system based on a spatial-phase code-division multiple-access technique with multiplexed Fourier holography is described. In this technique a signal beam is spread over wide spatial frequencies by an M-sequence pseudorandom phase code. At a receiver side a selected signal beam is properly decoded, and at the same time its spatial pattern is shaped with a Fourier hologram, which is recorded by light that is encoded with the same M-sequence phase mask as the desired signal beam and by light whose spatial beam pattern is shaped to a signal routing pattern. Using the multiplexed holography, we can simultaneously route multisignal flows into individually specified receiver elements. The routing pattern can also be varied by means of switching the encoding phase code or replacing the hologram. We demonstrated a proof-of-principle experiment with a doubly multiplexed hologram that enables simultaneous routing of two signal beams. Using a numerical model, we showed that the proposed scheme can manage more than 250 routing patterns for one signal flow with one multiplexed hologram at a signal-to-noise ratio of ~5.
Leszczyński, Adam
2015-01-01
We present a method to calibrate wavefront distortion of the spatial light modulator setup by registering far field images of several gaussian beams diffracted off the modulator. The Fourier transform of resulting interference images reveals phase differences between typically 5 movable points on the modulator. Repeating this measurement yields wavefront surface. Next, the amplitude efficiency is calibrated be registering near field image. As a verification we produced a superposition of 7th and 8th Bessel beams with different phase velocities and observed their interference.
Leszczyński, Adam; Wasilewski, Wojciech
2016-04-01
We present a method to calibrate wavefront distortion of the spatial light modulator setup by registering far-field images of several Gaussian beams diffracted off the modulator. The Fourier transform of resulting interference images reveals phase differences among typically five movable points on the modulator. Repeating this measurement yields a wavefront surface. Next, the amplitude efficiency is calibrated for registering the near-field image. For verification, we produced a superposition of seventh and eighth Bessel beams with different phase velocities and observed their interference.
Directory of Open Access Journals (Sweden)
Giuseppe eMercurio
2014-01-01
Full Text Available We present an analysis method of normal incidence x-ray standing wave (NIXSW data that allows detailed adsorption geometries of complex molecules to be retrieved. This method (Fourier vector analysis is based on the comparison of both the coherence and phase of NIXSW data to NIXSW simulations of different molecular geometries as the relevant internal degrees of freedom are tuned. We introduce this analysis method using the prototypical molecular switch azobenzene (AB adsorbed on the Ag(111 surface as a model system. The application of the Fourier vector analysis to AB/Ag(111 provides, on the one hand, detailed adsorption geometries including dihedral angles, and on the other hand, insights into the dynamics of molecules and their bonding to the metal substrate. This analysis scheme is generally applicable to any adsorbate, it is necessary for molecules with potentially large distortions, and will be particularly valuable for molecules whose distortion on adsorption can be mapped on a limited number of internal degrees of freedom.
Evaluation of Attenuation/Minimum-Phase Pairs by Means of Two Fast Fourier Transforms
1980-01-31
Hilbert Transform Logarithmic Singularities Mini mum- Phase Filter Phase Poles and Zeros Principal Value Integral UNCLASSIFIED MCUNITV...minimum- phase filters , in terms of their group delay and rate of energy flow through the filter, are given in [5; pages 132-3]. In particular, the...minimum- phase filter has the smallest group delay of any stable filter with specified magnitude transfer function. ATTENUATION AND PHASE There is
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
Campbell, Joel
2008-01-01
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
Fourier Analysis of an Expanded Gravity Model for Spatio-Temporal Interactions
Chen, Yanguang
2013-01-01
Fourier analysis and cross-correlation function are successfully applied to improving the conventional gravity model of interaction between cities by introducing a time variable to the attraction measures (e.g., city sizes). The traditional model assumes spatial interaction as instantaneous, while the new model considers the interaction as a temporal process and measures it as an aggregation over a period of time. By doing so, the new model not only is more theoretically sound, but also enables us to integrate the analysis of temporal process into spatial interaction modeling. Based on cross-correlation function, the developed model is calibrated by Fourier analysis techniques, and the computation process is demonstrated in four steps. The paper uses a simple case study to illustrate the approach to modeling the interurban interaction, and highlight the relationship between the new model and the conventional gravity model.
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.
Advantages Of A Time Series Analysis Using Wavelet Transform As Compared With A Fourier Analysis
Directory of Open Access Journals (Sweden)
Sleziak Patrik
2015-06-01
Full Text Available The paper presents an analysis of changes in the structure of the average annual discharges, average annual air temperature, and average annual precipitation time series in Slovakia. Three time series with lengths of observation from 1961 to 2006 were analyzed. An introduction to spectral analysis with Fourier analysis (FA is given. This method is used to determine significant periods of a time series. Later in this article a description of a wavelet transform (WT is reviewed. This method is able to work with non-stationary time series and detect when significant periods are presented. Subsequently, models for the detection of potential changes in the structure of the time series analyzed were created with the aim of capturing changes in the cyclical components and the multiannual variability of the time series selected for Slovakia. Finally, some of the comparisons of the time series analyzed are discussed. The aim of the paper is to show the advantages of time series analysis using WT compared with FT. The results were processed in the R software environment.
Ogawa, T; Kawasaki, H; Takahashi, O; Aboshi, H; Kasai, K
2000-06-01
The shape of the mandible is used by orthodontists as an aid to orthodontic treatment planning, with different shapes displaying different growth characteristics and being associated with different functional patterns. However, the quantification of shape using conventional linear and angular variables does not always include details of some of the more subtle aspects of form. Fourier analysis enables accurate representation, with few coefficients, of a mandibular outer line from articulare to infradentale. The aim of this study was to investigate, using a cluster analysis, the relationship between variation in mandibular form and overall facial morphology. A cluster analysis of the Fourier amplitudes classified mandibular forms into one of seven groups for both males and females. The cluster analysis showed that the gonial angle and the inclination of lower incisor were associated with facial type according to the mandibular variables. Furthermore, the Fourier descriptions of mandibular form could be related to the observed variation in facial form, each of the clusters based on mandibular form being associated with demonstrable differences in dentofacial morphology.
Kilgour, David P A; Nagornov, Konstantin O; Kozhinov, Anton N; Zhurov, Konstantin O; Tsybin, Yury O
2015-06-15
Previously described methods for producing absorption mode Fourier transform ion cyclotron resonance (FTICR) mass spectra have all relied on the phase correction function being quadratic. This assumption has been found to be invalid for some instruments and spectra and so it has not been possible to produce absorption mode spectra for these cases. The Autophaser algorithm has been adapted to allow nth order polynomial phase correction functions to be optimized. The data was collected on a modified Thermo LTQ FTICR mass spectrometer, using electrospray ionization and a novel ICR cell design (NADEL). Peak assignment and mass calibration were undertaken using the pyFTMS framework. An nth-order phase correction function has been used to produce an absorption mode mass spectrum of the maltene fraction of a crude oil sample which was not possible using the previous assumption that the phase correction function must be quadratic. Data processing for this spectrum in absorption mode has shown the expected benefits in terms of increasing the number of assigned peaks and also improving the mass accuracy (i.e. confidence) of the assignments. It is possible to phase-correct time-domain data in FTICRMS to yield absorption mode mass spectra representation even when the data does not correspond to the theoretical quadratic phase correction function predicted by previous studies. This will allow a larger proportion of spectra to be processed in absorption mode. Copyright © 2015 John Wiley & Sons, Ltd.
Establishing the direct connection between detrended fluctuation analysis and Fourier analysis
Kiyono, Ken
2015-01-01
To understand methodological features of the detrended fluctuation analysis (DFA) using a higher-order polynomial fitting, we establish the direct connection between DFA and Fourier analysis. Based on an exact calculation of the single-frequency response of the DFA, the following facts are shown analytically: (1) in the analysis of stochastic processes exhibiting a power-law scaling of the power spectral density (PSD), $S(f) \\sim f^{-\\beta}$, a higher-order detrending in the DFA has no adverse effect in the estimation of the DFA scaling exponent $\\alpha$, which satisfies the scaling relation $\\alpha = (\\beta+1)/2$; (2) the upper limit of the scaling exponents detectable by the DFA depends on the order of polynomial fit used in the DFA, and is bounded by $m + 1$, where $m$ is the order of the polynomial fit; (3) the relation between the time scale in the DFA and the corresponding frequency in the PSD are distorted depending on both the order of the DFA and the frequency dependence of the PSD. We can improve th...
A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
DANCHIN; Raphaёl
2012-01-01
Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations.In this survey paper,we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space.We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.
Peterseim, Tobias; Dressel, Martin
2017-01-01
The time-dependent optical properties of molecular systems are investigated by step-scan Fourier-transform spectroscopy in order to explore the dynamics at phase transitions and molecular orientation in the milli- and microsecond range. The electrical switching of liquid crystals traced by vibrational spectroscopy reveals a rotation of the molecules with a relaxation time of 2 ms. The photo-induced neutral-ionic transition in TTF-CA takes place by a suppression of the dimerization in the ionic phase and creation of neutral domains. The time-dependent infrared spectra, employed to investigate the domain-wall dynamics, depend on temperature and laser pulse intensity; the relaxation of the spectra follows a stretched-exponential decay with relaxation times in the microsecond range strongly dependent on temperature and laser intensity. We present all details of the experimental setups and thoroughly discuss the technical challenges.
Peterseim, Tobias; Dressel, Martin
2016-06-01
The time-dependent optical properties of molecular systems are investigated by step-scan Fourier-transform spectroscopy in order to explore the dynamics at phase transitions and molecular orientation in the milli- and microsecond range. The electrical switching of liquid crystals traced by vibrational spectroscopy reveals a rotation of the molecules with a relaxation time of 2 ms. The photo-induced neutral-ionic transition in TTF-CA takes place by a suppression of the dimerization in the ionic phase and creation of neutral domains. The time-dependent infrared spectra, employed to investigate the domain-wall dynamics, depend on temperature and laser pulse intensity; the relaxation of the spectra follows a stretched-exponential decay with relaxation times in the microsecond range strongly dependent on temperature and laser intensity. We present all details of the experimental setups and thoroughly discuss the technical challenges.
Nonparaxial Fourier propagation tool for aberration analysis and point spread function calculation
Cain, Stephen C.; Watts, Tatsuki
2016-08-01
This paper describes a Fourier propagator for computing the impulse response of an optical system, while including terms ignored in Fresnel and Fraunhofer calculations. The propagator includes a Rayleigh-Sommerfeld diffraction formula calculation from a distant point through the optical system to its image point predicted by geometric optics. The propagator then approximates the neighboring field points via the traditional binomial approximation of the Taylor series expansion around that field point. This technique results in a propagator that combines the speed of a Fourier transform operation with the accuracy of the Rayleigh-Sommerfeld diffraction formula calculation and extends Fourier optics to cases that are nonparaxial. The proposed propagator facilitates direct calculation of aberration coefficients, making it more versatile than the angular spectrum propagator. Bounds on the phase error introduced by the approximations are derived, which show that it should be more widely applicable than the Fresnel propagator. Guidance on how to sample the pupil and detector planes of a simulated imaging system is provided. This report concludes by showing examples of diffraction calculations for a laboratory setup and comparing them to measured diffraction patterns to demonstrate the utility of the propagator.
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.
Bladed wheels damage detection through Non-Harmonic Fourier Analysis improved algorithm
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.
Measuring sperm movement within the female reproductive tract using Fourier analysis.
Nicovich, Philip R; Macartney, Erin L; Whan, Renee M; Crean, Angela J
2015-02-01
The adaptive significance of variation in sperm phenotype is still largely unknown, in part due to the difficulties of observing and measuring sperm movement in its natural, selective environment (i.e., within the female reproductive tract). Computer-assisted sperm analysis systems allow objective and accurate measurement of sperm velocity, but rely on being able to track individual sperm, and are therefore unable to measure sperm movement in species where sperm move in trains or bundles. Here we describe a newly developed computational method for measuring sperm movement using Fourier analysis to estimate sperm tail beat frequency. High-speed time-lapse videos of sperm movement within the female tract of the neriid fly Telostylinus angusticollis were recorded, and a map of beat frequencies generated by converting the periodic signal of an intensity versus time trace at each pixel to the frequency domain using the Fourier transform. We were able to detect small decreases in sperm tail beat frequency over time, indicating the method is sensitive enough to identify consistent differences in sperm movement. Fourier analysis can be applied to a wide range of species and contexts, and should therefore facilitate novel exploration of the causes and consequences of variation in sperm movement.
Short time Fourier analysis of the electromyogram - Fast movements and constant contraction
Hannaford, Blake; Lehman, Steven
1986-01-01
Short-time Fourier analysis was applied to surface electromyograms (EMG) recorded during rapid movements, and during isometric contractions at constant forces. A portion of the data to be transformed by multiplying the signal by a Hamming window was selected, and then the discrete Fourier transform was computed. Shifting the window along the data record, a new spectrum was computed each 10 ms. The transformed data were displayed in spectograms or 'voiceprints'. This short-time technique made it possible to see time-dependencies in the EMG that are normally averaged in the Fourier analysis of these signals. Spectra of EMGs during isometric contractions at constant force vary in the short (10-20 ms) term. Short-time spectra from EMGs recorded during rapid movements were much less variable. The windowing technique picked out the typical 'three-burst pattern' in EMG's from both wrist and head movements. Spectra during the bursts were more consistent than those during isometric contractions. Furthermore, there was a consistent shift in spectral statistics in the course of the three bursts. Both the center frequency and the variance of the spectral energy distribution grew from the first burst to the second burst in the same muscle. The analogy between EMGs and speech signals is extended to argue for future applicability of short-time spectral analysis of EMG.
A fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation.
Li, Haisen S; Romeijn, H Edwin; Dempsey, James F
2006-09-01
We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near monoenergetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the
Response of Autonomic Nervous System to Body Positions: Fourier and Wavelet Analysis
Xu, A; Federici, A; Stramaglia, S; Simone, F; Zenzola, A; Santostasi, R; Xu, Aiguo
2003-01-01
Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1), and the second half (HD2) of $90^{\\circ}$ head down tilt and during recovery (REC). The wavelet transform was performed using the Haar function of period $T=2^j$ ($% j=1$,2,$... $,6) to obtain wavelet coefficients. Power spectra components were analyzed within three bands, VLF (0.003-0.04), LF (0.04-0.15) and HF (0.15-0.4) with the frquency unit cycle/interval. Wavelet transform demonstrated a higher discrimination among all analyzed periods than the Fourier transform. For the Fourier analysis, the LF of R-R intervals and VLF of systolic blood pressure show more evident difference for different body positions. For the wavelet analysis, the systolic blood pressures show much more evident difference than the R-R intervals. This study s...
Analysis of tokamak plasma confinement modes using the fast Fourier transformation
Indian Academy of Sciences (India)
S R MIRMOEINI; A SALAR ELAHI; M GHORANNEVISS
2016-11-01
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 ‘presenceof 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 theexternal field.
Dong, Bing; Qin, Shun; Hu, Xinqi
2013-09-01
Large-aperture segmented primary mirror will be widely used in next-generation space-based and ground-based telescopes. The effects of intersegment gaps, obstructions, position and figure errors of segments, which are all involved in the pupil plane, on the image quality metric should be analyzed using diffractive imaging theory. Traditional Fast Fourier Transform (FFT) method is very time-consuming and costs a lot of memory especially in dealing with large pupil-sampling matrix. A Partial Fourier Transform (PFT) method is first proposed to substantially speed up the computation and reduce memory usage for diffractive imaging analysis. Diffraction effects of a 6-meter segmented mirror including 18 hexagonal segments are simulated and analyzed using PFT method. The influence of intersegment gaps and position errors of segments on Strehl ratio is quantitatively analyzed by computing the Point Spread Function (PSF). By comparing simulation results with theoretical results, the correctness and feasibility of PFT method is confirmed.
Fourier analysis of short-period SMC Cepheids: A comparison with Galactic Cepheids
Buchler, J. Robert; Moskalik, Pawel
1994-12-01
A Fourier analysis has been made of the Small Magellanic Cloud (SMC) classical Cepheid data of Smith et al. It is shown that the grouping into fundamental and first overtone pulsators, implied by the period-luminosity diagram, survives when the Fourier coefficients are plotted versus period. A comparison with the Galactic Cepheid data corroborates the existing evidence that the short period Galactic s-Cepheids are indeed first overtone pulsators. The only long period overtone Cepheid in the sample that is reliably covered (P = 3.49 d) also conforms with the corresponding s-Cepheids. On the other hand, the hypothesis of Gieren et al. that the long period s-Cepheids are fundamental pulsators is refuted. The data show systematic differences between the SMC Cepheids and their Galactic counterparts, differences that are of theoretical interest. The need for a further observational effort devoted to SMC and to Large Magellanic cloud (LMC) Cepheids is stressed.
Phase compensation in lensless Fourier transform digital holography%无透镜傅里叶变换数字全息中的相位补偿
Institute of Scientific and Technical Information of China (English)
张中恒; 李重光; 李靖哲; 缪正祥; 刘营
2013-01-01
The phase accuracy of numerically reconstructed images directly affects the result of the digital holographic measurement .How to find the phase distortion and adopt corresponding method to automatically correct the distortion is challenging .The phase correction problem of lensless Fourier transform digital holographic was analyzed .When reconstruct the numerical wave surface by means of single Fourier transform , there is an additional quadratic phase factor inducing the phase distortion of reconstructed images .The digital phase mask was calculated based on multiple-profile calculation by means of the least square method for curve fitting , the phase distribution was corrected .The theoretical analysis and experimental prove that it is better to correct phase distortion compared with frequently -used two-profile method , the result is helpful for the study of phase correction .% 数值再现像相位的准确性直接影响到数字全息检测的结果。为了找出再现过程中存在的相位畸变并采取相应的方法达到自动补偿，对无透镜傅里叶变换数字全息中的相位补偿问题进行了研究。因为经过单次傅里叶变换法进行数字波面重构时，存在一个附加的二次相位因子，该附加因子造成了再现像的相位畸变。采用最小二乘曲线拟合方法，通过多剖面计算得出数字相位掩膜进而对相位分布进行校正，并进行了理论分析和对比实验验证。结果表明，与常用的二剖面方法相比，能够对相位畸变进行更好的校正。这一结果对相位补偿问题的研究是有帮助的。
de Beer, N A M; Andriessen, P; Berendsen, R C M; Oei, S G; Wijn, P F F; Oetomo, S Bambang
2004-12-01
A customized filtering technique is introduced and compared with fast Fourier transformation (FFT) for analyzing heart rate variability (HRV) in neonates from short-term recordings. FFT is classically the most commonly used spectral technique to investigate cardiovascular fluctuations. FFT requires stability of the physiological signal within a 300 s time window that is usually analyzed in adults. Preterm infants, however, show characteristics of rapidly fluctuating heart rate and blood pressure due to an immature autonomic regulation, resulting in non-stationarity of these signals. Therefore neonatal studies use (half-overlapping or moving) windows of 64 s length within a recording time of 2-5 min. The proposed filtering technique performs a filtering operation in the frequency range of interest before calculating the spectrum, which allows it to perform an analysis of shorter periods of only 42 s. The frequency bands of interest are 0.04-0.15 Hz (low frequency, LF) and 0.4-1.5 Hz (high frequency, HF). Although conventional FFT analysis as well as the proposed alternative technique result in errors in the estimation of LF power, due to spectral leakage from the very low frequencies, FFT analysis is more sensitive to this effect. The response times show comparable behavior for both the techniques. Applying both the methods to heart rate data obtained from a neonate before and after atropine administration (inducing a wide range of HRV), shows a very significant correlation between the two methods in estimating LF and HF power. We conclude that a customized filtering technique might be beneficial for analyzing HRV in neonates because it reduces the necessary time window for signal stability.
Siminoff, R
1991-01-01
Fourier analysis is used to study resolution of images processed by the matrix of simulated red-center (BCR) and green-center (BCG) bipolar cells (BC) of the human central fovea. Simulated achromatic and chromatic sine and square waves, and a two-bar stimulus are used to activate the BCs. Due to the "honeycomb" packing of the cones and BC matrices Fourier transforms are computed row by row using a one-dimensional FFT. Resolution computed by the Fourier transform is compared with the resolution index (RI), which is a method for determining resolution based on two-point discrimination in the space domain. In general the harmonic with the maximum amplitude gives the best correlation with RI for the three stimuli. Amplitudes at all spatial frequencies are enhanced by increasing the number of cycles in the sine and square wave gratings. Results with simulated BCs compare favorably with human and macaque psychophysics measuring contrast sensitivity. Square wave gratings are better than sine wave greetings for studying resolution.
Tian, Lei; Yeh, Li-Hao; Chen, Michael; Waller, Laura
2015-01-01
For centuries, microscopes have had to trade field of view (FOV) for resolution. Recently, a new computational imaging technique, termed Fourier ptychographic microscopy (FPM), circumvents this limit in order to capture gigapixel-scale images having both wide FOV and high resolution. FPM has enormous potential for revolutionizing biomedical microscopy; however, it has until now been limited to fixed samples, since acquisition time is on the order of minutes. Live biological samples are continuously evolving on multiple spatial and temporal scales, which can cause motion blur. Here, we present a Fast FPM method to achieve sub-second capture times for FPM results with 0.8 NA resolution across a 4x objective's FOV. We demonstrate the first FPM quantitative phase results for both growing and confluent in vitro cell cultures. Experiments capture real-time videos of HeLa and human mammary epithelial (MCF10A) cell division and migration and subcellular dynamical phenomena in adult rat neural stem cells.
Shmueli, U; Rabinovich, S; Weiss, G H
1989-06-01
An exact expression is derived for the conditional probability density function of a three-phase invariant and the general result is applied to the space group P1. The expression for the conditional density is given in terms of a sixfold Fourier series. A straightforward numerical evaluation of this series, without further analysis, is extremely time consuming. Much of the present paper is therefore devoted to an exposition of symmetries hidden in the various summations. The computational effort required for the evaluation of the above expression is thereby reduced to manageable proportions in a number of interesting cases. Results of numerical computations of the exact conditional density are given in the second paper in this series. It is also shown that the exact expression for the conditional probability reduces to that given by Cochran [Acta Cryst. (1955), 8, 473-478].
Choi, Yun Seok
2011-01-01
First-arrival picking has long suffered from cycle skipping, especially when the first arrival is contaminated with noise or have experienced complex near surface phenomena. We propose a new algorithm for automatic picking of first arrivals using an approach based on unwrapping the phase. We unwrap the phase by taking the derivative of the Fourier-transformed wavefield with respect to the angular frequency and isolate its amplitude component. To do so, we first apply a damping function to the seismic trace, calculate the derivative of the wavefield with respect to the angular frequency, divide the derivative of wavefield by the wavefield itself, and finally take its imaginary part. We compare our derivative approach to the logarithmic one and show that the derivative approach does not suffer from the phase wrapping or cycle-skipping effects. Numerical examples show that our automatic picking algorithm gives convergent and reliable results for the noise-free synthetic data and noisy field data. © 2011 Society of Exploration Geophysicists.
Atakishiyev, Natig M; Wolf, Kurt Bernardo; 10.3390/sym2031461
2010-01-01
We propose a group-theoretical approach to the generalized oscillator algebra Ak recently investigated in J. Phys. A: Math. Theor. 43 (2010) 115303. The case k > or 0 corresponds to the noncompact group SU(1,1) (as for the harmonic oscillator and the Poeschl-Teller systems) while the case k < 0 is described by the compact group SU(2) (as for the Morse system). We construct the phase operators and the corresponding temporally stable phase eigenstates for Ak in this group-theoretical context. The SU(2) case is exploited for deriving families of mutually unbiased bases used in quantum information. Along this vein, we examine some characteristics of a quadratic discrete Fourier transform in connection with generalized quadratic Gauss sums and generalized Hadamard matrices.
A Novel Model of Interaural Time Difference Based on Spatial Fourier Analysis
Institute of Scientific and Technical Information of China (English)
ZHONG Xiao-Li; XIE Bo-Sun
2007-01-01
Based on the spatial Fourier analysis, a statistical model of the individualized interaural time difference (ITD) is derived from the head-related transfer function database for a Chinese subject. The model reflects the spatial left-right symmetry and front-back asymmetry of ITD. Moreover, by using three anatomical parameters of head and pinna, the model is able to predict individualized ITD in the horizontal plane. Performance of the four subjects outside the database demonstrates that the mean of the total error is less than 20 us, while the lateral performance is inferior to that at other directions.
Fourier and Wavelet Transform Analysis of Pressure Signals during Explosive Boiling
Institute of Scientific and Technical Information of China (English)
YIN Tie-Nan; HUAI Xiu-Lan
2008-01-01
@@ The transient pressure in a liquid-pool during explosive boiling of acetone is measured by a micro-pressure-measuring system.The Fast Fourier transform and continuous wavelet transform methods are applied to investigate the frequency characteristics.The results show that the dominant frequency of the explosive boiling is 0-2MHz,and the bubble cluster formed by numerous tiny bubbles departs twice.Analysis and discussions are also conducted to explain the bubble evolution during the explosive boiling.
Discrete Fourier analysis and wavelets applications to signal and image processing
Broughton, S Allen
2008-01-01
A thorough guide to the classical and contemporary mathematical methods of modern signal and image processing. Discrete Fourier Analysis and Wavelets presents a thorough introduction to the mathematical foundations of signal and image processing. Key concepts and applications are addressed in a thought-provoking manner and are implemented using vector, matrix, and linear algebra methods. With a balanced focus on mathematical theory and computational techniques, this self-contained book equips readers with the essential knowledge needed to transition smoothly from mathematical models to practic
Hanafi, Abdelmalek; Gharbi, Tijani; Cornu, Jean-Yves
2005-07-01
We explore the potential use of the Fourier-transform profilometry technique in in vivo studies of muscular contractions through the variation of muscle-group cross sections. Thanks to a tensorial analysis of the technique, a general expression of its sensitivity vector is established. It allows derivation of the expression of the resolution and the limit condition imposed by the spatial sampling of the fringe pattern. Key parameters that maximize the sensitivity are then simulated. A measurement system is accordingly built up and characterized. It is then successfully applied to the evaluation of the deformation of the forearm muscles during grasping exertions.
Null test fourier domain alignment technique for phase-shifting point diffraction interferometer
Naulleau, Patrick; Goldberg, Kenneth Alan
2000-01-01
Alignment technique for calibrating a phase-shifting point diffraction interferometer involves three independent steps where the first two steps independently align the image points and pinholes in rotation and separation to a fixed reference coordinate system, e.g, CCD. Once the two sub-elements have been properly aligned to the reference in two parameters (separation and orientation), the third step is to align the two sub-element coordinate systems to each other in the two remaining parameters (x,y) using standard methods of locating the pinholes relative to some easy to find reference point.
Energy Technology Data Exchange (ETDEWEB)
Espada, L.; Sanjurjo, M.; Urrejola, S.; Bouzada, F.; Rey, G.; Sanchez, A.
2003-07-01
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.
Modeling and analysis of polarization effects in Fourier domain mode-locked lasers.
Jirauschek, Christian; Huber, Robert
2015-05-15
We develop a theoretical model for Fourier domain mode-locked (FDML) lasers in a non-polarization-maintaining configuration, which is the most widely used type of FDML source. This theoretical approach is applied to analyze a widely wavelength-swept FDML setup, as used for picosecond pulse generation by temporal compression of the sweeps. We demonstrate that good agreement between simulation and experiment can only be obtained by including polarization effects due to fiber bending birefringence, polarization mode dispersion, and cross-phase modulation into the theoretical model. Notably, the polarization dynamics are shown to have a beneficial effect on the instantaneous linewidth, resulting in improved coherence and thus compressibility of the wavelength-swept FDML output.
Fourier transform infrared spectroscopy techniques for the analysis of drugs of abuse
Kalasinsky, Kathryn S.; Levine, Barry K.; Smith, Michael L.; Magluilo, Joseph J.; Schaefer, Teresa
1994-01-01
Cryogenic deposition techniques for Gas Chromatography/Fourier Transform Infrared (GC/FT-IR) can be successfully employed in urinalysis for drugs of abuse with detection limits comparable to those of the established Gas Chromatography/Mass Spectrometry (GC/MS) technique. The additional confidence of the data that infrared analysis can offer has been helpful in identifying ambiguous results, particularly, in the case of amphetamines where drugs of abuse can be confused with over-the-counter medications or naturally occurring amines. Hair analysis has been important in drug testing when adulteration of urine samples has been a question. Functional group mapping can further assist the analysis and track drug use versus time.
Hu, Yong; Peng, Silong; Bi, Yiming; Tang, Liang
2012-12-21
A traditional multivariate calibration transfer method such as piecewise direct standardization (PDS) is usually applied to quantitative analysis. To make the method apply to qualitative analysis of Fourier Transform Infrared spectroscopy (FTIR), we propose an improved calibration transfer method based on the maximum margin criterion (CTMMC). The new method not only considers the spectral changes under different conditions, but also takes into account the geometric characteristics of spectra from different classes, so the transformed spectra from different classes will be separated as far as possible, and this will improve the performance of the follow-up qualitative analysis. A comparative study is provided between the proposed method CTMMC and other traditional calibration transfer methods on two data sets. Experimental results show that the proposed method can achieve better performance than previous methods.
Institute of Scientific and Technical Information of China (English)
Muthuramalingam Uthaya Siva; Mohideen Abdul Badhul Haq; Deivasigamani Selvam; Ganesan Dinesh Babu; Rathinam Bakyaraj
2013-01-01
Objective: To investigate functional groups of toxic spines in stingray by Fourier transform infrared spectroscopic analysis.Methods:sephen were centrifuged at 6000 r/min for 10 min. The supernatant was collected and preserved separately in methanol, ethanol, chloroform, acetone (1:2) and then soaked in the mentioned solvents for 48 h. Then extracts were filtered and used for Fourier transform infrared spectroscopic analysis.Results:The venom extract of Himantura gerrardi, Himantura imbricata and Pastinachus and random coiled secondary structure. The presence of O-H stretch, C=O stretch, C-H stretch, N-H deformation, O-H deformation and C-O stretch in the sample aligned with standard bovine serum albumin. The influence of functional groups within the molecule was because of the impact of preferred spatial orientation, chemical and physical interaction on the molecule. In conclusion, compared to bovine serum albumin, Himantura imbricata consists of two C=O stretch, are involved in the hydrogen bonding that takes place between the different elements of secondary structure.Conclusions:The results identified that the presence of free amino acids and protein having β-sheet medicine not available for treatment against injuries causing stingray. Therefore, it's the baseline study, to motivate further process and produce effective antibiotics. The venom of poisonous animals has been extensively studied, since standard.
Directory of Open Access Journals (Sweden)
Muthuramalingam Uthaya Siva
2013-10-01
Full Text Available Objective: To investigate functional groups of toxic spines in stingray by Fourier transform infrared spectroscopic analysis. Methods: The venom extract of Himantura gerrardi, Himantura imbricata and Pastinachus sephen were centrifuged at 6 000 r/min for 10 min. The supernatant was collected and preserved separately in methanol, ethanol, chloroform, acetone (1:2 and then soaked in the mentioned solvents for 48 h. Then extracts were filtered and used for Fourier transform infrared spectroscopic analysis. Results: The results identified that the presence of free amino acids and protein having β-sheet and random coiled secondary structure. The presence of O-H stretch, C=O stretch, C-H stretch, N-H deformation, O-H deformation and C-O stretch in the sample aligned with standard bovine serum albumin. The influence of functional groups within the molecule was because of the impact of preferred spatial orientation, chemical and physical interaction on the molecule. In conclusion, compared to bovine serum albumin, Himantura imbricata consists of two C=O stretch, are involved in the hydrogen bonding that takes place between the different elements of secondary structure. Conclusions: The venom of poisonous animals has been extensively studied, since standard medicine not available for treatment against injuries causing stingray. Therefore, it's the baseline study, to motivate further process and produce effective antibiotics.
Giant magnetoimpedance modelling using Fourier analysis in soft magnetic amorphous wires
Gómez-Polo, C.; Knobel, M.; Pirota, K. R.; Vázquez, M.
2001-06-01
In this work, the Fourier analysis is employed to investigate the giant magnetoimpedance (GMI) effect in a FeCoSiB amorphous wire with vanishing magnetostriction. In order to modify the initial quenched-in anisotropy, pieces 8 cm in length were submitted to Joule heating treatments below the corresponding Curie point. The induced circumferential anisotropy determines the field evolution of the electrical impedance of the sample upon the application of an axial magnetic field. The experimental results are interpreted within the framework of the classical electrodynamical theory, where a simple rotational model is used to estimate the circular magnetization process of the sample. The mean value of the circumferential permeability is obtained through Fourier analysis of the time derivative of the estimated circular magnetization. Moreover, the existence of a second harmonic component of the GMI voltage is also experimentally detected. Its amplitude sensitively evolves with the axial DC magnetic field and its appearance is associated to an asymmetry in the circular magnetization process.
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
Error analysis for satellite gravity field determination based on two-dimensional Fourier methods
Cai, Lin; Hsu, Houtse; Gao, Fang; Zhu, Zhu; Luo, Jun
2012-01-01
The time-wise and space-wise approaches are generally applied to data processing and error analysis for satellite gravimetry missions. But both the approaches, which are based on least-squares collocation, address the whole effect of measurement errors and estimate the resolution of gravity field models mainly from a numerical point of indirect view. Moreover, requirement for higher accuracy and resolution gravity field models could make the computation more difficult, and serious numerical instabilities arise. In order to overcome the problems, this study focuses on constructing a direct relationship between power spectral density of the satellite gravimetry measurements and coefficients of the Earth's gravity potential. Based on two-dimensional Fourier transform, the relationship is analytically concluded. By taking advantage of the analytical expression, it is efficient and distinct for parameter estimation and error analysis of missions. From the relationship and the simulations, it is analytically confir...
Institute of Scientific and Technical Information of China (English)
CAO Gan; TAN Zhong-wen; LIANG Ji-nan; LONG Yong-hui; ZHOU Xue-qiu
2003-01-01
With the technique of Fourier transform near infrared (FT-NIR) spectroscopy, the calibration models for quantitative analysis of sucrose and polarization in sugarcane juice were developed by using transmission mode and calibrating with partial least square (PIS) algorithm. The determination coefficients (R2)of the predicted models for sucrose and polarization in juice were 0. 9980 and 0. 9979 respectively; the root mean square errors of cross validation (RMSECV) were 0. 143 and 0. 155% for sucrose and polarization in juice respectively. The predictive errors measured by FT-NIR were close to those by routine laboratory methods. The results demonstrated that the FT-NIR methods had high accuracy and they were able to replace the routine laboratory analysis. It was also demonstrated that as a rapid and accurate measurement, the FT-NIR technique had potential applications in quality control of mill sugarcane, establishment of payment system based on sugarcane quality, and selection of clones in sugarcane breeding.
Fourier mode analysis of slab-geometry transport iterations in spatially periodic media
Energy Technology Data Exchange (ETDEWEB)
Larsen, E; Zika, M
1999-04-01
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.
Fourier mode analysis of slab-geometry transport iterations in spatially periodic media
Energy Technology Data Exchange (ETDEWEB)
Larsen, E W; Zika, M R
1999-05-07
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.
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.
Marica, Aurora
2014-01-01
This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quad...
Fourier Photometric Analysis of Isolated Galaxies in the Context of the AMIGA Project
Durbala, A; Sulentic, J W; Verdes-Montenegro, L
2009-01-01
We present the results of a Fourier photometric decomposition of a representative sample of ~100 isolated Sb-Sc CIG/AMIGA galaxies. It complements the analysis presented in Durbala et al. 2008 for the same sample by allowing a description of the spiral structure morphology. We estimate dynamical measures like torque strength for bar and spiral, and also the total nonaxisymmetric torque. We explore the interplay between the spiral and bar components of galaxies. Both the length and the contrast of the Fourier bars decrease along the morphological sequence Sb-Sbc-Sc, with bars in earlier types being longer and showing higher contrast. Bars of Sb galaxies are ~3x longer than bars in Sc types. We find that longer bars are not necessarily stronger (as quantified by the torque Q_{b} measure), but longer bars show a higher contrast, in very good agreement with theoretical predictions. Our data suggests that bar and spiral components are rather independent in the sense that the torque strengths of the two components ...
Laremore, Tatiana N; Leach, Franklin E; Amster, I Jonathan; Linhardt, Robert J
2011-08-15
A mixture of glycosaminoglycan (GAG) chains from a plasma proteoglycan bikunin was fractionated using native, continuous-elution polyacrylamide gel electrophoresis, and the resulting fractions were analyzed by electrospray ionization Fourier transform mass spectrometry (ESI FTMS). Molecular mass analysis of the intact GAG afforded information about the length and composition of GAG chains in the mixture. Ambiguity in the interpretation of the intact GAG mass spectra was eliminated by conducting an additional experiment in which the GAG chains of known molecular mass were treated with a GAG-degrading enzyme, chondroitinase ABC, and the digestion products were analyzed by ESI FTMS. The plasma bikunin GAG chains consisted predominantly of odd number of saccharides, although few chains consisting of even number of saccharides were also detected. Majority of the analyzed chains were tetrasulfated or pentasulfated and comprised by 29 to 41 monosaccharides.
[Monitoring and analysis of urban ozone using open path Fourier transform infrared spectrometry].
Li, Sheng; Gao, Min-guang; Zhang, Yu-jun; Liu, Wen-qing; Xu, Liang; Tong, Jing-jing; Cheng, Si-yang; Jin, Ling; Wei, Xiu-li; Wang, Ya-ping; Chen, Jun
2011-12-01
An ozone monitoring system was developed by the method of open path Fourier transform infrared (OP-FTIR) spectrometry based on our FTIR spectrometer. In order to improve measurement precision and detection limit, the quantitative analysis was completed to get ozone concentration by combining synthetic background spectrum method which uses information from HITRAN database and instrumental line shape, and nonlinear least squares (NLLSQ) method. The measurement methods for system detection limit were discussed and the result is 1.42 nmol x mol(-1) with sixteen times averages. The authors developed continuous monitoring experiments in the suburban area of Hefei. For the day and month measurement results, the authors analyzed their variations with the generation sources. The result has shown that this system is reliable and precise and can be used as a new device and method for national ozone monitoring.
Huck-Pezzei, V A; Pallua, J D; Pezzei, C; Bittner, L K; Schönbichler, S A; Abel, G; Popp, M; Bonn, G K; Huck, C W
2012-10-01
In the present study, Fourier transform infrared (FTIR) imaging and data analysis methods were combined to study morphological and molecular patterns of St. John's wort (Hypericum perforatum) in detail. For interpretation, FTIR imaging results were correlated with histological information gained from light microscopy (LM). Additionally, we tested several evaluation processes and optimized the methodology for use of complex FTIR microscopic images to monitor molecular patterns. It is demonstrated that the combination of the used spectroscopic method with LM enables a more distinct picture, concerning morphology and distribution of active ingredients, to be gained. We were able to obtain high-quality FTIR microscopic imaging results and to distinguish different tissue types with their chemical ingredients.
Rohman, A; Man, Yb Che; Sismindari
2009-10-01
Today, virgin coconut oil (VCO) is becoming valuable oil and is receiving an attractive topic for researchers because of its several biological activities. In cosmetics industry, VCO is excellent material which functions as a skin moisturizer and softener. Therefore, it is important to develop a quantitative analytical method offering a fast and reliable technique. Fourier transform infrared (FTIR) spectroscopy with sample handling technique of attenuated total reflectance (ATR) can be successfully used to analyze VCO quantitatively in cream cosmetic preparations. A multivariate analysis using calibration of partial least square (PLS) model revealed the good relationship between actual value and FTIR-predicted value of VCO with coefficient of determination (R2) of 0.998.
Fourier based analysis of the acoustic attenuation length in ice with SPATS
Energy Technology Data Exchange (ETDEWEB)
Schunck, Matthias; Bissok, Martin; Laihem, Karim; Wiebusch, Christopher [RWTH, Aachen (Germany)
2009-07-01
The SPATS project (South Pole Acoustic Test Setup) investigates the feasibility of acoustic neutrino detection at extremely high energies at the site of the IceCube detector at South Pole. An important prerequisite is a small attenuation of the sound waves generated by neutrino interactions via the thermoacoustic effect. To measure the attenuation length, a retrievable acoustic pinger was lowered into the open IceCube holes before the deployment of the optical strings while the SPATS sensors were taking data. The basic idea of our study is to analyze the amplitudes of the Fourier-transformed signals as a function of distance and frequency. The method of the analysis is motivated, first results are given and the systematic uncertainties are discussed.
Zhang, Xiaoxing; Liu, Heng; Ren, Jiangbo; Li, Jian; Li, Xin
2015-02-05
Gas-insulated switchgear (GIS) internal SF6 gas produces specific decomposition components under partial discharge (PD). By detecting these characteristic decomposition components, such information as the type and level of GIS internal insulation deterioration can be obtained effectively, and the status of GIS internal insulation can be evaluated. SF6 was selected as the background gas for Fourier transform infrared spectroscopy (FTIR) detection in this study. SOF2, SO2F2, SO2, and CO were selected as the characteristic decomposition components for system analysis. The standard infrared absorption spectroscopy of the four characteristic components was measured, the optimal absorption peaks were recorded and the corresponding absorption coefficient was calculated. Quantitative detection experiments on the four characteristic components were conducted. The volume fraction variation trend of four characteristic components at different PD time were analyzed. And under five different PD quantity, the quantitative relationships among gas production rate, PD time, and PD quantity were studied.
Singular Spectrum Analysis: A Note on Data Processing for Fourier Transform Hyperspectral Imagers.
Rafert, J Bruce; Zabalza, Jaime; Marshall, Stephen; Ren, Jinchang
2016-09-01
Hyperspectral remote sensing is experiencing a dazzling proliferation of new sensors, platforms, systems, and applications with the introduction of novel, low-cost, low-weight sensors. Curiously, relatively little development is now occurring in the use of Fourier transform (FT) systems, which have the potential to operate at extremely high throughput without use of a slit or reductions in both spatial and spectral resolution that thin film based mosaic sensors introduce. This study introduces a new physics-based analytical framework called singular spectrum analysis (SSA) to process raw hyperspectral imagery collected with FT imagers that addresses some of the data processing issues associated with the use of the inverse FT. Synthetic interferogram data are analyzed using SSA, which adaptively decomposes the original synthetic interferogram into several independent components associated with the signal, photon and system noise, and the field illumination pattern.
Nagornov, Konstantin O; Gorshkov, Mikhail V; Kozhinov, Anton N; Tsybin, Yury O
2014-09-16
A multielectrode ion cyclotron resonance (ICR) cell, herein referred to as the "4X cell", for signal detection at the quadruple frequency multiple was implemented and characterized on a commercial 10 T Fourier transform ICR mass spectrometer (FT-ICR MS). Notably, with the 4X cell operating at a 10 T magnetic field we achieved a 4-fold increase in MS acquisition rate per unit of resolving power for signal detection periods typically employed in FTMS, viz., shorter than 6 s. Effectively, the obtained resolution performance represents the limit of the standard measurement principle with dipolar signal detection and FT signal processing at an equivalent magnetic field of 40 T. In other words, the achieved resolving powers are 4 times higher than those provided by 10 T FT-ICR MS with a standard ICR cell. For example, resolving powers of 170,000 and 70,000 were obtained in magnitude-mode Fourier spectra of 768 and 192 ms apodized transient signals acquired for a singly charged fluorinated phosphazine (m/z 1422) and a 19-fold charged myoglobin (MW 16.9 kDa), respectively. In peptide analysis, the baseline-resolved isotopic fine structures were obtained with as short as 768 ms transients. In intact protein analysis, the average resolving power of 340,000 across the baseline-resolved (13)C isotopic pattern of multiply charged ions of bovine serum albumin was obtained with 1.5 s transients. The dynamic range and the mass measurement accuracy of the 4X cell were found to be comparable to the ones obtained for the standard ICR cell on the same mass spectrometer. Overall, the reported results validate the advantages of signal detection at frequency multiples for increased throughput in FT-ICR MS, essential for numerous applications with time constraints, including proteomics.
Group-level spatial independent component analysis of Fourier envelopes of resting-state MEG data.
Ramkumar, Pavan; Parkkonen, Lauri; Hyvärinen, Aapo
2014-02-01
We developed a data-driven method to spatiotemporally and spectrally characterize the dynamics of brain oscillations in resting-state magnetoencephalography (MEG) data. The method, called envelope spatial Fourier independent component analysis (eSFICA), maximizes the spatial and spectral sparseness of Fourier energies of a cortically constrained source current estimate. We compared this method using a simulated data set against 5 other variants of independent component analysis and found that eSFICA performed on par with its temporal variant, eTFICA, and better than other ICA variants, in characterizing dynamics at time scales of the order of minutes. We then applied eSFICA to real MEG data obtained from 9 subjects during rest. The method identified several networks showing within- and cross-frequency inter-areal functional connectivity profiles which resemble previously reported resting-state networks, such as the bilateral sensorimotor network at ~20Hz, the lateral and medial parieto-occipital sources at ~10Hz, a subset of the default-mode network at ~8 and ~15Hz, and lateralized temporal lobe sources at ~8Hz. Finally, we interpreted the estimated networks as spatiospectral filters and applied the filters to obtain the dynamics during a natural stimulus sequence presented to the same 9 subjects. We observed occipital alpha modulation to visual stimuli, bilateral rolandic mu modulation to tactile stimuli and video clips of hands, and the temporal lobe network modulation to speech stimuli, but no modulation of the sources in the default-mode network. We conclude that (1) the proposed method robustly detects inter-areal cross-frequency networks at long time scales, (2) the functional relevance of the resting-state networks can be probed by applying the obtained spatiospectral filters to data from measurements with controlled external stimulation.
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.
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.
An improved model for whole genome phylogenetic analysis by Fourier transform.
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
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.
Fourier-Domain Analysis of Hydriding Kinetics Using Pneumato-Chemical Impedance Spectroscopy
Directory of Open Access Journals (Sweden)
P. Millet
2007-10-01
Full Text Available Analysis of phase transformation processes observed in hydrogen absorbing materials (pure metals, alloys, or compounds is still a matter of active research. Using pneumato-chemical impedance spectroscopy (PIS, it is now possible to analyze the mechanism of hydriding reactions induced by the gas phase. Experimental impedance diagrams, measured on activated LaNi5 in single- and two-phase domains, are reported in this paper. It is shown that their shape is mostly affected by the slope of the isotherm at the measurement point. By considering the details of the multistep reaction paths involved in the hydriding reaction, model impedance equations have been derived for single- and two-phase domains, and fitted to experimental impedance diagrams. The possibility of separately measuring surface and phase transformation resistances, hydrogen diffusion coefficient, and hydrogen solubility in each composition domain is discussed.
Hourani, Nadim
2013-10-01
Rationale Polycyclic aromatic sulfur heterocycles (PASHs) are detrimental species for refining processes in petroleum industry. Current mass spectrometric Methods that determine their composition are often preceded by derivatization and dopant addition approaches. Different ionization Methods have different impact on the molecular assignment of complex PASHs. The analysis of such species under atmospheric pressure chemical ionization (APCI) is still considered limited due to uncontrolled ion generation with low- and high-mass PASHs. Methods The ionization behavior of a model mixture of five selected PASH standards was investigated using an APCI source with nitrogen as the reagent gas. A complex thiophenic fraction was separated from a vacuum gas oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same ionization pattern was observed for the real thiophenic sample. It was found that S1 class species were the major sulfur-containing species found in the VGO sample. These species indicated the presence of alkylated benzothiophenic (BT), dibenzothiophenic (DBT) and benzonaphthothiophenic (BNT) series that were detected by APCI-FTICR MS. CONCLUSIONS This study provides an established APCI-FTICR MS method for the analysis of complex PASHs. PASHs were detected without using any derivatization and without fragmentation. The method can be used for the analysis of S-containing crude oil samples. © 2013 John Wiley & Sons, Ltd.
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.
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
Energy Technology Data Exchange (ETDEWEB)
Anderson, Timothy J. [Ames Laboratory; Ai, Yongfeng [Iowa State University; Jones, Roger W. [Ames Laboratory; Houk, Robert S. [Ames Laboratory; Jane, Jay-lin [Iowa State University; Zhao, Yinsheng [Iowa State University; Birt, Diane F. [Iowa State University; McClelland, John F. [Ames Laboratory
2013-01-29
Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) qualitatively and quantitatively measured resistant starch (RS) in rat cecal contents. Fisher 344 rats were fed diets of 55% (w/w, dry basis) starch for 8 weeks. Cecal contents were collected from sacrificed rats. A corn starch control was compared against three RS diets. The RS diets were high-amylose corn starch (HA7), HA7 chemically modified with octenyl succinic anhydride, and stearic-acid-complexed HA7 starch. To calibrate the FTIR-PAS analysis, samples from each diet were analyzed using an enzymatic assay. A partial least-squares cross-validation plot generated from the enzymatic assay and FTIR-PAS spectral results for starch fit the ideal curve with a R2 of 0.997. A principal component analysis plot of components 1 and 2 showed that spectra from diets clustered significantly from each other. This study clearly showed that FTIR-PAS can accurately quantify starch content and identify the form of starch in complex matrices.
Fourier Transform Infrared Spectroscopy (FTIR for MUN analysis in normal and adulterated Milk
Directory of Open Access Journals (Sweden)
M.C.P.P. Oliveira
2012-10-01
Full Text Available The objective of this study was to evaluate the CombiScope FTIR equipment based on Fourier Transform Infrared methodology (FTIR, to assess the content of milk urea nitrogen (MUN in Brazil. Repeatability and reproducibility of CombiScopeTM FTIR (Delta Instruments, and comparison with an enzymatic automated method (Chemspec® 150; Bentley Instruments were tested to measure raw milk urea nitrogen (MUN. Additionally, MUN levels stability after storage of raw milk samples at 4ºC, and 20ºC for up to 15 days, and capability and precision to detect extraneous urea added as an adulterant to the milk were evaluated by FTIR equipment. There was a high correlation coefficient for the analysis of MUN by FTIR equipment, when compared with the automated enzymatic method, with no significant difference between both. MUN concentration in raw milk remained stable at temperatures of 4ºC for up to 15 days of storage, but after 3 days of storage at 20ºC there was an increase in the MUN levels. The CombiScope FTIR equipment proved to be a reliable method for analysis of MUN content in raw milk. However, results for MUN were not linear with the amount of extraneous urea added to raw milk, having a significant difference for samples when 40mg/dL of urea was added to milk.
Directory of Open Access Journals (Sweden)
Lia Campos Lemes
Full Text Available Abstract Introduction Fourier-transform infrared (FT-IR spectroscopy is a technique with great potential for body fluids analyses. The aim of this study was to examine the impact of session training on cortisol concentrations in rugby players by means of infrared analysis of serum. Methods Blood collections were performed pre, post and 24 hours after of rugby training sessions. Serum cortisol was analyzed by FT-IR spectroscopy and chemiluminescent immunoassay. Results There was a significant difference between the integrated area, in the region of 1180-1102 cm-1, of the spectra for pre, post and post 24 h serums. The cortisol concentration obtained by chemiluminescent immunoassay showed no significant difference between pre, post and post 24 h. Positive correlations were obtained between the techniques (r = 0.75, post (r = 0.83 and post 24 h (r = 0.73. Conclusion The results showed no increase in cortisol levels of the players after the training sessions, as well as positive correlations indicating that FT-IR spectroscopy have produced promising results for the analysis of serum for diagnosis of stress.
Ambekar Ramachandra Rao, Raghu; Mehta, Monal R.; Toussaint, Kimani C., Jr.
2010-02-01
We demonstrate the use of Fourier transform-second-harmonic generation (FT-SHG) imaging of collagen fibers as a means of performing quantitative analysis of obtained images of selected spatial regions in porcine trachea, ear, and cornea. Two quantitative markers, preferred orientation and maximum spatial frequency are proposed for differentiating structural information between various spatial regions of interest in the specimens. The ear shows consistent maximum spatial frequency and orientation as also observed in its real-space image. However, there are observable changes in the orientation and minimum feature size of fibers in the trachea indicating a more random organization. Finally, the analysis is applied to a 3D image stack of the cornea. It is shown that the standard deviation of the orientation is sensitive to the randomness in fiber orientation. Regions with variations in the maximum spatial frequency, but with relatively constant orientation, suggest that maximum spatial frequency is useful as an independent quantitative marker. We emphasize that FT-SHG is a simple, yet powerful, tool for extracting information from images that is not obvious in real space. This technique can be used as a quantitative biomarker to assess the structure of collagen fibers that may change due to damage from disease or physical injury.
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.
Cai, Xi-lan; Wu, Guo-ping
2007-12-01
In the present paper, using Fourier transform infrared (FTIR) absorption spectrometry, the characteristic peaks of fingerprint infrared spectra of heroin samples from different routes were identified with clustering analysis successfully. It is a very fast, simple and reliable method. That is to say, a new method for the discrimination of heroin seizured from different routes is provided.
Directory of Open Access Journals (Sweden)
Runze Zhang
2016-01-01
Full Text Available This paper presents a free vibration analysis of three-dimensional coupled beams with arbitrary coupling angle using an improved Fourier method. The displacement and rotation of the coupled beams are represented by the improved Fourier series which consisted of Fourier cosine series and closed-form auxiliary functions. The coupling and boundary conditions are accomplished by setting coupling and boundary springs and assigning corresponding stiffness values to the springs. Modal parameters are determined through the application of Rayleigh-Ritz procedure to the system energy formulation. The accuracy and convergence of the present method are demonstrated by finite element method (FEM result. Investigation on vibration of the propulsion shafting structure shows the extensive applicability of present method. The studies on the vibration suppression devices are also reported.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The mass spectra of five peptides with biological activities are reported. All mass spectra were recorded using a 4.7-T Fourier transform ion cyclotron resonance mass spectrometer equipped with an external electrospray source. The accurate molecular weights for the five peptides prepared by solid phase synthesis were measured as 1765.9013, 1063.5420, 1092.5254, 820.3804 and 1078.5193, respectively. All the data were obtained with the external calibration. Differences between observed and theoretical monoisotopic molecular weights were in the (0.2-1.0)×10-6 range. The complete primary sequence for the five polypep-tides were determined using the method of in-source electro-spray ionization/collision induced dissociation (ESI/CID). All the intact y series ions and b series ions were obtained from various peptides respectively, thus determining the sequences of the five polypeptides. We found that the measured accura-te molecular mass of sample 4 was not in agreement with that expected from the planned synthetic peptide. The se-quences of sample 4 were determined through analysis. The corresponding accurate masses of b series ions and y series ions were gained, which proved that it was correct to re-determine the sequences.
Hamidian, M. H.; Firmo, I. A.; Fujita, K.; Mukhopadhyay, S.; Orenstein, J. W.; Eisaki, H.; Uchida, S.; Lawler, M. J.; Kim, E.-A.; Davis, J. C.
2012-05-01
Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). By studying the Bragg peaks in Fourier transforms of electronic structure images and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit-cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such a Bragg-peak Fourier analysis. Exemplary of this challenge is the high-temperature superconductor Bi2Sr2CaCu2O8+δ for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a ˜2%(2π) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unit-cell rotational symmetry breaking at the CuO2 plane (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for the Bragg-peak Fourier analysis of intra-unit-cell symmetry.
Theoretical Analysis and Experimental Evidence of NonFourier Heat Conduction Behavior
Institute of Scientific and Technical Information of China (English)
蒋方明; 刘登瀛; 蔡睿贤
2001-01-01
This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.
Hogan, J D; Laude, D A
1990-11-01
The superior sensitivity , dynamic range, and mass measurement accuracy of suspended trapping pulse sequences for gas chromatography combined with Fourier transform mass spectrometry (GC/FTMS) separations of complex organic mixtures is demonstrated. By combining intense ionization conditions with a suspended trapping event prior to detection the working range of the trapped ion cell is increased by 10(3) . Improved detection limits are shown for the GC/FTMS separation of a peppermint oil, with the suspended trapping total ion chromatogram yielding 28 peaks, compared with 15 with a conventional trapping pulse sequence. A fivefold to fifteenfold improvement in signal-to-noise for suspended trapping measurements is also demonstrated with comparison spectra from separations of an unleaded gasoline sample. Suspended trapping spectra show little mass discrimination when an external ion reservoir is used, and chromatographic peak heights differ from conventional spectra by less than 30% if the initial ion population is within the space charge limit of the cell. Finally, average wide band mass measurement errors for components differing in concentration by several orders of magnitude are improved by a factor of 6 to 20 with suspended trapping compared with conventional trapping . For example, average errors of 8.7 ppm are obtained for a suspended trapping GC/FTMS separation of peppermint oil from a single calibration table in which the analysis is perfonned in the absence of calibrant.
Fourier spectral-based modal curvature analysis and its application to damage detection in beams
Yang, Zhi-Bo; Radzienski, Maciej; Kudela, Pawel; Ostachowicz, Wieslaw
2017-02-01
In this paper, a simple Fourier spectral-based method is proposed to calculate the modal curvature (MC) of beams instead of the traditional central difference method. Based on the present method, damages in beam-like structures are localized. The present method provides an alternative selection to estimate MC in damage detection. There are two advantages of the present method. Firstly, the spectral calculation of spatial derivatives is conducted globally, which provides the suppression for noise. In addition, signal processing in the wavenumber domain provides an alternative choice for spatial filtering for mode shapes. Secondly, the proposed method provides a precise estimation of the MC which is related to original definition. With the absence of numerical derivative, the estimated results can be more stable and robust. Statistical analysis is conducted to show the effectiveness and noise immunity of the proposed method. In order to obtain the better identification, the MC calculated by the proposed method is employed as the input of continuous wavelet transform, and then the hybrid method is generated. The validations of the present method and comparison with the traditional central difference method are numerically and experimentally demonstrated.
Vrbanović Mijatović, Vilena; Šerman, Ljiljana; Gamulin, Ozren
2017-02-21
Pulmonary surfactant, consisting primarily of phospholipids and four surfactant-specific proteins, is among the first structures that is exposed to inhalation anesthetics. Consequently, changes of pulmonary surfactant due to this exposure could cause respiratory complications after long anesthetic procedures. Fourier transform infrared (FTIR) spectroscopy was used to explore the effects of two inhalation anesthetics, sevoflurane and isoflurane, on a commercially available pulmonary surfactant. The research was primarily focused on the effect of anesthetics on the lipid component of the surfactant. Four different concentrations of anesthetics were added, and the doses were higher from the low clinical doses typically used. Recorded spectra were analyzed using principal component analysis, and the Student's t-test was performed to confirm the results. The exposure to both anesthetics induced similar changes, consistent with the increase of the anesthetic concentration. The most pronounced effect was on the hydrophilic head group of phospholipids, which is in agreement with the disruption of the hydrogen bond, caused by the anesthetics. A change in the band intensities of CH2 stretching vibrations, indicative of a disordering effect of anesthetics on the hydrophobic tails of phospholipids, was also observed. Changes induced by isoflurane appear to be more pronounced than those induced by sevoflurane. Furthermore, our results suggest that FTIR spectroscopy is a promising tool in studying anesthetic effects on pulmonary surfactant.
Kandpal, Lalit Mohan; Tewari, Jagdish; Gopinathan, Nishanth; Stolee, Jessica; Strong, Rick; Boulas, Pierre; Cho, Byoung-Kwan
2017-09-01
Determination of the content uniformity, assessed by the amount of an active pharmaceutical ingredient (API), and hardness of pharmaceutical materials is important for achieving a high-quality formulation and to ensure the intended therapeutic effects of the end-product. In this work, Fourier transform near infrared (FT-NIR) spectroscopy was used to determine the content uniformity and hardness of a pharmaceutical mini-tablet and standard tablet samples. Tablet samples were scanned using an FT-NIR instrument and tablet spectra were collected at wavelengths of 1000-2500 nm. Furthermore, multivariate analysis was applied to extract the relationship between the FT-NIR spectra and the measured parameters. The results of FT-NIR spectroscopy for API and hardness prediction were as precise as the reference high-performance liquid chromatography and mechanical hardness tests. For the prediction of mini-tablet API content, the highest coefficient of determination for the prediction (R2p) was found to be 0.99 with a standard error of prediction (SEP) of 0.72 mg. Moreover, the standard tablet hardness measurement had a R2p value of 0.91 with an SEP of 0.25 kg. These results suggest that FT-NIR spectroscopy is an alternative and accurate nondestructive measurement tool for the detection of the chemical and physical properties of pharmaceutical samples.
Verification of the helioseismic Fourier-Legendre analysis for meridional flow measurements
Roth, Markus; Hartlep, Thomas
2016-01-01
Measuring the Sun's internal meridional flow is one of the key issues of helioseismology. Using the Fourier-Legendre analysis is a technique for addressing this problem. We validate this technique with the help of artificial helioseismic data. The analysed data set was obtained by numerically simulating the effect of the meridional flow on the seismic wave field in the full volume of the Sun. In this way, a 51.2-hour long time series was generated. The resulting surface velocity field is then analyzed in various settings: Two $360^\\circ \\times 90^\\circ$ halfspheres, two $120^\\circ \\times 60^\\circ$ patches on the front and farside of the Sun (North and South, respectively) and two $120^\\circ \\times 60^\\circ$ patches on the northern and southern frontside only. We compare two possible measurement setups: observations from Earth and from an additional spacecraft on the solar farside, and observations from Earth only, in which case the full information of the global solar oscillation wave field was available. We ...
Energy Technology Data Exchange (ETDEWEB)
Dishberger, Debra McLean
1983-04-01
This report represents a continuation of gravity work in the Cascade Mountains of Washington supported by the Division of Geology and Earth Resources since 1974. The purpose of this research has been collection of baseline gravity data for use in geothermal resource evaluation. Results of the Division's gravity studies to date are given in Danes and Phillips (1983a, 1983b). One of the problems encountered when analyzing gravity data is distinguishing between those parts of the data that represent geologic structures of interest, and those that do not. In many cases, the features of interest are relatively small, near-surface features, such as those sought in mineral, petroleum, or geothermal exploration. Gravity anomalies caused by such structures may be distorted or masked by anomalies caused by larger, deeper geologic structures. Gravity anomalies caused by relatively shallow, small geologic structures are termed residual anomalies. Those due to broad, deep-seated features can be described as regional anomalies. The purpose of this report is to describe a Fourier analysis method for separating residual and regional gravity anomalies from a complete Bouguer gravity anomaly field. The technique has been applied to gravity data from the Southern Cascade Mountains, Washington. Residual gravity anomaly maps at a scale of 1:250,000 are presented for various regional wavelength filters, and a power spectrum of the frequency components in the South Cascade gravity data is displayed. No attempt is made to interpret the results of this study in terms of geologic structures.
Mello, Maria Luiza S; Vidal, Benedicto C
2014-06-01
The Fourier transform-infrared (FT-IR) signature of dry samples of DNA and DNA-polypeptide complexes, as studied by IR microspectroscopy using a diamond attenuated total reflection (ATR) objective, has revealed important discriminatory characteristics relative to the PO2(-) vibrational stretchings. However, DNA IR marks that provide information on the sample's richness in hydrogen bonds have not been resolved in the spectral profiles obtained with this objective. Here we investigated the performance of an "all reflecting objective" (ARO) for analysis of the FT-IR signal of hydrogen bonds in DNA samples differing in base richness types (salmon testis vs calf thymus). The results obtained using the ARO indicate prominent band peaks at the spectral region representative of the vibration of nitrogenous base hydrogen bonds and of NH and NH2 groups. The band areas at this spectral region differ in agreement with the DNA base richness type when using the ARO. A peak assigned to adenine was more evident in the AT-rich salmon DNA using either the ARO or the ATR objective. It is concluded that, for the discrimination of DNA IR hydrogen bond vibrations associated with varying base type proportions, the use of an ARO is recommended.
Prudhomme, G.; Berthe, L.; Bénier, J.; Bozier, O.; Mercier, P.
2017-01-01
Photonic Doppler Velocimetry is a plug-and-play and versatile diagnostic used in dynamic physic experiments to measure velocities. When signals are analyzed using a Short-Time Fourier Transform, multiple velocities can be distinguished: for example, the velocities of moving particle-cloud appear on spectrograms. In order to estimate the back-scattering fluxes of target, we propose an original approach "PDV Radiometric analysis" resulting in an expression of time-velocity spectrograms coded in power units. Experiments involving micron-sized particles raise the issue of detection limit; particle-size limit is very difficult to evaluate. From the quantification of noise sources, we derive an estimation of the spectrogram noise leading to a detectivity limit, which may be compared to the fraction of the incoming power which has been back-scattered by the particle and then collected by the probe. This fraction increases with their size. At last, some results from laser-shock accelerated particles using two different PDV systems are compared: it shows the improvement of detectivity with respect to the Effective Number of Bits (ENOB) of the digitizer.
Portable Fourier Transform Spectroscopy for Analysis of Surface Contamination and Quality Control
Pugel, Diane
2012-01-01
Progress has been made into adapting and enhancing a commercially available infrared spectrometer for the development of a handheld device for in-field measurements of the chemical composition of various samples of materials. The intent is to duplicate the functionality of a benchtop Fourier transform infrared spectrometer (FTIR) within the compactness of a handheld instrument with significantly improved spectral responsivity. Existing commercial technology, like the deuterated L-alanine triglycine sulfide detectors (DLATGS), is capable of sensitive in-field chemical analysis. This proposed approach compares several subsystem elements of the FTIR inside of the commercial, non-benchtop system to the commercial benchtop systems. These subsystem elements are the detector, the preamplifier and associated electronics of the detector, the interferometer, associated readout parameters, and cooling. This effort will examine these different detector subsystem elements to look for limitations in each. These limitations will be explored collaboratively with the commercial provider, and will be prioritized to meet the deliverable objectives. The tool design will be that of a handheld gun containing the IR filament source and associated optics. It will operate in a point-and-shoot manner, pointing the source and optics at the sample under test and capturing the reflected response of the material in the same handheld gun. Data will be captured via the gun and ported to a laptop.
Bhat, Gopalakrishna K.
1994-10-01
A fringe analysis technique, which makes use of the spatial filtering property of the Fourier transform method, for the elimination of random impulsive noise in the wrapped phase maps obtained using the phase stepping technique, is presented. Phase noise is converted into intensity noise by transforming the wrapped phase map into a continuous fringe pattern inside the digital image processor. Fourier transform method is employed to filter out the intensity noise and recover the clean wrapped phase map. Computer generated carrier fringes are used to preserve the sign information. This technique makes the two dimensional phase unwrapping process less involved, because it eliminates the local phase fluctuations, which act as pseudo 2π discontinuities. The technique is applied for the elimination of noise in a phase map obtained using electro-optic holography.
Long, C. L.
1991-02-01
Multivariate calibration techniques can reduce the time required for routine testing and can provide new methods of analysis. Multivariate calibration is commonly used with near infrared reflectance analysis (NIRA) and Fourier transform infrared (FTIR) spectroscopy. Two feasibility studies were performed to determine the capability of NIRA, using multivariate calibration techniques, to perform analyses on the types of samples that are routinely analyzed at this laboratory. The first study performed included a variety of samples and indicated that NIRA would be well-suited to perform analyses on selected materials properties such as water content and hydroxyl number on polyol samples, epoxy content on epoxy resins, water content of desiccants, and the amine values of various amine cure agents. A second study was performed to assess the capability of NIRA to perform quantitative analysis of hydroxyl numbers and water contents of hydroxyl-containing materials. Hydroxyl number and water content were selected for determination because these tests are frequently run on polyol materials and the hydroxyl number determination is time consuming. This study pointed out the necessity of obtaining calibration standards identical to the samples being analyzed for each type of polyol or other material being analyzed. Multivariate calibration techniques are frequently used with FTIR data to determine the composition of a large variety of complex mixtures. A literature search indicated many applications of multivariate calibration to FTIR data. Areas identified where quantitation by FTIR would provide a new capability are quantitation of components in epoxy and silicone resins, polychlorinated biphenyls (PCBs) in oils, and additives to polymers.
Fourier Analysis and Structure Determination--Part III: X-ray Crystal Structure Analysis.
Chesick, John P.
1989-01-01
Discussed is single crystal X-ray crystal structure analysis. A common link between the NMR imaging and the traditional X-ray crystal structure analysis is reported. Claims that comparisons aid in the understanding of both techniques. (MVL)
Philip Ye, X; Liu, Lu; Hayes, Douglas; Womac, Alvin; Hong, Kunlun; Sokhansanj, Shahab
2008-10-01
The objectives of this research were to determine the variation of chemical composition across botanical fractions of cornstover, and to probe the potential of Fourier transform near-infrared (FT-NIR) techniques in qualitatively classifying separated cornstover fractions and in quantitatively analyzing chemical compositions of cornstover by developing calibration models to predict chemical compositions of cornstover based on FT-NIR spectra. Large variations of cornstover chemical composition for wide calibration ranges, which is required by a reliable calibration model, were achieved by manually separating the cornstover samples into six botanical fractions, and their chemical compositions were determined by conventional wet chemical analyses, which proved that chemical composition varies significantly among different botanical fractions of cornstover. Different botanic fractions, having total saccharide content in descending order, are husk, sheath, pith, rind, leaf, and node. Based on FT-NIR spectra acquired on the biomass, classification by Soft Independent Modeling of Class Analogy (SIMCA) was employed to conduct qualitative classification of cornstover fractions, and partial least square (PLS) regression was used for quantitative chemical composition analysis. SIMCA was successfully demonstrated in classifying botanical fractions of cornstover. The developed PLS model yielded root mean square error of prediction (RMSEP %w/w) of 0.92, 1.03, 0.17, 0.27, 0.21, 1.12, and 0.57 for glucan, xylan, galactan, arabinan, mannan, lignin, and ash, respectively. The results showed the potential of FT-NIR techniques in combination with multivariate analysis to be utilized by biomass feedstock suppliers, bioethanol manufacturers, and bio-power producers in order to better manage bioenergy feedstocks and enhance bioconversion.
Directory of Open Access Journals (Sweden)
G.J.J. Silva
2009-04-01
Full Text Available The autonomic nervous system plays an important role in physiological and pathological conditions, and has been extensively evaluated by parametric and non-parametric spectral analysis. To compare the results obtained with fast Fourier transform (FFT and the autoregressive (AR method, we performed a comprehensive comparative study using data from humans and rats during pharmacological blockade (in rats, a postural test (in humans, and in the hypertensive state (in both humans and rats. Although postural hypotension in humans induced an increase in normalized low-frequency (LFnu of systolic blood pressure, the increase in the ratio was detected only by AR. In rats, AR and FFT analysis did not agree for LFnu and high frequency (HFnu under basal conditions and after vagal blockade. The increase in the LF/HF ratio of the pulse interval, induced by methylatropine, was detected only by FFT. In hypertensive patients, changes in LF and HF for systolic blood pressure were observed only by AR; FFT was able to detect the reduction in both blood pressure variance and total power. In hypertensive rats, AR presented different values of variance and total power for systolic blood pressure. Moreover, AR and FFT presented discordant results for LF, LFnu, HF, LF/HF ratio, and total power for pulse interval. We provide evidence for disagreement in 23% of the indices of blood pressure and heart rate variability in humans and 67% discordance in rats when these variables are evaluated by AR and FFT under physiological and pathological conditions. The overall disagreement between AR and FFT in this study was 43%.
Real Clifford Windowed Fourier Transform
Institute of Scientific and Technical Information of China (English)
Mawardi BAHRI; Sriwulan ADJI; Ji Man ZHAO
2011-01-01
We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation,reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform (WFT) and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.
Selective Weighted Least Squares Method for Fourier Transform Infrared Quantitative Analysis.
Wang, Xin; Li, Yan; Wei, Haoyun; Chen, Xia
2016-10-26
Classical least squares (CLS) regression is a popular multivariate statistical method used frequently for quantitative analysis using Fourier transform infrared (FT-IR) spectrometry. Classical least squares provides the best unbiased estimator for uncorrelated residual errors with zero mean and equal variance. However, the noise in FT-IR spectra, which accounts for a large portion of the residual errors, is heteroscedastic. Thus, if this noise with zero mean dominates in the residual errors, the weighted least squares (WLS) regression method described in this paper is a better estimator than CLS. However, if bias errors, such as the residual baseline error, are significant, WLS may perform worse than CLS. In this paper, we compare the effect of noise and bias error in using CLS and WLS in quantitative analysis. Results indicated that for wavenumbers with low absorbance, the bias error significantly affected the error, such that the performance of CLS is better than that of WLS. However, for wavenumbers with high absorbance, the noise significantly affected the error, and WLS proves to be better than CLS. Thus, we propose a selective weighted least squares (SWLS) regression that processes data with different wavenumbers using either CLS or WLS based on a selection criterion, i.e., lower or higher than an absorbance threshold. The effects of various factors on the optimal threshold value (OTV) for SWLS have been studied through numerical simulations. These studies reported that: (1) the concentration and the analyte type had minimal effect on OTV; and (2) the major factor that influences OTV is the ratio between the bias error and the standard deviation of the noise. The last part of this paper is dedicated to quantitative analysis of methane gas spectra, and methane/toluene mixtures gas spectra as measured using FT-IR spectrometry and CLS, WLS, and SWLS. The standard error of prediction (SEP), bias of prediction (bias), and the residual sum of squares of the errors
Villiger, Nathan J.; Weinschenk, Sedrick; Hettinger, Paul T.; Murphy, Brian W.
2017-01-01
Globular clusters are excellent objects to study to help us understand the ways in which stars evolve. Key to this understanding are RR Lyrae variable stars. This research focused on the RR Lyrae stars in the globular cluster NGC 6584 to gain a better knowledge of post main sequence stellar evolution, horizontal branch morphology, and interstellar reddening to cluster variables. Using the 0.6 m SARA telescope at CTIO, we obtained nearly 1000 images in B, V, and I bands from July 2014 through July 2015. In addition to our prior work in V-band, this research adds B and I bands. By using difference image analysis, we found 77 variable stars in our 13’ x 13’ field of view. These consisted of 66 RR Lyrae stars, 7 long period variables, and 4 eclipsing binaries. The RR Lyrae stars were divided into 50 RR0 type stars, of which 14 exhibit the Blazhko effect, and 16 RR1 type stars. We found an average period for the RR0 variables of 0.56465 days and 0.30610 for the RR1 variables. By applying Fourier decomposition and examining the light curves in B, V, and I bands for each RR Lyrae variable, we were able to determine an average [Fe/H]JKZW of -1.619 ± 0.090, an average E(B-V) of 0.100 ± 0.032, and a distance to the cluster of 13527 ± 939 pc. This is the first detailed study to use RR Lyrae variable stars to estimate these parameters and the results are consistent with those obtained by other methods.
Wang, Ya-Mei; Ma, Shu-Ling; Feng, Li-Qun
2014-03-01
Wood preservative treatment can improve defects of plantation wood such as easy to corrupt and moth eaten. Among them heat-treatment is not only environmental and no pollution, also can improve the corrosion resistance and dimension stability of wood. In this test Poplar and Mongolian Seoteh Pine was treated by soybean oil as heat-conducting medium, and the heat treatment wood was studied for indoor decay resistance; wood chemical components before and after treatment, the effect of heat treatment on wood decay resistance performance and main mechanism of action were analysed by Fourier infrared spectrometric. Results showed that the mass loss rate of poplar fell from 19.37% to 5% and Mongolian Seoteh Pine's fell from 8.23% to 3.15%, so oil heat treatment can effectively improve the decay resistance. Infrared spectrum analysis shows that the heat treatment made wood's hydrophilic groups such as hydroxyl groups in largely reduced, absorbing capacity decreased and the moisture of wood rotting fungi necessary was reduced; during the heat treatment wood chemical components such as cellulose, hemicellu lose were degraded, and the nutrient source of wood rotting fungi growth necessary was reduced. Wood decay fungi can grow in the wood to discredit wood is because of that wood can provide better living conditions for wood decay fungi, such as nutrients, water, oxygen, and so on. The cellulose and hemicellulose in wood is the main nutrition source of wood decay fungi. So the oil heat-treatment can reduce the cellulose, hemicellulose nutrition source of wood decay fungi so as to improve the decay resistance of wood.
Bochner's theorem on Fourier-Stieltjes integrals in the framework of quaternion analysis
Georgiev, S.; Morais, J.
2012-11-01
Let σ(x) be a nondecreasing function, such that σ(-∞) = 0,σ(∞) = 1 and let us denote by B the class of functions which can be represented by a Fourier-Stieltjes integral f(t) = ∫ -∞∞eitxdσ(x). In continuation to [12], we prove a generalization of the classical theorem of Bochner on Fourier integral transforms to quaternion functions belonging to a subclass of B. The underlying functions are continuous functions of bounded variation defined in R2 and taking values on the quaternion algebra. Additionally, we introduce the definition of convolution of quaternion functions of bounded variation.
Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation
Energy Technology Data Exchange (ETDEWEB)
Aldea, N; Pintea, S; Rednic, V [National Institute for Research and Development of Isotopic and Molecular Technologies, 65-103 Donath, 400293 Cluj-Napoca (Romania); Matei, F [University of Agricultural Sciences and Veterinary Medicine, 3-5 Calea Manastur, 400372 Cluj-Napoca (Romania); Hu Tiandou; Xie Yaning, E-mail: nicolae.aldea@itim-cj.r [Beijing Synchrotron Radiation Facilities of Beijing Electron Positron Collider National Laboratory (China)
2009-08-01
The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe{sub 3}O{sub 4} core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.
Fourier series analysis of fractal lenses: theory and experiments with a liquid-crystal display.
Davis, Jeffrey A; Sigarlaki, Sean P; Craven, Julia M; Calvo, María Luisa
2006-02-20
We report on a Fourier series approach that predicts the focal points and intensities produced by fractal zone plate lenses. This approach allows us to separate the effects of the fractal order from those of the lens aperture. We implement these fractal lenses onto a liquid-crystal display and show experimental verification of our theory.
Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method
Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.
2013-01-01
Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…
Fourier Descriptor Analysis and Unification of Voice Range Profile Contours: Method and Applications
Pabon, Peter; Ternstrom, Sten; Lamarche, Anick
2011-01-01
Purpose: To describe a method for unified description, statistical modeling, and comparison of voice range profile (VRP) contours, even from diverse sources. Method: A morphologic modeling technique, which is based on Fourier descriptors (FDs), is applied to the VRP contour. The technique, which essentially involves resampling of the curve of the…
Fourier Descriptor Analysis and Unification of Voice Range Profile Contours: Method and Applications
Pabon, Peter; Ternstrom, Sten; Lamarche, Anick
2011-01-01
Purpose: To describe a method for unified description, statistical modeling, and comparison of voice range profile (VRP) contours, even from diverse sources. Method: A morphologic modeling technique, which is based on Fourier descriptors (FDs), is applied to the VRP contour. The technique, which essentially involves resampling of the curve of the…
De Koninck, Anne-Sophie; Nys, Karen; Vandenheede, Brent; Van Biervliet, Stephanie; Speeckaert, Marijn M; Delanghe, Joris R
2016-11-01
Fourier transform infrared (FTIR) spectroscopic determination of faecal fat is a simple and elegant alternative for the classical Van De Kamer approach. Besides quantification of the total amount of fat, analysis of the lipase hydrolysis efficiency (fatty acid/triglyceride ratio), fatty acid chain length and trans-unsaturated fatty acids could provide a better monitoring of dietary treatment. Stool samples (26 routine samples and 36 cystic fibrosis patients) were analysed with the Perkin Elmer Spectrum Two® spectrometer (3500-450cm(-1)). Fatty acid/triglyceride ratio was calculated using the absorbance ratio at 2855:1746cm(-1). To estimate lipase hydrolysis efficiency, sample ratios were compared with the ratio of butter and pure free fatty acids. Mean fatty acid chain length was calculated using the absorbance ratio at 2855:1709cm(-1). The absorbance at 966cm(-1) was used to trace the presence of trans-type unsaturated fatty acids. Butter showed a low fatty acid/triglyceride ratio (1.21) and pure free fatty acids a high fatty acid/triglyceride ratio (6.76). Mean fatty acid/triglyceride ratio of routine stool samples was 4.16±1.01. The applicability of fatty acid/triglyceride ratios was also tested in cystic fibrosis patients under treatment with a mean of 4.92±0.98. Relative absorbance contribution per carbon atom was 0.06 (ratio 1.06 for C18 standard, 0.91 for C16 standard). The mean ratio of the stool samples was 1.12 (mean acyl chain length of C19), with values ranging from 0.73 (C12) to 1.68 (C28). The presence of traceable amounts of trans-unsaturated fatty acids was also demonstrated. For the analysis of faecal material, FTIR provides unique information, difficult to obtain using other techniques. These findings offer perspectives for diet monitoring in patients with (non-)pancreatic malabsorption. Copyright © 2016 The Canadian Society of Clinical Chemists. Published by Elsevier Inc. All rights reserved.
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...
Fourier transformation for pedestrians
Butz, Tilman
2015-01-01
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
Fourier transform mass spectrometry.
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-07-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.
Energy Technology Data Exchange (ETDEWEB)
Ramamoorthy, Sripriya [Oregon Hearing Research Center, Oregon Health & Science University, Portland, Oregon (United States); Zhang, Yuan; Jacques, Steven [Department of Biomedical Engineering, Oregon Health & Science University, Portland, Oregon (United States); Petrie, Tracy; Wang, Ruikang [Department of Bioengineering, University of Washington, Seattle, Washington (United States); Nuttall, Alfred L. [Oregon Hearing Research Center, Oregon Health & Science University, Portland, Oregon (United States); Kresge Hearing Research Institute, The University of Michigan, Ann Arbor, Michigan (United States)
2015-12-31
In this study, we have developed a phase-sensitive Fourier-domain optical coherence tomography system to simultaneously measure the in vivo inner ear vibrations in the hook area and second turn of the mouse cochlea. This technical development will enable measurement of intra-cochlear distortion products at ideal locations such as the distortion product generation site and reflection site. This information is necessary to un-mix the complex mixture of intra-cochlear waves comprising the DPOAE and thus leads to the non-invasive identification of the local region of cochlear damage.
Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Jacques, Steven; Wang, Ruikang; Nuttall, Alfred L.
2015-12-01
In this study, we have developed a phase-sensitive Fourier-domain optical coherence tomography system to simultaneously measure the in vivo inner ear vibrations in the hook area and second turn of the mouse cochlea. This technical development will enable measurement of intra-cochlear distortion products at ideal locations such as the distortion product generation site and reflection site. This information is necessary to un-mix the complex mixture of intra-cochlear waves comprising the DPOAE and thus leads to the non-invasive identification of the local region of cochlear damage.
Artefacts in geometric phase analysis of compound materials
Energy Technology Data Exchange (ETDEWEB)
Peters, Jonathan J.P., E-mail: j.j.p.peters@warwick.ac.uk [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom); Beanland, Richard; Alexe, Marin [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom); Cockburn, John W.; Revin, Dmitry G.; Zhang, Shiyong Y. [Department of Physics and Astronomy, University of Sheffield, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Sanchez, Ana M., E-mail: a.m.sanchez@warwick.ac.uk [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL (United Kingdom)
2015-10-15
The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. - Highlights: • GPA is shown to produce incorrect strains when applied to images of compound materials. • A mathematical description is laid out for why GPA can produce artefacts. • The artefact is demonstrated using experimental and simulated data. • A ‘rule’ is set to avoid this artefact in GPA.
DEFF Research Database (Denmark)
Batina, N.; Reyna-Cordova, A.; Trinidad-Reyes, Y.
2005-01-01
Thin films of crude oil samples were prepared for atomic force microscopy (AFM) analysis on the gold substrate. Sample preparation involved evaporation during a long (24 h) but mild thermal exposure (80 °C). Fourier transform infrared (FTIR) microscopy (reflectance spectroscopy) was employed...... of oxidation state was compared to surface morphology data by AFM previously reported. The reported results emphasize the advantage of complementary techniques (AFM/FTIR microscopy) in the analysis of petroleum thin films that should be considered during analysis and interpretation of this type of data....
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.
Tian, Jialin; Smith, William L.; Gazarik, Michael J.
2008-10-01
The ultimate remote sensing benefits of the high resolution Infrared radiance spectrometers will be realized with their geostationary satellite implementation in the form of imaging spectrometers. This will enable dynamic features of the atmosphere's thermodynamic fields and pollutant and greenhouse gas constituents to be observed for revolutionary improvements in weather forecasts and more accurate air quality and climate predictions. As an important step toward realizing this application objective, the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) Engineering Demonstration Unit (EDU) was successfully developed under the NASA New Millennium Program, 2000-2006. The GIFTS-EDU instrument employs three focal plane arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw GIFTS interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. The radiometric calibration is achieved using internal blackbody calibration references at ambient (260 K) and hot (286 K) temperatures. The absolute radiometric performance of the instrument is affected by several factors including the FPA off-axis effect, detector/readout electronics induced nonlinearity distortions, and fore-optics offsets. The GIFTS-EDU, being the very first imaging spectrometer to use ultra-high speed electronics to readout its large area format focal plane array detectors, operating at wavelengths as large as 15 microns, possessed non-linearity's not easily removable in the initial calibration process. In this paper, we introduce a refined calibration technique that utilizes Principle Component (PC) analysis to compensate for instrument distortions and artifacts remaining after the initial radiometric calibration process, thus, further enhance the absolute calibration accuracy. This method is
The analysis of linear partial differential operators I distribution theory and Fourier analysis
Hörmander, Lars
2003-01-01
The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comm...
Sasmita, Yoga; Darmawan, Gumgum
2017-08-01
This research aims to evaluate the performance of forecasting by Fourier Series Analysis (FSA) and Singular Spectrum Analysis (SSA) which are more explorative and not requiring parametric assumption. Those methods are applied to predicting the volume of motorcycle sales in Indonesia from January 2005 to December 2016 (monthly). Both models are suitable for seasonal and trend component data. Technically, FSA defines time domain as the result of trend and seasonal component in different frequencies which is difficult to identify in the time domain analysis. With the hidden period is 2,918 ≈ 3 and significant model order is 3, FSA model is used to predict testing data. Meanwhile, SSA has two main processes, decomposition and reconstruction. SSA decomposes the time series data into different components. The reconstruction process starts with grouping the decomposition result based on similarity period of each component in trajectory matrix. With the optimum of window length (L = 53) and grouping effect (r = 4), SSA predicting testing data. Forecasting accuracy evaluation is done based on Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The result shows that in the next 12 month, SSA has MAPE = 13.54 percent, MAE = 61,168.43 and RMSE = 75,244.92 and FSA has MAPE = 28.19 percent, MAE = 119,718.43 and RMSE = 142,511.17. Therefore, to predict volume of motorcycle sales in the next period should use SSA method which has better performance based on its accuracy.
Raveloson, Herimalala; Le Minor, Jean-Marie; Rumpler, Yves; Schmittbuhl, Matthieu
2005-01-01
While several morphometric analyses in lemurids have focused on the craniofacial complex, the characterization of their mandibular morphology has received less attention. The mandibular outline, in lateral perspective, was quantified using elliptical Fourier analysis, in an osteological sample encompassing 189 lemurid mandibles (66 Eulemur, 51 Hapalemur, 22 Lemur and 50 Varecia), and compared using multivariate statistical techniques. The taxonomic value of this outline in Lemuridae was demonstrated by the existence of significant separations between the four genera studied. In particular, the mandibular morphology of Hapalemur was markedly different from that in the group Eulemur-Lemur-Varecia. Excluding Hapalemur from analysis, the distinctions between Eulemur, Lemur and Varecia were enhanced suggesting the existence of more subtle intergeneric differences in mandibular morphology. Variation in mandibular form was greatest in Hapalemur and smallest in Eulemur and Varecia (as demonstrated by the mean values of interindividual distances); variation was higher in Lemur than in Eulemur and Varecia, but not higher than in Hapalemur. This morphological diversity may be related to functional adaptation in response to particular dietary habits. The patterns of intergeneric and intrageneric shape variations of the mandible in Lemuridae presented here provide a valuable resource for the analysis of variation among living and fossil lemurids.
Directory of Open Access Journals (Sweden)
Davide Barbieri
2016-12-01
Full Text Available This is a joint work with E. Hernández, J. Parcet and V. Paternostro. We will discuss the structure of bases and frames of unitary orbits of discrete groups in invariant subspaces of separable Hilbert spaces. These invariant spaces can be characterized, by means of Fourier intertwining operators, as modules whose rings of coefficients are given by the group von Neumann algebra, endowed with an unbounded operator valued pairing which defines a noncommutative Hilbert structure. Frames and bases obtained by countable families of orbits have noncommutative counterparts in these Hilbert modules, given by countable families of operators satisfying generalized reproducing conditions. These results extend key notions of Fourier and wavelet analysis to general unitary actions of discrete groups, such as crystallographic transformations on the Euclidean plane or discrete Heisenberg groups.
Energy Technology Data Exchange (ETDEWEB)
Bartosch, T. [Erlanger-Nuernberg Univ., Erlanger (Germany). Lehrstul fuer Nachrichtentechnik I; Seidl, D. [Seismologisches Zentralobservatorium Graefenberg, Erlanegen (Greece). Bundesanstalt fuer Geiwissenschaften und Rohstoffe
1999-06-01
Among a variety of spectrogram methods short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were selected to analyse transients in non-stationary signals. Depending on the properties of the tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli (Italy).
Osbin, K.; Jayan, Manuel; Bhadrakumari, S.; Predeep, P.
2017-06-01
This study investigates the presence of various amide bands present in different spider silk species, which provides extraordinary physical properties. Three different spider silks were collected from Western Ghats region. The collected spider silks samples belonging to the spider Heteropoda venatoria (species 1), Hersilia savignyi (species 2) and Pholcus phalangioides (species 3). Fourier transform infrared (FTIR) spectra reveals the protein peaks in the amide I, II, and III regions in all the three types of spider silk species.
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
Dean, Bruce H. (Inventor)
2012-01-01
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
Institute of Scientific and Technical Information of China (English)
Jian Ye(叶坚); Zichun Le(乐孜纯); Jingqiu Liang(梁静秋); Kai Liu(刘恺); Bisheng Quan(全必胜); Yali Qin(覃亚丽); Guangxin Zhu(朱广信)
2004-01-01
It is important to predict the intensity distribution in focusing plane for designing the X-ray compound refractive lenses. On the basis of analyzing the structure of X-ray compound lenses and comparing it with Fraunhofer diffraction system, it is concluded that the X-ray focusing system can be regarded as a kind of Fraunhofer diffraction system. Therefore, a method based on Fourier spectrum analysis is presented to predict the intensity distribution in the focusing plane for the X-ray lenses. A brief analysis on the relationship between the parameters of X-ray lenses and their focusing performance is also given in this paper.
Marikhin, V. A.; Myasnikova, L. P.; Radovanova, E. I.; Volchek, B. Z.; Medvedeva, D. A.
2017-02-01
The structural changes in crystalline lamella cores of tridecanoic acid CH3(CH2)11COOH during heating in the range from the temperature T 1 = 13.5°C to T 2 > T m = 41.6°C have been investigated using Fourier transform infrared spectroscopy. The behavior of the bands of rocking (in the region of 720 cm-1) and bending (in the region of 1470 cm-1) vibrations of CH2 groups in tridecanoic acid methylene segments has been analyzed. It has been shown that, in the first-order phase transition region ( T s-s 36°C) within a narrow temperature range (Δ T 1 ≤ 1 K), there is a gradual transformation of the initial triclinic subcell into the hexagonal subcell. The mechanism of this transition has been considered in terms of the theory of diffuse first-order phase transitions.
Phase analysis of the cosmic microwave background from an incomplete sky coverage
Chiang, Lung-Yih
2007-01-01
Phases of the spherical harmonic analysis of full-sky cosmic microwave background (CMB) temperature data contain useful information complementary to the ubiquitous angular power spectrum. In this letter we present a new method of phase analysis on incomplete sky maps. They are the Fourier phases of equal-latitude pixel rings of the map, which are related to the mean angle of the trigonometric moments from the full-sky phases. They have an advantage for probing regions of interest without tapping polluted Galactic plane area, and can localize non-Gaussian features and departure from statistical isotropy in the CMB.
Directory of Open Access Journals (Sweden)
D. Seidl
1999-06-01
Full Text Available Among a variety of spectrogram methods Short-Time Fourier Transform (STFT and Continuous Wavelet Transform (CWT were selected to analyse transients in non-stationary tremor signals. Depending on the properties of the tremor signal a more suitable representation of the signal is gained by CWT. Three selected broadband tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli.
Error analysis in Fourier methods for option pricing for exponential Lévy processes
Crocce, Fabian
2015-01-07
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 for the existence of a L? bound that separates the dynamical contribution from that arising from the type of the option n in question. The bound achieved does not rely on information of the asymptotic behaviour of option prices at extreme asset values. In addition, we demonstrate improved numerical performance for select examples of practical relevance when compared to established bounding methods.
[The principle and analysis of micro-Fourier transform spectrometer based on MEMS micro-mirror].
Chen, Jian-Jun; Zhu, Yong; Liu, Bo; Wei, Wei; Zhang, Jie; Wang, Ning
2012-11-01
The present paper puts forward a novel micro-Fourier transform infrared spectrometer based on programmable MEMS micro-mirror. This design uses a MEMS micro-mirror and a slantwise reflector to replace the moving mirror system on traditional spectrometer. This paper analyzes the operating principle of this spectrometer and gives the simulation result to prove the feasibility of this method. The results show that the spectral resolution is less than 5 nm in near-infrared wave band, the wave-length accuracy is approximately 1 nm and the sampling period of this spectrometer is approximately 50 ms. This method can use Hadamard transform to improve the SNR.
Beecken, Brian P.; Kleinman, Randall R.
2004-01-01
New developments in infrared sensor technology have potentially made possible a new space-based system which can measure far-infrared radiation at lower costs (mass, power and expense). The Stationary Imaging Fourier Transform Spectrometer (SIFTS) proposed by NASA Langley Research Center, makes use of new detector array technology. A mathematical model which simulates resolution and spectral range relationships has been developed for analyzing the utility of such a radically new approach to spectroscopy. Calculations with this forward model emulate the effects of a detector array on the ability to retrieve accurate spectral features. Initial computations indicate significant attenuation at high wavenumbers.
Analysis of the Interference Modulation Depth in the Fourier Transform Spectrometer
Directory of Open Access Journals (Sweden)
Rilong Liu
2015-01-01
Full Text Available Based on the principle of the Michelson interferometer, the paper briefly describes the theoretical significance and calculates and deduces three expressions of the interference modulation depth. The influence of the surface shape error of plane mirror on modulation depth is analyzed, and the tolerance of error is also pointed out. Moreover, the dependence of modulation depth on the reflectance change of beam splitter interface is also analyzed, and the curve is given. It is concluded that this paper is of general significance for the Fourier transform spectrometer based on the principle of the Michelson two-beam interference.
Characterizing the Nanoscale Layers of Tomorrow___s Electronics An Application of Fourier Analysis
Energy Technology Data Exchange (ETDEWEB)
Payne, Christopher Bishop; /Princeton U. /SLAC
2012-08-24
Thin film applications are of great interest to the semiconductor industry due to the important role they play in cutting edge technology such as thin film solar cells. X-Ray Reflectivity (XRR) characterizes thin films in a non-destructive and efficient manner yet complications exist in extracting these characteristics from raw XRR data. This study developed and tested two different algorithms to extract quantity of layers and thickness information on the nanometer scale from XRR data. It was concluded that an algorithm involving a local averaging technique revealed this information clearly in Fourier space.
Fluorescence spectrum analysis using Fourier series modeling for Fluorescein solution in Ethanol
Hadi, Mahasin F
2011-01-01
We have measured the fluorescence spectrum for fluorescein solution in ethanol with concentration 1 {\\times} 10-3 mol/liter at different temperatures from room temperature to freezing point of solvent, (T = 153, 183, 223, 253, and 303 K) using liquid nitrogen. Table curve 2D version 5.01 program has been used to determine the fitting curve and fitting equation for each fluorescence spectrum. Fourier series (3 {\\times} 2) was the most suitable fitting equation for all spectra. Theoretical fluorescence spectrum of fluorescein in ethanol at T = 183K was calculated and compared with experimental fluorescence spectrum at the same temperature. There is a good similarity between them.
A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp.
Barlow, Euan; Mulholland, Anthony J
2011-11-01
The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.
Dupont, S.; Gazalet, J.; Kastelik, J. C.
2014-03-01
Phononic crystal is a structured media with periodic modulation of its physical properties that influences the propagation of elastic waves and leads to a peculiar behaviour, for instance the phononic band gap effect by which elastic waves cannot propagate in certain frequency ranges. The formulation of the problem leads to a second order partial differential equation with periodic coefficients; different methods exist to determine the structure of the eigenmodes propagating in the material, both in the real or Fourier domain. Brillouin explains the periodicity of the band structure as a direct result of the discretization of the crystal in the real domain. Extending the Brillouin vision, we introduce digital signal processing tools developed in the frame of distribution functions theory. These tools associate physical meaning to mathematical expressions and reveal the correspondence between real and Fourier domains whatever is the physical domain under consideration. We present an illustrative practical example concerning two dimensions phononic crystals and highlight the appreciable shortcuts brought by the method and the benefits for physical interpretation.
Fourier analysis of Solar atmospheric numerical simulations accelerated with GPUs (CUDA).
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.
Directory of Open Access Journals (Sweden)
Piotr CZECH
2007-01-01
Full Text Available This paper presents the results of an experimental application of artificial neural network as a classifier of the degree of cracking of a tooth root in a gear wheel. The neural classifier was based on the artificial neural network of Probabilistic Neural Network type (PNN. The input data for the classifier was in a form of matrix composedof statistical measures, obtained from fast Fourier transform (FFT and principal component analysis (PCA. The identified model of toothed gear transmission, operating in a circulating power system, served for generation of the teaching and testing set applied for the experiment.
Puyo, L; Rancillac, A; Simonutti, M; Paques, M; Sahel, J A; Fink, M; Atlan, M
2015-01-01
We report on wide-field imaging of pulsatile microvascular blood flow in the exposed cerebral cortex of a mouse by holographic interferometry. We recorded interferograms of laser light backscattered by the tissue, beating against an off-axis reference beam with a 50 kHz framerate camera. Videos of local Doppler contrasts were rendered numerically by Fresnel transformation and short-time Fourier transform analysis. This approach enabled instantaneous imaging of pulsatile blood flow contrasts in superficial blood vessels over 256 x 256 pixels with a spatial resolution of 10 microns and a temporal resolution of 20 ms.
Directory of Open Access Journals (Sweden)
Mariachiara Stani
2014-01-01
Full Text Available Some dynastic and pre-dynastic Egyptian mummies from the Giovanni Marro Museum of Anthropology and Ethnography, University of Turin, Italy have been studied by means of the combined approach of both Fourier transform infrared spectroscopy and histological analysis, with the aim of investigating the preservation state of the skin of ancient archaeological remains, as a consequence of the differences between the two kinds of mummification processes, i.e. natural and by means of embalming substances. The results suggest that the balms used in the dynastic mummies embalming process really could have played an important role in the prevention of corpse deterioration.
Wang, Xiaogang; Zhao, Daomu; Chen, Yixiang
2014-08-10
We present a study about information disclosure in phase-truncation-based cryptosystems. The main information of the original image to be encoded can be obtained by using a decryption key in the worst case. The problem cannot be thoroughly solved by imaginary part truncating, keeping the encryption keys as private keys, or applying different phase keys for different plaintexts during each encryption process as well as the phase modulation in the frequency domain. In order to eliminate the risk of unintended information disclosure, we further propose a nonlinear spatial and spectral encoding technique using a random amplitude mask (RAM). The encryption process involving two security layers can be fully controlled by a RAM. The spatial encoding of the plaintext images and the simultaneous encryption of the plaintext images and the encryption key greatly enhance the security of system, avoiding several attacks that have cracked the phase-truncation-based cryptosystems. Besides, the hybrid encryption system retains the advantage of a trap door one-way function of phase truncation. Numerical results have demonstrated the feasibility and effectiveness of the proposed encryption algorithm.
Analytical determination of orbital elements using Fourier analysis. I. The radial velocity case
Delisle, J.-B.; Ségransan, D.; Buchschacher, N.; Alesina, F.
2016-05-01
We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is mainly limited by the accuracy of the computation of the Fourier decomposition of the signal which is sensitive to sampling and noise. Our method is complementary with more accurate (and more expensive in computer time) numerical algorithms (e.g. Levenberg-Marquardt, Markov chain Monte Carlo, genetic algorithms). Indeed, the analytical approximation can be used as an initial condition to accelerate the convergence of these numerical methods. Our method can be applied iteratively to search for multiple planets in the same system.
Zimmerman, G. A.; Gulkis, S.
1991-01-01
The sensitivity of a matched filter-detection system to a finite-duration continuous wave (CW) tone is compared with the sensitivities of a windowed discrete Fourier transform (DFT) system and an ideal bandpass filter-bank system. These comparisons are made in the context of the NASA Search for Extraterrestrial Intelligence (SETI) microwave observing project (MOP) sky survey. A review of the theory of polyphase-DFT filter banks and its relationship to the well-known windowed-DFT process is presented. The polyphase-DFT system approximates the ideal bandpass filter bank by using as few as eight filter taps per polyphase branch. An improvement in sensitivity of approx. 3 dB over a windowed-DFT system can be obtained by using the polyphase-DFT approach. Sidelobe rejection of the polyphase-DFT system is vastly superior to the windowed-DFT system, thereby improving its performance in the presence of radio frequency interference (RFI).
Fourier-transform infrared spectroscopy (FTIR) analysis of triclinic and hexagonal birnessites.
Ling, Florence T; Post, Jeffrey E; Heaney, Peter J; Kubicki, James D; Santelli, Cara M
2017-05-05
The characterization of birnessite structures is particularly challenging for poorly crystalline materials of biogenic origin, and a determination of the relative concentrations of triclinic and hexagonal birnessite in a mixed assemblage has typically required synchrotron-based spectroscopy and diffraction approaches. In this study, Fourier-transform infrared spectroscopy (FTIR) is demonstrated to be capable of differentiating synthetic triclinic Na-birnessite and synthetic hexagonal H-birnessite. Furthermore, IR spectral deconvolution of peaks resulting from MnO lattice vibrations between 400 and 750cm(-1) yield results comparable to those obtained by linear combination fitting of synchrotron X-ray absorption fine structure (EXAFS) data when applied to known mixtures of triclinic and hexagonal birnessites. Density functional theory (DFT) calculations suggest that an infrared absorbance peak at ~1628cm(-1) may be related to OH vibrations near vacancy sites. The integrated intensity of this peak may show sensitivity to vacancy concentrations in the Mn octahedral sheet for different birnessites.
Energy Technology Data Exchange (ETDEWEB)
Narayanamurthy, C S [Department of Physics, Indian Institute of Space Science and Technology (IIST), Department of Space (Govt of India), ATF Campus, VSSC, ISRO - PO, Thiruvananthapuram 695 022 (India)], E-mail: naamu.s@gmail.com
2009-01-15
Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in Principles of Optics by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer have never been analysed seriously in any book. Because Michelson's interferometer is one of the important and fundamental optical experiments taught at both undergraduate and graduate levels, it would be appropriate to explain the localization of these fringes. In this paper, we analyse the localization of Michelson interferometer fringes using Fourier optics and temporal coherence, and show that they never localize at any plane even at infinity.
Fourier Power Spectrum Analysis of Exons for the Period-3 Behavior
Institute of Scientific and Technical Information of China (English)
Yuan Xin TIAN; Chao CHEN; Xiao Yong ZOU; Jian Ding QIU; Pei Xiang CAI; Jin Yuan MO
2005-01-01
The period-3 behaviors of 105 exons from 20 genes in human were studied by Fourier power spectrum. The results indicated that not all exons show the period-3 behavior. The exons were adjusted in order to make them accord with the order of the protein translated, and we found that the period-3 character is relation to the length of exons and the bases distribution in the three codon position. Furthermore, as long as the exons with period-3 behavior accord with the order of protein translated, they would exhibit the synonymous codons usage preference, and the codons with g/c at the third position are used in higher frequency. The results are significant to the gene prediction and the research on the introns.
SOUND AND VIBRATION SIGNAL ANALYSIS USING IMPROVED SHORT-TIME FOURIER REPRESENTATION
Directory of Open Access Journals (Sweden)
June-Yule Lee
2013-06-01
Full Text Available Time-frequency imaging provides a straightforward means to understanding machinery conditions. The methods of short-time Fourier transform (STFT, Wigner-Ville distribution (WVD and smooth-windowed Wigner-Ville distribution (SWWVD are applied to the condition monitoring of rotating machines. The sound and vibration signals of a rotating fan are tested, and time-frequency images are illustrated in terms of STFT, WVD and SWWVD. The results show that the resolution of STFT is low, and the resolution of WVD is high but with interference. To overcome the interference in the WVD image, a variable smooth-windowed weighting function is applied. The smoothing window function resulted in interference attenuation but also in reducing the concentration. The SWWVD is a compromise between STFT and WVD. The SWWVD exhibits better resolution than STFT and has less interference than WVD.
Analysis of collagen fiber domain organization by Fourier second harmonic generation microscopy
Ghazaryan, Ara; Tsai, Halley F.; Hayrapetyan, Gor; Chen, Wei-Liang; Chen, Yang-Fang; Jeong, Myung Yung; Kim, Chang-Seok; Chen, Shean-Jen; Dong, Chen-Yuan
2013-03-01
We present an automated and systematic two-dimensional discrete Fourier transform (2D-FFT) approach to analyze collagen fiber organization through the use of second harmonic generation (SHG) microscopy. Average orientations of individual domains and Ising-like order parameters introduced to characterize the correlation between orientations of adjacent domains may be used to quantitatively characterize fibrous tissues. Our approach was applied to analyze tissues including rat tail tendon, mouse skin, bovine corneas, and human corneas. We also show that collagen fiber organization in normal and keratokonus human corneas may be distinguished. The current approach may be used for the quantitative differentiation of SHG collagen fiber morphology in different tissues and may be applied for diagnostic purposes.
Directory of Open Access Journals (Sweden)
Nurrulhidayah, A. F.
2013-09-01
Full Text Available Butter may be adulterated with cheaper animal fats, such as chicken fat (CF. Thus, the detection and quantification of butter adulteration with CF was monitored using Fourier transform infrared (FTIR spectroscopy, combined with chemometric of partial least square (PLS at the frequency regions of 1200-1000cm–1. FTIR measurements were made on pure butter and that adulterated with varying concentrations of CF (0-100% w/w in butter. PLS calibration exhibits a good relationship between actual and FTIR predicted values of CF with a coefficient of determination (R2 of 0.981. The root means standard error of calibration (RMSEC and during cross validation (RMSECV obtained using six principal components (PCs are 2.08 and 4.33% v/v, respectively.La mantequilla puede ser adulterada con grasas animales más baratas, como la grasa de pollo (GP. Así, la detección y cuantificación de la adulteración de mantequilla con GP se controló usando transformada de Fourier infrarroja (FTIR, combinada con técnicas quimiométricas de mínimos cuadrados parciales (PLS en las regiones de frecuencia de 1200-1000cm–1. Las medidas FTIR se realizaron sobre la mantequilla pura y adulterada con diferentes concentraciones de GP (0-100% w/w en la mantequilla. La calibración de PLS presenta una buena relación entre los valores reales y los valores pronosticados de FTIR de la GP con un coeficiente de determinación (R2 de 0.981. La raíz del error estándar de calibración (RMSEC durante la validación cruzada (RMSECV obtenido utilizando seis componentes principales (PC fueron 2,08 y 4,33% v/v, respectivamente.
Directory of Open Access Journals (Sweden)
Cheshmedzhiev Mihail V.
2014-08-01
Full Text Available AIM: To assess infrainguinal arterial reconstructions by intraoperative flowmetry under the distal anastomosis using a fast Fourier transformation; calculate and compare the amplitude ratios of peripheral arterial blood pressure and volume flow before and after drug-induced vasodilation of occluded bypass grafts and bypass grafts that have been patent at least for 1 year. To find what magnitude of the change of these ratios indicate a long-term patency of the bypass grafting. PATIENTS AND METHODS: We compared the results of the intraoperative flowmetry tests of 97 patients with infrainguinal arterial reconstructions. The patients were divided into two groups based on the graft status: the grafts in 49 patients were patent for at least a year, and 48 patients had failed bypass. We used a fast Fourier transform (FFT of the pressure and blood flow waves and compared the ratios of their amplitudes before and after administration of a vasodilator drug into the graft. Comparing the ratios obtained before and those after administration of the drug we quantified their change in each group and analysed them. RESULTS: After a drug-induced vasodilation, the blood pressure and flow amplitude ratios for the group with compromised reconstructions were less than 1.9 times smaller than those before drug infusion, while for the group with bypass grafts that had been functional for at least 12 months the ratios declined by more than 1.9≈2 times. CONCLUSION: The magnitude of the change of amplitude ratios of the peripheral pressure and volume flow after drug-induced vasodilation can be used to make an assessment of the bypass graft and the distal arterial segment.
Fourier and Laplace Transforms
Beerends, R.J.; Morsche, ter H.G.; Berg, van den J.C.
2003-01-01
This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the a
Introduction to Fourier Optics
Huggins, Elisha
2007-01-01
Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…
Introduction to Fourier Optics
Huggins, Elisha
2007-01-01
Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…
Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Fridberger, Anders; Ren, Tianying; Wang, Ruikang; Jacques, Steven L.; Nuttall, Alfred L.
2015-02-01
In this study, we measure the in vivo apical-turn vibrations of the guinea pig organ of Corti in both axial and radial directions using phase-sensitive Fourier domain optical coherence tomography. The apical turn in guinea pig cochlea has best frequencies around 100 - 500 Hz which are relevant for human speech. Prior measurements of vibrations in the guinea pig apex involved opening the otic capsule, which has been questioned on the basis of the resulting changes to cochlear hydrodynamics. Here this limitation is overcome by measuring the vibrations through bone without opening the otic capsule. Furthermore, we have significantly reduced the surgery needed to access the guinea pig apex in the axial direction by introducing a miniature mirror inside the bulla. The method and preliminary data are discussed in this article.
Choudhury, Niloy; Zeng, Yaguang; Fridberger, Anders; Chen, Fangyi; Zha, Dingjun; Nuttall, Alfred L.; Wang, Ruikang K.
2011-03-01
Studying the sound stimulated vibrations of various membranes that form the complex structure of the organ of Corti in the cochlea of the inner ear is essential for understanding how the travelling sound wave of the basilar membrane couples its energy to the organ structures. In this paper we report the feasibility of using phase-sensitive Fourier domain optical coherence tomography (FD-OCT) to image the vibration of various micro-structures of the cochlea at the same time. An excised cochlea of a guinea pig was stimulated using sounds at various frequencies and vibration image was obtained. When measuring the apex area, vibration signal from different turns, which have different best response frequencies are obtained in the same image. The method has the potential to measure the response from a much wider region of the cochlea than any other currently used method. The noise floor for vibration image for the system at 200 Hz was ~0.3nm.
Kochunas, Brendan; Fitzgerald, Andrew; Larsen, Edward
2017-09-01
A central problem in nuclear reactor analysis is calculating solutions of steady-state k-eigenvalue problems with thermal hydraulic feedback. In this paper we propose and utilize a model problem that permits the theoretical analysis of iterative schemes for solving such problems. To begin, we discuss a model problem (with nonlinear cross section feedback) and its justification. We proceed with a Fourier analysis for source iteration schemes applied to the model problem. Then we analyze commonly-used iteration schemes involving non-linear diffusion acceleration and feedback. For each scheme we show (1) that they are conditionally stable, (2) the conditions that lead to instability, and (3) that traditional relaxation approaches can improve stability. Lastly, we propose a new iteration scheme that theory predicts is an improvement upon the existing methods.
Yamahata, Christophe; Sarajlic, Edin; Krijnen, Gijs J.M.; Gijs, Martin A.M.
2010-01-01
Abstract—In-plane linear displacements of microelectromechanical systems are measured with subnanometer accuracy by observing the periodic micropatterns with a charge-coupled device camera attached to an optical microscope. The translation of the microstructure is retrieved from the video by phase-s
DEFF Research Database (Denmark)
Thomsen, C; Ståhlberg, F; Stubgaard, M;
1990-01-01
An interleaved pseudocinematographic FLASH (fast low-angle shot) sequence with additional pulsed gradients for flow encoding was used to quantify cerebrospinal fluid (CSF) flow velocities and CSF production. Flow-dependent phase information was obtained by subtracting two differently encoded phase...
Directory of Open Access Journals (Sweden)
Christian Nansen
2010-03-01
Full Text Available Many food products are subjected to quality control analyses for detection of surface residue/contaminants, and there is a trend of requiring more and more documentation and reporting by farmers regarding their use of pesticides. Recent outbreaks of food borne illnesses have been a major contributor to this trend. With a growing need for food safety measures and “smart applications” of insecticides, it is important to develop methods for rapid and accurate assessments of surface residues on food and feed items. As a model system, we investigated detection of a miticide applied to maize leaves and its miticidal bioactivity over time, and we compared two types of reflectance data: fourier transformed infrared (FTIR data and hyperspectral imaging (HI data. The miticide (bifenazate was applied at a commercial field rate to maize leaves in the field, with or without application of a surfactant, and with or without application of a simulated “rain event”. In addition, we collected FTIR and HI from untreated control leaves (total of five treatments. Maize leaf data were collected at seven time intervals from 0 to 48 hours after application. FTIR data were analyzed using conventional analysis of variance of miticide-specific vibration peaks. Two unique FTIR vibration peaks were associated with miticide application (1,700 cm−1 and 763 cm−1. The integrated intensities of these two peaks, miticide application, surfactant, rain event, time between miticide application, and rain event were used as explanatory variables in a linear multi-regression fit to spider mite mortality. The same linear multi-regression approach was applied to variogram parameters derived from HI data in five selected spectral bands (664, 683, 706, 740, and 747 nm. For each spectral band, we conducted a spatial structure analysis, and the three standard variogram parameters (“sill”, “range”, and “nugget” were examined as possible “indicators” of miticide
Wavelet-fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
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.
Analysis of hyper-spectral data derived from an imaging Fourier transform: A statistical perspective
Energy Technology Data Exchange (ETDEWEB)
Sengupta, S.K.; Clark, G.A.; Fields, D.J.
1996-01-10
Fourier transform spectrometers (FTS) using optical sensors are increasingly being used in various branches of science. Typically, a FTS generates a three-dimensional data cube with two spatial dimensions and one frequency/wavelength dimension. The number of frequency dimensions in such data cubes is generally very large, often in the hundreds, making data analytical procedures extremely complex. In the present report, the problem is viewed from a statistical perspective. A set of procedures based on the high degree of inter-channel correlation structure often present in such hyper-spectral data, has been identified and applied to an example data set of dimension 100 x 128 x 128 comprising 128 spectral bands. It is shown that in this case, the special eigen-structure of the correlation matrix has allowed the authors to extract just a few linear combinations of the channels (the significant principal vectors) that effectively contain almost all of the spectral information contained in the data set analyzed. This in turn, enables them to segment the objects in the given spatial frame using, in a parsimonious yet highly effective way, most of the information contained in the data set.
Attenuated total reflectance fourier transform infrared analysis of fly ash geopolymer gel aging.
Rees, Catherine A; Provis, John L; Lukey, Grant C; van Deventer, Jannie S J
2007-07-17
Structural changes in fly ash geopolymers activated with different sodium hydroxide and silicate concentrations are investigated using attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy over a period of 200 days. A strong correlation is found between the concentration of silicate monomer in the activating solution and the position of the main Si-O-T stretching band in the FTIR spectrum, which gives an indication of the relative changes in the gel Si/Al ratio. The FTIR spectra of geopolymer samples with activating solution concentrations of up to 1.2 M SiO2 indicate that an Al-rich gel forms before the final gel composition is reached. The time required for the system to reach a steady gel composition depends on the silicate activating solution concentration and speciation. Geopolymers activated with solutions containing predominantly high-order silicate species rapidly reach a steady gel composition without first forming an Al-rich gel. A minimum silicate monomer concentration of approximately 0.6 M is required to shift the geopolymer synthesis mechanism from hydroxide activation to silicate activation. Silicate speciation in the activating solutions also affects zeolite formation and geopolymer microstructures, with a more homogeneous microstructure and less zeolite formation observed at a higher SiO2 content.
Messaoudi, Imen; Elloumi-Oueslati, Afef; Lachiri, Zied
2014-01-01
Investigating the roles and functions of DNA within genomes is becoming a primary focus of genomic research. Thus, the research works are moving towards cooperation between different scientific disciplines which aims at facilitating the interpretation of genetic information. In order to characterize the DNA of living organisms, signal processing tools appear to be very suitable for such study. However, a DNA sequence must be converted into a numerical sequence before processing; which defines the concept of DNA coding. In line with this, we propose a new one dimensional model based on the chaos game representation theory called Frequency Chaos Game Signal: FCGS. Then, we perform a Smoothed Fourier Transform to enhance hidden periodicities in the C.elegans DNA sequences. Through this study, we demonstrate the performance of our coding approach in highlighting characteristic periodicities. Indeed, several periodicities are shown to be involved in the 1D spectra and the 2D spectrograms of FCGSs. To investigate further about the contribution of our method in the enhancement of characteristic spectral attributes, a comparison with a range of binary indicators is established.
Fourier-transform infrared spectroscopy (FTIR) analysis of triclinic and hexagonal birnessites
Energy Technology Data Exchange (ETDEWEB)
Ling, Florence T.; Post, Jeffrey E.; Heaney, Peter J.; Kubicki, James D.; Santelli, Cara M.
2017-05-01
The characterization of birnessite structures is particularly challenging for poorly crystalline materials of biogenic origin, and a determination of the relative concentrations of triclinic and hexagonal birnessite in a mixed assemblage has typically required synchrotron-based spectroscopy and diffraction approaches. In this study, Fourier-transform infrared spectroscopy (FTIR) is demonstrated to be capable of differentiating synthetic triclinic Na-birnessite and synthetic hexagonal H-birnessite. Furthermore, IR spectral deconvolution of peaks resulting from Mnsingle bondO lattice vibrations between 400 and 750 cm^{- 1} yield results comparable to those obtained by linear combination fitting of synchrotron X-ray absorption fine structure (EXAFS) data when applied to known mixtures of triclinic and hexagonal birnessites. Density functional theory (DFT) calculations suggest that an infrared absorbance peak at ~ 1628 cm^{- 1} may be related to OH vibrations near vacancy sites. The integrated intensity of this peak may show sensitivity to vacancy concentrations in the Mn octahedral sheet for different birnessites.
THE SPECTRUM AND TERM ANALYSIS OF CO iii MEASURED USING FOURIER TRANSFORM AND GRATING SPECTROSCOPY
Energy Technology Data Exchange (ETDEWEB)
Smillie, D. G.; Pickering, J. C. [Blackett Laboratory, Imperial College London, London SW7 2AZ (United Kingdom); Nave, G. [National Institute of Standards and Technology, Gaithersburg, MD 20899-8422 (United States); Smith, P. L., E-mail: j.pickering@imperial.ac.uk [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
2016-03-15
The spectrum of Co iii has been recorded in the region 1562–2564 Å (64,000 cm{sup −1}–39,000 cm{sup −1}) by Fourier transform (FT) spectroscopy, and in the region 1317–2500 Å (164,000 cm{sup −1}–40,000 cm{sup −1}) using a 10.7 m grating spectrograph with phosphor image plate detectors. The spectrum was excited in a cobalt–neon Penning discharge lamp. We classified 514 Co iii lines measured using FT spectroscopy, the strongest having wavenumber uncertainties approaching 0.004 cm{sup −1} (approximately 0.2 mÅ at 2000 Å, or 1 part in 10{sup 7}), and 240 lines measured with grating spectroscopy with uncertainties between 5 and 10 mÅ. The wavelength calibration of 790 lines of Raassen and Ortí Ortin and 87 lines from Shenstone has been revised and combined with our measurements to optimize the values of all but one of the 288 previously reported energy levels. Order of magnitude reductions in uncertainty for almost two-thirds of the 3d{sup 6}4s and almost half of the 3d{sup 6}4p revised energy levels are obtained. Ritz wavelengths have been calculated for an additional 100 forbidden lines. Eigenvector percentage compositions for the energy levels and predicted oscillator strengths have been calculated using the Cowan code.
Boonen, Hennie A L; Koskamp, Janou A; Theiss, Wolfgang; Iedema, Piet D; Willemse, Robin X E
2017-01-01
The curing characteristics of an ultraviolet (UV) ink layer are of utmost importance for the development of UV inks. Measuring either bulk or bottom cure in itself is not new and has been the subject of many articles. In this article, two methods are described based on Fourier transform infrared (FT-IR) spectrometry to measure in real time and simultaneously the bulk and bottom cure of a thin UV ink layer. The procedure consists of applying a thin (10-12 µm) layer of UV-curing ink on an attenuated total reflection (ATR) crystal. The bottom cure is measured with ATR. The bulk cure is measured simultaneously with a reflection analysis (method 1) or a transmission analysis (method 2). With both methods, the bulk and bottom cure can be determined. To overcome problems with the interference in the ATR reflection setup, it is recommended to use the ATR transmission setup.
Zhao, Ming; Li, Yu; Peng, Leilei
2014-09-22
We report a fast non-iterative lifetime data analysis method for the Fourier multiplexed frequency-sweeping confocal FLIM (Fm-FLIM) system [Opt. Express 22, 10221 (2014)]. The new method, named R-method, allows fast multi-channel lifetime image analysis in the system's FPGA data processing board. Experimental tests proved that the performance of the R-method is equivalent to that of single-exponential iterative fitting, and its sensitivity is well suited for time-lapse FLIM-FRET imaging of live cells, for example cyclic adenosine monophosphate (cAMP) level imaging with GFP-Epac-mCherry sensors. With the R-method and its FPGA implementation, multi-channel lifetime images can now be generated in real time on the multi-channel frequency-sweeping FLIM system, and live readout of FRET sensors can be performed during time-lapse imaging.
Al-Holy, Murad A; Lin, Mengshi; Alhaj, Omar A; Abu-Goush, Mahmoud H
2015-02-01
Alicyclobacillus is a causative agent of spoilage in pasteurized and heat-treated apple juice products. Differentiating between this genus and the closely related Bacillus is crucially important. In this study, Fourier transform infrared spectroscopy (FT-IR) was used to identify and discriminate between 4 Alicyclobacillus strains and 4 Bacillus isolates inoculated individually into apple juice. Loading plots over the range of 1350 and 1700 cm(-1) reflected the most distinctive biochemical features of Bacillus and Alicyclobacillus. Multivariate statistical methods (for example, principal component analysis and soft independent modeling of class analogy) were used to analyze the spectral data. Distinctive separation of spectral samples was observed. This study demonstrates that FT-IR spectroscopy in combination with multivariate analysis could serve as a rapid and effective tool for fruit juice industry to differentiate between Bacillus and Alicyclobacillus and to distinguish between species belonging to these 2 genera.
Rebuffo-Scheer, Cecilia A; Schmitt, Jürgen; Scherer, Siegfried
2007-02-01
A classification system based on Fourier transform infrared (FTIR) spectroscopy combined with artificial neural network analysis was designed to differentiate 12 serovars of Listeria monocytogenes using a reference database of 106 well-defined strains. External validation was performed using a test set of another 166 L. monocytogenes strains. The O antigens (serogroup) of 164 strains (98.8%) could be identified correctly, and H antigens were correctly determined in 152 (91.6%) of the test strains. Importantly, 40 out of 41 potentially epidemic serovar 4b strains were unambiguously identified. FTIR analysis is superior to PCR-based systems for serovar differentiation and has potential for the rapid, simultaneous identification of both species and serovar of an unknown Listeria isolate by simply measuring a whole-cell infrared spectrum.
Institute of Scientific and Technical Information of China (English)
Liu Zhi-Ming; Liu Wen-qing; Gao Ming-Guang; Tong Jing-Jing; Zhang Wian-Shu; Xu Liang; Wei Xiuai
2008-01-01
Passive Fourier transform infrared (FTIR) remote sensing measurement of chemical gas cloud is a vital technology.It takes an important part in many fields for the detection of released gases.The principle of concentration measurement is based on the Beer-Lambert law.Unlike the active measurement,for the passive remote sensing,in most cases,the difference between the temperature of the gas cloud and the brightness temperature of the background is usually a few kelvins.The gas cloud emission is almost equal to the background emission,thereby the emission of the gas cloud cannot be ignored.The concentration retrieval algorithm is quite different from the active measurement.In this paper,the concentration retrieval algorithm for the passive FTIR remote measurement of gas cloud is presented in detail,which involves radiative transfer model,radiometric calibration,absorption coefficient calculation,et al.The background spectrum has a broad feature,which is a slowly varying function of frequency.In this paper,the background spectrum is fitted with a polynomial by using the Levenberg-Marquardt method which is a kind of nonlinear least squares fitting algorithm.No background spectra are required.Thus,this method allows mobile,real-time and fast measurements of gas clouds.
Liu, Y; Yao, X; Liu, Y W; Wang, Y
2014-01-01
It is well known that caries invasion leads to the differentiation of dentin into zones with altered composition, collagen integrity and mineral identity. However, understanding of these changes from the fundamental perspective of molecular structure has been lacking so far. In light of this, the present work aims to utilize Fourier transform infrared spectroscopy (FTIR) to directly extract molecular information regarding collagen's and hydroxyapatite's structural changes as dentin transitions from the transparent zone (TZ) into the normal zone (NZ). Unembedded ultrathin dentin films were sectioned from carious teeth, and an FTIR imaging system was used to obtain spatially resolved FTIR spectra. According to the mineral-to-matrix ratio image generated from large-area low-spectral-resolution scan, the TZ, the NZ and the intermediate subtransparent zone (STZ) were identified. High-spectral-resolution spectra were taken from each zone and subsequently examined with regard to mineral content, carbonate distribution, collagen denaturation and carbonate substitution patterns. The integrity of collagen's triple helical structure was also evaluated based on spectra collected from demineralized dentin films of selected teeth. The results support the argument that STZ is the real sclerotic layer, and they corroborate the established knowledge that collagen in TZ is hardly altered and therefore should be reserved for reparative purposes. Moreover, the close resemblance between the STZ and the NZ in terms of carbonate content, and that between the STZ and the TZ in terms of being A-type carbonate-rich, suggest that the mineral that initially occludes dentin tubules is hydroxyapatite newly generated from odontoblastic activities, which is then transformed into whitlockite in the demineralization/remineralization process as caries progresses.
Mandibular shape analysis in fossil hominins: Fourier descriptors in norma lateralis.
Lestrel, P E; Wolfe, C A; Bodt, A
2013-08-01
Biological shape can be defined as the boundary of a form in 2-space (R(2)). An earlier study (Lestrel et al., 2010, HOMO-J. Comp. Hum. Biol.) of the cranial vault found that there were statistically significant differences between each of the three groups: H. erectus, H. heidelbergensis, and H. neanderthalensis compared with H. sapiens. In contrast, there was no statistically significant difference among the first three groups. These results suggest that these three groups may have formed single evolving lineage while H. sapiens represents a separate evolutionary development. The purpose of the current research was to discern if the mandible reflected a similar pattern as the cranial vault data. This study used lateral jpeg images of the mandible. Five fossil samples were used: A. robustus (n=7), H. erectus (n=12), H. heidelbergensis (n=4), H. neanderthalensis (n=22) and H. sapiens (n=61). Each mandible image was pre-processed with Photoshop Elements. Each image was then submitted to a specially written routine that digitized the 84 points along the mandible boundary. Each mandible was fitted with elliptical Fourier functions (EFFs). Procrustes superimposition was imposed to insure minimum shape differences. The mandible results largely mirrored the earlier cranial vault study with one exception. Statistically significant results were obtained for the mandible between the H. erectus and H. neanderthalensis samples in contrast to the earlier cranial vault data. F-tests disclosed that the statistical significance was limited to the anterior symphysis of the mandible. This mosaic pattern may be explained by the reduction in prognathism with the concomitant if rudimentary development of the chin as seen in H. neanderthalensis compared to H. erectus.
Lucassen, Gerald W.; Bakker, Bernard L.; Neerken, Sieglinde; Hendriks, Rob F. M.
2003-07-01
We present results from 2D Fourier analysis on 3D stacks of images obtained by confocal laser scanning reflectance microscopy (CLSM) and two-photon fluorescence microscopy (2PM) on human skin in vivo. CLSM images were obtained with a modified commercial system (Vivascope1000, Lucid Inc, excitation wavelength 830 nm) equipped with a piezo-focusing element (350 μm range) for depth positioning of the objective lens. 2PM was performed with a specially designed set-up with excitation wavelength 730 nm. Mean cell size in the epidermal layer and structural orientation in the dermal layer have been determined as a function of depth by 2D Fourier analysis. Fourier analysis on microscopic images enables automatic non-invasive quantitative structural analysis (mean cell size and orientation) of living human skin.
Fourier processing of quantum light
Poem, Eilon; Lahini, Yoav; Silberberg, Yaron
2012-01-01
It is shown that a classical optical Fourier processor can be used for the shaping of quantum correlations between two or more photons, and the class of Fourier masks applicable in the multiphoton Fourier space is identified. This concept is experimentally demonstrated using two types of periodic phase masks illuminated with path-entangled photon pairs, a highly non-classical state of light. Applied first were sinusoidal phase masks, emulating two-particle quantum walk on a periodic lattice, yielding intricate correlation patterns with various spatial bunching and anti-bunching effects depending on the initial state. Then, a periodic Zernike-like filter was applied on top of the sinusoidal phase masks. Using this filter, phase information lost in the original correlation measurements was retrieved.
Mueller, Daniela; Ferrão, Marco Flôres; Marder, Luciano; da Costa, Adilson Ben; Schneider, Rosana de Cássia de Souza
2013-03-28
The main objective of this study was to use infrared spectroscopy to identify vegetable oils used as raw material for biodiesel production and apply multivariate analysis to the data. Six different vegetable oil sources--canola, cotton, corn, palm, sunflower and soybeans--were used to produce biodiesel batches. The spectra were acquired by Fourier transform infrared spectroscopy using a universal attenuated total reflectance sensor (FTIR-UATR). For the multivariate analysis principal component analysis (PCA), hierarchical cluster analysis (HCA), interval principal component analysis (iPCA) and soft independent modeling of class analogy (SIMCA) were used. The results indicate that is possible to develop a methodology to identify vegetable oils used as raw material in the production of biodiesel by FTIR-UATR applying multivariate analysis. It was also observed that the iPCA found the best spectral range for separation of biodiesel batches using FTIR-UATR data, and with this result, the SIMCA method classified 100% of the soybean biodiesel samples.
Kwon, Yong-Kook; Ahn, Myung Suk; Park, Jong Suk; Liu, Jang Ryol; In, Dong Su; Min, Byung Whan; Kim, Suk Weon
2013-01-01
To determine whether Fourier transform (FT)-IR spectral analysis combined with multivariate analysis of whole-cell extracts from ginseng leaves can be applied as a high-throughput discrimination system of cultivation ages and cultivars, a total of total 480 leaf samples belonging to 12 categories corresponding to four different cultivars (Yunpung, Kumpung, Chunpung, and an open-pollinated variety) and three different cultivation ages (1 yr, 2 yr, and 3 yr) were subjected to FT-IR. The spectral data were analyzed by principal component analysis and partial least squares-discriminant analysis. A dendrogram based on hierarchical clustering analysis of the FT-IR spectral data on ginseng leaves showed that leaf samples were initially segregated into three groups in a cultivation age-dependent manner. Then, within the same cultivation age group, leaf samples were clustered into four subgroups in a cultivar-dependent manner. The overall prediction accuracy for discrimination of cultivars and cultivation ages was 94.8% in a cross-validation test. These results clearly show that the FT-IR spectra combined with multivariate analysis from ginseng leaves can be applied as an alternative tool for discriminating of ginseng cultivars and cultivation ages. Therefore, we suggest that this result could be used as a rapid and reliable F1 hybrid seed-screening tool for accelerating the conventional breeding of ginseng. PMID:24558311
Rajiv, P.; Rajeshwari, Sivaraj; Venckatesh, Rajendran
2013-12-01
Fourier transform infrared spectroscopy (FT-IR) and Gas chromatography-mass spectroscopy have been carried out to investigate the chemical composition of Parthenium mediated vermicompost. Four different concentrations of Parthenium and cow dung mixtures were vermicomposted using the earthworms (Eudrilus eugeniae). FT-IR spectra reveal the absence of Parthenin toxin (sesquiterpene lactone) and phenols in vermicompost which was obtained from high concentration of cow dung mixed treatments. GC-MS analysis shows no phenolic compounds and predominant level of intermediate metabolites such as 4,8,12,16-Tetramethylheptadecan-4-olide (7.61%), 2-Pentadecanone, 6,10,14-trimethyl- (5.29%) and Methyl 16-methyl-heptadecanoate (4.69%) during the vermicomposting process. Spectral results indicated that Parthenin toxin and phenols can be eradicated via vermicomposting if mixed with appropriate quantity of cow dung.
Directory of Open Access Journals (Sweden)
Robert W. Johnson
2013-06-01
Full Text Available The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can satisfy numerically the energy and reconstruction theorems; however, transform pairs based on a variable window or nonuniform frequency sampling in general do not. Instead of selecting the shape of the window as some function of the central frequency, we propose constructing a single window with unit energy from an arbitrary set of windows that is applied over the entire frequency axis. By virtue of using a fixed window with uniform frequency sampling, such a transform satisfies the energy and reconstruction theorems. The shape of the window can be tailored to meet the requirements of the investigator in terms of time/frequency resolution. The algorithm extends naturally to the case of nonuniform signal sampling without modification beyond identification of the Nyquist interval.
Energy Technology Data Exchange (ETDEWEB)
Aldea, N.; Indrea, E. (Institute for Isotopic and Molecular Technology, Cluj (Romania))
1990-08-01
The computer program presented is based on the Fourier analysis of a singel X-ray diffraction profile. An X-ray diffraction method is presented which is capable of determining the average particle size, microstrain, stacking fault probability as well as the particle size distribution function in crystalline materials. The main numerical methods used are: (i) Smoothing and interpolation by 3rd-order piecewise polynomial functions or by cubic splines with the least squares method; (ii) numerical integration by successive five points formulae and numerical derivative by cubic splines with the least squares method; (iii) estimation of parameters by the weighted least squares method. The results for supported platinum catalysts used in the H/D isotopic exchange reaction are illustrated. (orig.).
Hożejowska, Sylwia; Piasecka, Magdalena; Piasecki, Artur
This paper presents the results of investigations into flow boiling heat transfer in an asymmetrically heated vertical minichannel of 1.7 mm depth. The heated element for FC-72 flowing in the minichannel was an alloy plate 0.45 mm thick, microstructured on one side, in direct contact with the flowing fluid. The computational part of the study contains approximate steady state solutions of the heat transfer problems described by Poisson.s equation and the energy equation for the heated plate and the fluid, respectively. For both equations, the boundary conditions were specified on the basis of experimental data. Temperature of the outer plate surface, measured by infrared thermography, and heat losses to ambient air were included in the calculations. For the energy equation we assumed parabolic profile of fluid velocity and the equality of temperatures and heat fluxes at the interface between the heated surface and the fluid. The void fraction was taken from a single-phase flow model. Two-dimensional temperature distributions were obtained by the Trefftz method and, due to the Robin condition at the interface between them, it was possible to calculate the heat transfer coefficient. Its values were compared to those obtained by other correlations known from literature.
Directory of Open Access Journals (Sweden)
Hożejowska Sylwia
2017-01-01
Full Text Available This paper presents the results of investigations into flow boiling heat transfer in an asymmetrically heated vertical minichannel of 1.7 mm depth. The heated element for FC-72 flowing in the minichannel was an alloy plate 0.45 mm thick, microstructured on one side, in direct contact with the flowing fluid. The computational part of the study contains approximate steady state solutions of the heat transfer problems described by Poisson.s equation and the energy equation for the heated plate and the fluid, respectively. For both equations, the boundary conditions were specified on the basis of experimental data. Temperature of the outer plate surface, measured by infrared thermography, and heat losses to ambient air were included in the calculations. For the energy equation we assumed parabolic profile of fluid velocity and the equality of temperatures and heat fluxes at the interface between the heated surface and the fluid. The void fraction was taken from a single-phase flow model. Two-dimensional temperature distributions were obtained by the Trefftz method and, due to the Robin condition at the interface between them, it was possible to calculate the heat transfer coefficient. Its values were compared to those obtained by other correlations known from literature.
Brito, Ana C.; Fernandes, Teresa F.; Newton, Alice; Facca, Chiara; Tett, Paul
2012-09-01
Shallow coastal lagoons, especially the ones with clear waters and lighted substrata, are likely to have large microphytobenthos (MPB) communities. MPB is an important component of these systems, representing up to 99% of the chlorophyll concentration when compared to phytoplankton. It is therefore expected that MPB resuspension play a key role in the dynamics of phytoplankton due to the tide and wind action. Water samples were collected twice per month inside and outside Ria Formosa lagoon (Portugal), for nutrients and chlorophyll a (chl a). Sediment samples were also collected for MPB chl a. Chl a was also analysed in water and sediment samples from Venice lagoon (Italy), at least once per month. A truncated Fourier series was fitted to the data to investigate the seasonal and high-frequency components of the time-series. In the Ria Formosa, the best significant fit for MPB was obtained considering the sum of 26 wave-pairs (sin and cosine), which explained 31% of the variability. The seasonal cycle (1-3 waves) explained approximately 5% of the total variability. Within-day variability which includes spatial heterogeneity explained 61% of the variability. The best fit for phytoplankton inside Ria Formosa was obtained considering the sum of 23 wave-pairs. Outside the lagoon the best fit was obtained using only the sum of 16 wave-pairs. For both cases, the sum of waves explained more than 64% of the variability and the seasonal cycle explained more than 31% of the variability. It is expected that primary producers in the water column have a strong seasonal factor due to the direct effect of the solar cycle, which is the case of other clear waters. In the Venice lagoon, which is microtidal, the best fit for MPB was obtained using 10 wave-pairs. However, the best fit for phytoplankton was obtained with only 3 wave-pairs, indicating the importance of the seasonal cycle. Significant relationships were found between phytoplankton inside and outside the Ria Formosa, as
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The values of mosaic block size and microstrain measured by the method of Voigt function are sometimes largely erroneous and difficult to be revised. In this paper, the causes of the “hook effect” which inevitably exists in the method of Fourier analysis are explained; then the method for resolving this effect is put forward; and finally the method of hypothetical function is used to simplify the method of the Fourier analysis from multi-peak to single-peak. By introducing the parameter m, this method can not only indicate the degree of errors, but also revise them as well. It is simple, clear and able to accomplish the intricate pattern calculation quickly by the aid of computer. In the end, we argue the identity between method of the approximate function and the Fourier analysis, and give a more accurate proportional coefficient k.
Marr, Greg C.
2003-01-01
The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.
Fourier spectra from exoplanets with polar caps and ocean glint
Visser, P M
2015-01-01
The weak orbital-phase dependent reflection signal of an exoplanet contains information on the planet surface, such as the distribution of continents and oceans on terrestrial planets. This light curve is usually studied in the time domain, but because the signal from a stationary surface is (quasi)periodic, analysis of the Fourier series may provide an alternative, complementary approach. We study Fourier spectra from reflected light curves for geometrically simple configurations. Depending on its atmospheric properties, a rotating planet in the habitable zone could have circular polar ice caps. Tidally locked planets, on the other hand, may have symmetric circular oceans facing the star. These cases are interesting because the high-albedo contrast at the sharp edges of the ice-sheets and the glint from the host star in the ocean may produce recognizable light curves with orbital periodicity, which could also be interpreted in the Fourier domain. We derive a simple general expression for the Fourier coeffici...
Testing Jitter on PLL Clocks Based on Analysis of Instantaneous Phase
Institute of Scientific and Technical Information of China (English)
ZHU Yanqing; HE Yigang; FANG Gefeng; YANG Hui; QI Shaozhong; LIU Hui
2007-01-01
A novel method based on the analysis of instantaneous phase is proposed to extract the jitter on phase-locked loops output clock. The method utilizes the Hilbert transform to extend the real signal of PLLs output into an analytic signal, and the implementation of Hilbert transform is based on the Fourier transform windowed with Hamming window. Then, the jitter of clock is extracted from the instantaneous phase of analytic signal. The experimental results of simulations validate that the proposed method can effectively extract the jitter on PLL clock, and it has better performance by comparing the sinusoidal jitter extraction results with the other methods.
The Asymmetric Pupil Fourier Wavefront Sensor
Martinache, Frantz
2013-01-01
This paper introduces a novel wavefront sensing approach that relies on the Fourier analysis of a single conventional direct image. In the high Strehl ratio regime, the relation between the phase measured in the Fourier plane and the wavefront errors in the pupil can be linearized, as was shown in a previous work that introduced the notion of generalized closure-phase, or kernel-phase. The technique, to be usable as presented requires two conditions to be met: (1) the wavefront errors must be kept small (of the order of one radian or less) and (2) the pupil must include some asymmetry, that can be introduced with a mask, for the problem to become solvable. Simulations show that this asymmetric pupil Fourier wavefront sensing or APF-WFS technique can improve the Strehl ratio from 50 to over 90 % in just a few iterations, with excellent photon noise sensitivity properties, suggesting that on-sky close loop APF-WFS is possible with an extreme adaptive optics system.
DEFF Research Database (Denmark)
Budnik, Bogdan A.; Jensen, Kenneth Bendix; Jørgensen, Thomas J. D.
2000-01-01
A 2.94 microm Er:YAG laser was used together with a commercial Fourier transform mass spectrometer to study labile biomolecules. The combination has shown superior performance over conventional 337 nm ultraviolet matrix-assisted laser desorption/ionization (UV-MALDI) Fourier transform mass...... spectrometry (FTMS), especially for the analysis of peptides with post-translational modifications. With succinic acid as a matrix, the sensitivity of the single-shot analysis was increased by an order of magnitude to the low femtomole level, with significantly less fragmentation observed. Intact molecular...
Zhu, Ying; Tan, Tuck Lee
2016-04-01
An effective and simple analytical method using Fourier transform infrared (FTIR) spectroscopy to distinguish wild-grown high-quality Ganoderma lucidum (G. lucidum) from cultivated one is of essential importance for its quality assurance and medicinal value estimation. Commonly used chemical and analytical methods using full spectrum are not so effective for the detection and interpretation due to the complex system of the herbal medicine. In this study, two penalized discriminant analysis models, penalized linear discriminant analysis (PLDA) and elastic net (Elnet),using FTIR spectroscopy have been explored for the purpose of discrimination and interpretation. The classification performances of the two penalized models have been compared with two widely used multivariate methods, principal component discriminant analysis (PCDA) and partial least squares discriminant analysis (PLSDA). The Elnet model involving a combination of L1 and L2 norm penalties enabled an automatic selection of a small number of informative spectral absorption bands and gave an excellent classification accuracy of 99% for discrimination between spectra of wild-grown and cultivated G. lucidum. Its classification performance was superior to that of the PLDA model in a pure L1 setting and outperformed the PCDA and PLSDA models using full wavelength. The well-performed selection of informative spectral features leads to substantial reduction in model complexity and improvement of classification accuracy, and it is particularly helpful for the quantitative interpretations of the major chemical constituents of G. lucidum regarding its anti-cancer effects.
Zhu, Ying; Tan, Tuck Lee
2016-04-15
An effective and simple analytical method using Fourier transform infrared (FTIR) spectroscopy to distinguish wild-grown high-quality Ganoderma lucidum (G. lucidum) from cultivated one is of essential importance for its quality assurance and medicinal value estimation. Commonly used chemical and analytical methods using full spectrum are not so effective for the detection and interpretation due to the complex system of the herbal medicine. In this study, two penalized discriminant analysis models, penalized linear discriminant analysis (PLDA) and elastic net (Elnet),using FTIR spectroscopy have been explored for the purpose of discrimination and interpretation. The classification performances of the two penalized models have been compared with two widely used multivariate methods, principal component discriminant analysis (PCDA) and partial least squares discriminant analysis (PLSDA). The Elnet model involving a combination of L1 and L2 norm penalties enabled an automatic selection of a small number of informative spectral absorption bands and gave an excellent classification accuracy of 99% for discrimination between spectra of wild-grown and cultivated G. lucidum. Its classification performance was superior to that of the PLDA model in a pure L1 setting and outperformed the PCDA and PLSDA models using full wavelength. The well-performed selection of informative spectral features leads to substantial reduction in model complexity and improvement of classification accuracy, and it is particularly helpful for the quantitative interpretations of the major chemical constituents of G. lucidum regarding its anti-cancer effects.
Laak, J.A.W.M. van der; Dijkman, H.B.P.M.; Pahlplatz, M.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 pre
Harthcock, Matthew A.
1985-12-01
Fourier self-deconvolution (FSD) has been applied to several regions of the infrared spectra of ethylene/acrylic and methacrylic acid copolymers to obtain detailed information on the structure of these copolymers. The computer assisted technique has been applied to the 1050-830 cm-1 region of the infrared spectrum of the copolymers to resolve the vinyl (909 cm-1) and vinylidene (887 cm-1) CH2 wagging vibrations from the in-phase out-of-plane hydrogen deformation vibration of the acid dimer (943 cm-1). The technique was applied to the carbonyl stretching vibration region (1820-1660 cm-1) to study the structure of the acid groups. Two distinct hydrogen bonded (1710 and 1696 cm-1) and free (1758 and 1745 cm-1) acid group structures were observed for the 9% acrylic acid copolymers, while the methacrylic acid copolymer showed predominantly one hydrogen bonded (1696 cm-1) and one free (1758 cm-1) acid group structure. Also, the 6.5% acrylic acid copolymers showed essentially one type of hydrogen bonded (1706 cm-1) carbonyl and two free carbonyl stretching absorptions (1758 and 1745 cm-1).
Fourier techniques in X-ray timing
M. van der Klis
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
Energy Technology Data Exchange (ETDEWEB)
Vernardou, D. [Institute for Materials Research, University of Salford, Cockroft Building, Salford, Manchester, M5 4WT (United Kingdom); Pemble, M.E. [Tyndall National institute, Lee Maltings, Prospect Row, Cork (Ireland)], E-mail: martyn.pemble@tyndall.ie; Sheel, D.W. [Institute for Materials Research, University of Salford, Cockroft Building, Salford, Manchester, M5 4WT (United Kingdom)
2008-05-30
This paper describes the use of in-situ Fourier transform infrared spectroscopy to monitor the gas phase reactions of the formation of VO{sub 2} thin films from VO(acac){sub 2} under atmospheric pressure chemical vapour deposition conditions. In the absence of O{sub 2}, it is found that anhydride species may form, while there is also some evidence of ester species. In the presence of O{sub 2}, the spectra obtained are almost identical to those in the absence of O{sub 2}. However in this case, there is also some indication for the enhanced production of CO and the suppression of the formation of C-H species. A possible mechanism for the formation of VO{sub 2} is proposed, which involves the release of two C{sub 3}H{sub 4} molecules and the decomposition of vanadyl (IV) acetylacetonate into VO(CH{sub 3}COO){sub 2}, which then further decomposes to yield (CH{sub 3}CO){sub 2}O and VO{sub 2}. However, while spectroscopic evidence for the formation of these species is presented, the mechanism proposed cannot be confirmed on the basis of these data alone.
Energy Technology Data Exchange (ETDEWEB)
Faires, L.M.; Palmer, B.A.; Brault, J.W.
1984-01-01
High resolution Fourier transform spectrometry has been used to perform line width and line shape analysis of eighty-one iron I emision lines in the spectral range 290 to 390nm originating in the normal analytical zone of an inductively coupled plasma. Computer programs using non-linear least squares fitting techniques for line shape analysis were applied to the fully resolved spectra to determine Gaussian and Lorentzian components of the total observed line width. The effect of noise in the spectrum on the precision of the line fitting technique was assessed, and the importance of signal to noise ratio for line shape analysis is discussed. Translational (Doppler) temperatures were calculated from the Gaussian components of the line width and were found to be on the order of 6300/sup 0/K. The excitation temperature of iron I was also determined from the same spectral data by the spectroscopic slope method based on the Einstein-Boltzmann expression for spectral intensity and was found to be on the order of 4700/sup 0/K. 31 references.
Marcos-Garcés, V; Harvat, M; Molina Aguilar, P; Ferrández Izquierdo, A; Ruiz-Saurí, A
2017-03-20
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
Analysis on reconstruction of virtual images of Fourier telescopy%傅里叶望远镜重构图像虚像分析
Institute of Scientific and Technical Information of China (English)
于树海; 董磊; 刘欣悦; 凌剑勇
2015-01-01
Fourier telescopy can realize high resolution imaging to remote, small and dim target by using laser as the light source. The signal-to-noise ratio of imaging system is easy to improve by increasing the area of receiver. However, numerical simulation shows that the reconstruction images sometimes has a virtual phenomenon. It reduces the quality of reconstruction images, and even cannot have a resolution to the imaging target. Based on Fourier telescopy imaging principle, using T type transmitting array, the reason of forming virtual images is indicated by mathematical deduction. The spatial frequency error between the actual getting and setting would be produced when the laser beams scan the x or y axis with pitch error. The error would cause the random phase influence when calculating the single Fourier frequency of target by using phase closure on the axis and quadrant scan. Using integrated spatial frequency of transmitter array to reconstruct the image of target would cause a virtual phenomenon. By contrasting reconstruction images it is found that the image quality is reduced seriously, even the virtual phenomenon appears when the transmitting system is axially scanned with pitch error, and it decreases slightly on quadrant scan. In the present paper, we consider the reason of the phase closure of quadrant of T type transmitting array relies on axial frequency. At the same pitch error, different scan methods would cause different reconstruction images. The directions of virtual images are the same within the axial error. The computer simulation confirms the validity of the above analysis by three different modes of transmitter array through using the next field experiment parameters.%研究了采用T型激光发射阵列情况下傅里叶望远镜重构图像的虚像问题, 基于系统成像基本原理, 明确了虚像的来源. 分析认为, 发射光束在x和y轴扫描时, 在俯仰角误差的作用下, 抽取目标的空间频率和设定值之间存
Mass Spectrometry and Fourier Transform Infrared Spectroscopy for Analysis of Biological Materials
Energy Technology Data Exchange (ETDEWEB)
Anderson, Timothy J. [Iowa State Univ., Ames, IA (United States)
2014-12-01
Time-of-flight mass spectrometry along with statistical analysis was utilized to study metabolic profiles among rats fed resistant starch (RS) diets. Fischer 344 rats were fed four starch diets consisting of 55% (w/w, dbs) starch. A control starch diet consisting of corn starch was compared against three RS diets. The RS diets were high-amylose corn starch (HA7), HA7 chemically modified with octenyl succinic anhydride, and stearic-acid-complexed HA7 starch. A subgroup received antibiotic treatment to determine if perturbations in the gut microbiome were long lasting. A second subgroup was treated with azoxymethane (AOM), a carcinogen. At the end of the eight week study, cecal and distal-colon contents samples were collected from the sacrificed rats. Metabolites were extracted from cecal and distal colon samples into acetonitrile. The extracts were then analyzed on an accurate-mass time-of-flight mass spectrometer to obtain their metabolic profile. The data were analyzed using partial least-squares discriminant analysis (PLS-DA). The PLS-DA analysis utilized a training set and verification set to classify samples within diet and treatment groups. PLS-DA could reliably differentiate the diet treatments for both cecal and distal colon samples. The PLS-DA analyses of the antibiotic and no antibiotic treated subgroups were well classified for cecal samples and modestly separated for distal-colon samples. PLS-DA analysis had limited success separating distal colon samples for rats given AOM from those not treated; the cecal samples from AOM had very poor classification. Mass spectrometry profiling coupled with PLS-DA can readily classify metabolite differences among rats given RS diets.
Analysis of lard in meatball broth using Fourier transform infrared spectroscopy and chemometrics.
Kurniawati, Endah; Rohman, Abdul; Triyana, Kuwat
2014-01-01
Meatball is one of the favorite foods in Indonesia. For the economic reason (due to the price difference), the substitution of beef meat with pork can occur. In this study, FTIR spectroscopy in combination with chemometrics of partial least square (PLS) and principal component analysis (PCA) was used for analysis of pork fat (lard) in meatball broth. Lard in meatball broth was quantitatively determined at wavenumber region of 1018-1284 cm(-1). The coefficient of determination (R(2)) and root mean square error of calibration (RMSEC) values obtained were 0.9975 and 1.34% (v/v), respectively. Furthermore, the classification of lard and beef fat in meatball broth as well as in commercial samples was performed at wavenumber region of 1200-1000 cm(-1). The results showed that FTIR spectroscopy coupled with chemometrics can be used for quantitative analysis and classification of lard in meatball broth for Halal verification studies. The developed method is simple in operation, rapid and not involving extensive sample preparation.
Energy Technology Data Exchange (ETDEWEB)
Caraveo, M; McNamara, J; Rimner, A; Yorke, E; Li, G [Memorial Sloan Kettering Cancer Center, New York, NY (United States); Wei, J [City College of New York, New York, NY (United States)
2014-06-15
Purpose: Motion artifacts are common in patient 4DCT, leading to an illdefined tumor volume with variation up to 110% or setting up a poor foundation with low imaging fidelity for tumor motion study. We developed a method to estimate 4DCT image quality by establishing a correlation between the severity of motion artifacts in 4DCT images and the periodicity of corresponding 1D respiratory wave-function (1DRW) surrogate used for 4DCT reconstruction. Methods: Fast Fourier Transformation (FFT) was applied to analyze 1DRW periodicity, defined as the sum of the 5 largest Fourier coefficients, ranging in 0–1. Distortional motion artifacts of cine-scan 4DCT at the junctions of adjacent couchposition scans around the diaphragm were identified in 3 categories: incomplete, overlapping and duplicate. To quantify these artifacts, the discontinuity of the diaphragm at the junctions was measured in distance and averaged along 6 directions in 3 orthogonal views. Mean and sum artifacts per junction (APJ) across the entire diaphragm were calculated in each breathing phase. To make the APJ inter-patient comparable, patientspecific motion was removed from APJ by dividing patient-specific diaphragmatic velocity (displacement divided by the mean period, from FFT analysis of the 1DRW) and the normalized APJ was defined as motion artifact severity (MAS). Twenty-five patients with free-breathing 10-phase 4DCT and corresponding 1DRW surrogate datasets were studied. Results: A mild correlation of 0.56 was found between 1DRW periodicity and 4DCT artifact severity. Higher MAS tends to appear around mid inhalation and mid exhalation and the lowest MAS tends to be around full exhalation. The breathing periodicity of >0.8 possesses minimal motion artifacts. Conclusion: The 1D-4D correlation provides a fast means to estimate 4DCT image quality. Using 1DRW signal, we can retrospectively screen out high-quality 4DCT images for clinical research (periodicity>0.8) and prospectively identify poor
Phase Spectral Analysis of EEG Signals
Institute of Scientific and Technical Information of China (English)
YOURong-yi; CHENZhong
2004-01-01
A new method of phase spectral analysis of EEG is proposed for the comparative analysis of phase spectra between normal EEG and epileptic EEG signals based on the wavelet decomposition technique. By using multiscale wavelet decomposition, the original EEGs are mapped to an orthogonal wavelet space, such that the variations of phase can be observed at multiscale. It is found that the phase (and phase difference) spectra of normal EEGs are distinct from that of epileptic EEGs. That is the variations of phase (and phase difference) of normal EEGs have a distinct periodic pattern with the electrical activity proceeds in the brain, but do not the epileptic EEGs. For epileptic EEGs, only at those transient points, the phase variations are obvious. In order to verify these results with the observational data, the phase variations of EEGs in principal component space are observed and found that, the features of phase spectra is in correspondence with that the wavelet space. These results make it possible to view the behavior of EEG rhythms as a dynamic spectrum.
Institute of Scientific and Technical Information of China (English)
熊坤来; 罗景青
2012-01-01
利用多相码雷达信号在某个分数阶域内呈现多个间隔相等的冲击这一特性,提出了一种基于分数阶Fourier变换的多相码雷达信号分离算法,首先将混合信号以特定的旋转角作分数阶Fourier变换,然后通过窄带通滤波器抽取多相码雷达信号,去除大量噪声和其他干扰信号,最后再经过分数阶Fourier反变换,恢复出时域的多相码雷达信号.理论分析和仿真实验表明,该算法计算量小,分离效果好,可实现较低信噪比下的多相码雷达信号分离.%By using the characteristics of poly-phase code radar signals that its energy are concentrated in one fractional domain, a separation algorithm of poly-phase code radar signals based on fractional Fourier transform (FrFT) is proposed in this paper. First, a mixed signal is rotated to a certain angle by the FrFT. Then, a narrow band filter is exploited to extract the poly-phase code radar signal and depress most of noise and other signals. Finally, the poly-phase code radar signal is rotated back to the time domain by the inverse FrFT. The theoretical analysis and simulation results demonstrate the validity of the method.
Directory of Open Access Journals (Sweden)
Glaucia Braz Alcantara
2010-06-01
Full Text Available This paper describes the potentiality of Fourier transform infrared (FT-IR spectroscopy associated to chemometric analysis for assessment of conventional and genetically modified soybean crops. Recently, genetically modified organisms have been queried about their influence on the environment and their safety as food/feed. In this regard, chemical investigations are ever more required. Thus three different soybean cultivars distributed in transgenic Roundup ReadyTM soybean and theirs conventional counterparts were directly investigated by FT-IR spectroscopy and chemometric analysis. The application of PCA and KNN methods permitted the discrimination and classification of the genetically modified samples from conventional ones when they were separately analysed. The analyses showed the chemical variation according to genetic modification. Furthermore, this methodology was efficient for cultivar grouping and highlights cultivar dependence for discrimination between transgenic and non-transgenic samples. According to this study, FT-IR and chemometrics could be used as a quick, easy and low cost tool to assess the chemical composition variation in genetically modified organisms.
Hartnett, John G
2007-01-01
A Fourier analysis has been carried out on the galaxy number count as a function of redshift, the $N$-$z$ relation, calculated from redshift data of both the Sloan Digital Sky Survey (SDSS) and the 2dF Galaxy Redshift Survey (2dF GRS). Regardless of the interpretation of those redshifts, the results indicate that galaxies have preferred periodic redshifts. This is the \\textit{picket-fence} structure observed by some. Application of the Hubble law, at low redshift, results in galaxies preferentially located on concentric shells with periodic spacings. This analysis finds significant redshift spacings of $\\Delta z =$ 0.0102, 0.0246, and 0.0448 in the SDSS and strong agreement with the results from 2dF GRS. The combined results from both surveys indicate regular real space spacings of $44.0 \\pm 2.5$ $Mpc$, $102 \\pm 8$ $Mpc$ and $176 \\pm 29$ $Mpc$, for an assumed Hubble's constant $H_0 = 72 km s^{-1} Mpc^{-1}$. These results indicate that it is a real effect and not some observational artifact. The effect is sign...
Badhan, Ajay; Wang, Yuxi; McAllister, Tim A
2017-01-01
Fourier transformed mid-infrared spectroscopy (FTIR) is a powerful tool for compositional analysis of plant cell walls (Acebes et al., Front Plant Sci 5:303, 2014; Badhan et al., Biotechnol Biofuels 7:1-15, 2014; Badhan et al., BioMed Res Int 2015: 562952, 2015; Roach et al., Plant Physiol 156:1351-1363, 2011). The infrared spectrum generates a fingerprint of a sample with absorption peaks corresponding to the frequency of vibrations between the bonds of the atoms making up the material. Here, we describe a method focused on the use of FTIR in combination with principal component analysis (PCA) to characterize the composition of the plant cell wall. This method has been successfully used to study complex enzyme saccharification processes like rumen digestion to identify recalcitrant moieties in low-quality forage which resist rumen digestion (Badhan et al., BioMed Res Int 2015: 562952, 2015), as well as to characterize cell wall mutant lines or transgenic lines expressing exogenous hydrolases (Badhan et al., Biotechnol Biofuels 7:1-15, 2014; Roach et al., Plant Physiol 156:1351-1363, 2011). The FTIR method described here facilitates high-throughput identification of the major compositional differences across a large set of samples in a low cost and nondestructive manner.
Li, Guoyun; Steppich, Julia; Wang, Zhenyu; Sun, Yi; Xue, Changhu; Linhardt, Robert J; Li, Lingyun
2014-07-01
Low molecular weight heparins (LMWHs) are heterogeneous, polydisperse, and highly negatively charged mixtures of glycosaminoglycan chains prescribed as anticoagulants. The detailed characterization of LMWH is important for the drug quality assurance and for new drug research and development. In this study, online hydrophilic interaction chromatography (HILIC) Fourier transform mass spectrometry (FTMS) was applied to analyze the oligosaccharide fragments of LMWHs generated by heparin lyase II digestion. More than 40 oligosaccharide fragments of LMWH were quantified and used to compare LMWHs prepared by three different manufacturers. The quantified fragment structures included unsaturated disaccharides/oligosaccharides arising from the prominent repeating units of these LMWHs, 3-O-sulfo containing tetrasaccharides arising from their antithrombin III binding sites, 1,6-anhydro ring-containing oligosaccharides formed during their manufacture, saturated uronic acid oligosaccharides coming from some chain nonreducing ends, and oxidized linkage region oligosaccharides coming from some chain reducing ends. This bottom-up approach provides rich detailed structural analysis and quantitative information with high accuracy and reproducibility. When combined with the top-down approach, HILIC LC-FTMS based analysis should be suitable for the advanced quality control and quality assurance in LMWH production.
均值有界变差条件及其在Fourier分析中的应用%Mean Bounded Variation Condition and Applications in Fourier Analysis
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
This announcement is to raise an ultimate generalization to monotonicity condition on the Fourier(trigonometric) coefficient sequences.We prove this condition cannot be weakened any further to guarantee the uniform convergence of the sine series.Some interesting and important classical results in Fourier analysis are re-established under this ultimate condition.Over ninty year research history is surveyed in this announcement.The first original paper of this series of papers is posted in arXiv:math.CA/0611805 vl,November 27,2006.
Vidyasagar, P B; Lokhandwalla, M N; Damle, P S
1986-01-01
Compound action potentials recorded from normal and M. leprae infected mice sciatic nerves were analysed in frequency domain using Fourier Series Analysis. Changes in myelinated fibre potentials were detected as early as 2nd post-inoculation month. This technique could be further developed to aid in early diagnosis of leprosy.
Pezzolo, Alessandra De Lorenzi
2011-01-01
The diffuse reflectance infrared Fourier transform (DRIFT) spectra of sand samples exhibit features reflecting their composition. Basic multivariate analysis (MVA) can be used to effectively sort subsets of homogeneous specimens collected from nearby locations, as well as pointing out similarities in composition among sands of different origins.…
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.
Polyimide analysis using diffuse reflectance-FTIR. [Fourier Transform IR Spectroscopy
Young, P. R.; Chang, A. C.
1985-01-01
The thermal imidization of a number of polyimide precursors in the form of powders, films, and prepregs was examined by an in situ diffuse reflectance-FTIR technique where infrared spectra were determined while the material was being heated. An analysis of these spectra revealed that, with the exception of one water soluble adhesive, each precursor developed an anhydride band around 1850 cm/cu during imidization. This band diminished in intensity during final stages of cure. Efforts were made to quantify the amount of anhydride in several samples. Evidence obtained could be interpreted to mean that poly(amic acid) resins undergo an initial reduction in molecular weight during imidization before recombining to achieve their ultimate molecular weights as polyimides. Several reports in the literature are cited to support this interpretation. This report serves both to document anhydride formation during imidization and to increase our fundamental understanding of how polyimides cure.
Téllez-Quiñones, Alejandro; Malacara-Doblado, Daniel; García-Márquez, Jorge
2012-04-01
From generalized phase-shifting equations, we propose a simple linear system analysis for algorithms with equally and nonequally spaced phase shifts. The presence of a finite number of harmonic components in the fringes of the intensity patterns is taken into account to obtain algorithms insensitive to these harmonics. The insensitivity to detuning for the fundamental frequency is also considered as part of the description of this study. Linear systems are employed to recover the desired insensitivity properties that can compensate linear phase shift errors. The analysis of the wrapped phase equation is carried out in the Fourier frequency domain.
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
Fourier series and orthogonal functions
Davis, Harry F
1963-01-01
This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging.
Zhao, An-Xin; Tang, Xiao-Jun; Zhang, Zhong-Hua; Liu, Jun-Hua
2014-10-01
The generalized two-dimensional correlation spectroscopy and Fourier transform infrared were used to identify hydrocarbon isomers in the mixed gases for absorption spectra resolution enhancement. The Fourier transform infrared spectrum of n-butane and iso-butane and the two-dimensional correlation infrared spectrum of concentration perturbation were used for analysis as an example. The all band and the main absorption peak wavelengths of Fourier transform infrared spectrum for single component gas showed that the spectra are similar, and if they were mixed together, absorption peaks overlap and peak is difficult to identify. The synchronous and asynchronous spectrum of two-dimensional correlation spectrum can clearly identify the iso-butane and normal butane and their respective characteristic absorption peak intensity. Iso-butane has strong absorption characteristics spectrum lines at 2,893, 2,954 and 2,893 cm(-1), and n-butane at 2,895 and 2,965 cm(-1). The analysis result in this paper preliminary verified that the two-dimensional infrared correlation spectroscopy can be used for resolution enhancement in Fourier transform infrared spectrum quantitative analysis.
Deswysen, A G; Dutilleul, P; Godfrin, J P; Ellis, W C
1993-10-01
Average daily and within-day nycterohemeral patterns of eating and ruminating behavior were determined in six Holstein-Friesian heifers (average BW = 427 kg) given ad libitum access to either corn or grass silage in a two-period crossover design. Rhythm components (number of cycles/24 h) were characterized by finite Fourier transform of the 24-h mastication activities as measured during 4 d by continuous jaw movement recordings. Average daily voluntary intake of corn silage was 8.2% greater (P = .05) than that for grass silage and was associated (P meals and shorter daily, unitary eating and ruminating times, and smaller number of rumination boli. Analysis of variance of the daily mean of hourly activities and Rhythm Components 1 to 12 indicated effects of (P time spent eating and ruminating, for both silage types and individual heifers. Relative importance of Rhythm Component 1 of time spent eating, indicative of a main circadian pattern, was related positively to pedigree value for milk production (P = .01) and negatively to milk protein concentration (P = .09).(ABSTRACT TRUNCATED AT 250 WORDS)
Directory of Open Access Journals (Sweden)
Wan-You Li
2014-01-01
Full Text Available A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM and the applicability of the finite element method (FEM, is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.
Nakata, M
1987-03-01
EEG alterations after 5 or 10 minutes of global ischemia were investigated for 6 hours of postischemic period in 18 adult cats, together with biophysiological parameters such as cerebral blood flow, intracranial pressure, systemic blood pressure, heart rate, and blood gases. Our EEG analytical system is composed of high fidelity pre-amplifier, AA 6 MK II (Medelec Limited, England) and signal processor 7T 08 (NEC-SanEi, Japan). It is qualified to analyze frequencies up to 20 kHz within 3 dB cut-off. Particular features of our EEG analytical method are focused on Fourier analysis about broad frequency bands, frequency and amplitude spectra to be expressed on bi-logarithmic graph and direct EEG recordings from various structures of the brain. On the basis of fluctuation theory following 3 types were divided; Type f which corresponds to 1/f fluctuation, Type L which corresponds to Lorentzian fluctuation, Type f+L which is the sum of Type f and L. The distribution of these types in the central nervous system corresponds with cortical structures, spinal cord and brain stem respectively. In conclusion, there was a good correlation between EEG and blood flow in the motor cortex. The functional reversibility after ischemia was different according to the types. Type f structures, namely the motor cortex, hippocampus and amygdala were vulnerable and Type f+L structures namely ventrolateral nucleus of the thalamus and midbrain reticular formation tended to recover or stay in preservation.
Mingwei, Zhang; Qingbo, Zhou; Zhongxin, Chen; Jia, Liu; Yong, Zhou; Chongfa, Cai
2008-12-01
Crop identification is the basis of crop monitoring using remote sensing. Remote sensing the extent and distribution of individual crop types has proven useful to a wide range of users, including policy-makers, farmers, and scientists. Northern China is not merely the political, economic, and cultural centre of China, but also an important base for grain production. Its main grains are wheat, maize, and cotton. By employing the Fourier analysis method, we studied crop planting patterns in the Northern China plain. Then, using time-series EOS-MODIS NDVI data, we extracted the key parameters to discriminate crop types. The results showed that the estimated area and the statistics were correlated well at the county-level. Furthermore, there was little difference between the crop area estimated by the MODIS data and the statistics at province-level. Our study shows that the method we designed is promising for use in regional spatial scale crop mapping in Northern China using the MODIS NDVI time-series.
Pounder, F Nell; Reddy, Rohith K; Bhargava, Rohit
2016-06-23
Breast cancer screening provides sensitive tumor identification, but low specificity implies that a vast majority of biopsies are not ultimately diagnosed as cancer. Automated techniques to evaluate biopsies can prevent errors, reduce pathologist workload and provide objective analysis. Fourier transform infrared (FT-IR) spectroscopic imaging provides both molecular signatures and spatial information that may be applicable for pathology. Here, we utilize both the spectral and spatial information to develop a combined classifier that provides rapid tissue assessment. First, we evaluated the potential of IR imaging to provide a diagnosis using spectral data alone. While highly accurate histologic [epithelium, stroma] recognition could be achieved, the same was not possible for disease [cancer, no-cancer] due to the diversity of spectral signals. Hence, we employed spatial data, developing and evaluating increasingly complex models, to detect cancers. Sub-mm tumors could be very confidently predicted as indicated by the quantitative measurement of accuracy via receiver operating characteristic (ROC) curve analyses. The developed protocol was validated with a small set and statistical performance used to develop a model that predicts study design for a large scale, definitive validation. The results of evaluation on different instruments, at higher noise levels, under a coarser spectral resolution and two sampling modes [transmission and transflection], indicate that the protocol is highly accurate under a variety of conditions. The study paves the way to validating IR imaging for rapid breast tumor detection, its statistical validation and potential directions for optimization of the speed and sampling for clinical deployment.
Directory of Open Access Journals (Sweden)
Charles W. Ross
2016-06-01
Full Text Available Ceramides are a central unit of all sphingolipids which have been identified as sites of biological recognition on cellular membranes mediating cell growth and differentiation. Several glycosphingolipids have been isolated, displaying immunomodulatory and anti-tumor activities. These molecules have generated considerable interest as potential vaccine adjuvants in humans. Accurate analyses of these and related sphingosine analogues are important for the characterization of structure, biological function, and metabolism. We report the complementary use of direct laser desorption ionization (DLDI, sheath flow electrospray ionization (ESI Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS and high-field nuclear magnetic resonance (NMR analysis for the rapid, accurate identification of hexacosanoylceramide and starting materials. DLDI does not require stringent sample preparation and yields representative ions. Sheath-flow ESI yields ions of the product and byproducts and was significantly better than monospray ESI due to improved compound solubility. Negative ion sheath flow ESI provided data of starting materials and products all in one acquisition as hexacosanoic acid does not ionize efficiently when ceramides are present. NMR provided characterization of these lipid molecules complementing the results obtained from MS analyses. NMR data was able to differentiate straight chain versus branched chain alkyl groups not easily obtained from mass spectrometry.
Wang, Jun; Kim, Kyung Ho; Kim, Sungkyun; Kim, Yong Soo; Li, Qing X; Jun, Soojin
2010-11-15
Bacterial contamination continues to be a serious concern for food safety. Although washing fresh produce helps in reducing pathogen levels, pathogen internalization often limits the effectiveness of washing. When pathogens internalize in leafy vegetables, the method of identification and quantitative measurement would be called into question. This study was aimed to use Fourier Transform Infrared (FTIR) spectroscopy integrated with an attenuated total reflectance kit for quantification of Escherichia coli K-12 internalized in baby spinach. The bacteria were inoculated into vascular and intracellar tissues of spinach leaves by syringe injection and the distribution of internalized E. coli K-12 cells was confirmed under scanning electron microscopy (SEM). FTIR measurement following the preparation of bacterial suspension from spinach leaves with high speed pulverizing enabled to detect the absorbance peaks in the amide II region between 1590 and 1490 cm⁻¹ as a fingerprint for the microbes. It was found that the estimated concentrations of E. coli K-12 agreed well with the concentrations determined by plate counting with R² values of 0.98 and 0.97 in peptone water and spinach extracts, respectively. The results demonstrated that FTIR can identify and quantify E. coli K-12 in baby spinach extracts at a limit of detection of approximately 100 CFU/mL in 5 min. The developed method is expected to be suitable for the analysis of pathogenic E. coli strains and other bacterial species in fresh vegetables.
Oinas, J; Rieppo, L; Finnilä, M A J; Valkealahti, M; Lehenkari, P; Saarakkala, S
2016-07-21
The changes in chemical composition of human articular cartilage (AC) caused by osteoarthritis (OA) were investigated using Fourier transform infrared microspectroscopy (FTIR-MS). We demonstrate the sensitivity of FTIR-MS for monitoring compositional changes that occur with OA progression. Twenty-eight AC samples from tibial plateaus were imaged with FTIR-MS. Hyperspectral images of all samples were combined for K-means clustering. Partial least squares regression (PLSR) analysis was used to compare the spectra with the OARSI grade (histopathological grading of OA). Furthermore, the amide I and the carbohydrate regions were used to estimate collagen and proteoglycan contents, respectively. Spectral peak at 1338 cm(-1) was used to estimate the integrity of the collagen network. The layered structure of AC was revealed using the carbohydrate region for clustering. Statistically significant correlation was observed between the OARSI grade and the collagen integrity in the superficial (r = -0.55) and the deep (r = -0.41) zones. Furthermore, PLSR models predicted the OARSI grade from the superficial (r = 0.94) and the deep (r = 0.77) regions of the AC with high accuracy. Obtained results suggest that quantitative and qualitative changes occur in the AC composition during OA progression, and these can be monitored by the use of FTIR-MS.
Hendrickson, Christopher L; Quinn, John P; Kaiser, Nathan K; Smith, Donald F; Blakney, Greg T; Chen, Tong; Marshall, Alan G; Weisbrod, Chad R; Beu, Steven C
2015-09-01
We describe the design and initial performance of the first 21 tesla Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. The 21 tesla magnet is the highest field superconducting magnet ever used for FT-ICR and features high spatial homogeneity, high temporal stability, and negligible liquid helium consumption. The instrument includes a commercial dual linear quadrupole trap front end that features high sensitivity, precise control of trapped ion number, and collisional and electron transfer dissociation. A third linear quadrupole trap offers high ion capacity and ejection efficiency, and rf quadrupole ion injection optics deliver ions to a novel dynamically harmonized ICR cell. Mass resolving power of 150,000 (m/Δm(50%)) is achieved for bovine serum albumin (66 kDa) for a 0.38 s detection period, and greater than 2,000,000 resolving power is achieved for a 12 s detection period. Externally calibrated broadband mass measurement accuracy is typically less than 150 ppb rms, with resolving power greater than 300,000 at m/z 400 for a 0.76 s detection period. Combined analysis of electron transfer and collisional dissociation spectra results in 68% sequence coverage for carbonic anhydrase. The instrument is part of the NSF High-Field FT-ICR User Facility and is available free of charge to qualified users.
Directory of Open Access Journals (Sweden)
Shijun eLi
2015-07-01
Full Text Available Background and objective: The relationship between EEG source signals and action-related visual and auditory stimulation is still not well understood. The objective of this study was to identify EEG source signals and their associated action-related visual and auditory responses, especially independent components of EEG.Methods: A hand-moving-Hanoi video paradigm was used to study neural correlates of the action-related visual and auditory information processing determined by mu rhythm (8-12 Hz in 16 healthy young subjects. Independent component analysis (ICA was applied to identify separate EEG sources, and further computed in the frequency domain by applying-Fourier transform ICA (F-ICA.Results: F-ICA found more sensory stimuli-related independent components located within the sensorimotor region than ICA did. The total number of independent components of interest from F-ICA was 768, twice that of 384 from traditional time-domain ICA (p0.05.Conclusions: These results support the hypothesis that mu rhythm was sensitive to detection of the cognitive expression, which could be reflected by the function in the parietal lobe sensory-motor region. The results of this study could potentially be applied into early diagnosis for those with visual and hearing impairments in the future.
Meier, D C; Benkstein, K D; Hurst, W S; Chu, P M
2017-05-01
Performance standard specifications for point chemical vapor detectors are established in ASTM E 2885-13 and ASTM E 2933-13. The performance evaluation of the detectors requires the accurate delivery of known concentrations of the chemical target to the system under test. Referee methods enable the analyte test concentration and associated uncertainties in the analyte test concentration to be validated by independent analysis, which is especially important for reactive analytes. This work extends the capability of a previously demonstrated method for using Fourier transform infrared (FT-IR) absorption spectroscopy for quantitatively evaluating the composition of vapor streams containing hazardous materials at Acute Exposure Guideline Levels (AEGL) to include test conditions colder than laboratory ambient temperatures. The described method covers the use of primary reference spectra to establish analyte concentrations, the generation of secondary reference spectra suitable for measuring analyte concentrations under specified testing environments, and the use of additional reference spectra and spectral profile strategies to mitigate the uncertainties due to impurities and water condensation within the low-temperature (7 °C, -5 °C) test cell. Important benefits of this approach include verification of the test analyte concentration with characterized uncertainties by in situ measurements co-located with the detector under test, near-real-time feedback, and broad applicability to toxic industrial chemicals.
Ross, Charles W; Simonsick, William J; Bogusky, Michael J; Celikay, Recep W; Guare, James P; Newton, Randall C
2016-06-28
Ceramides are a central unit of all sphingolipids which have been identified as sites of biological recognition on cellular membranes mediating cell growth and differentiation. Several glycosphingolipids have been isolated, displaying immunomodulatory and anti-tumor activities. These molecules have generated considerable interest as potential vaccine adjuvants in humans. Accurate analyses of these and related sphingosine analogues are important for the characterization of structure, biological function, and metabolism. We report the complementary use of direct laser desorption ionization (DLDI), sheath flow electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) and high-field nuclear magnetic resonance (NMR) analysis for the rapid, accurate identification of hexacosanoylceramide and starting materials. DLDI does not require stringent sample preparation and yields representative ions. Sheath-flow ESI yields ions of the product and byproducts and was significantly better than monospray ESI due to improved compound solubility. Negative ion sheath flow ESI provided data of starting materials and products all in one acquisition as hexacosanoic acid does not ionize efficiently when ceramides are present. NMR provided characterization of these lipid molecules complementing the results obtained from MS analyses. NMR data was able to differentiate straight chain versus branched chain alkyl groups not easily obtained from mass spectrometry.
Kim, Kyung Ah; Herigault, Gwenael; Kim, Myeong-Jin; Chung, Young Eun; Hong, Hye-Suk; Choi, Sun Young
2011-01-01
To compare the image quality of two variants of a three-dimensional (3D) gradient echo sequence (GRE) for hepatic MRI. Thirty-nine patients underwent hepatic MRI on a 3.0 Tesla (T) magnet (Intera Achieva; Philips Medical Systems). The clinical protocol included two variants of a 3D GRE with fat suppression: (i) a "centric" approach, with elliptical centric k-space ordering and (ii) an "enhanced" approach using linear sampling and partial Fourier in both the slice and phase encoding direction. "Centric" and "Enhanced" 3D GRE images were obtained both precontrast (n = 32) and after gadoxetic acid injection (n = 39). Two reviewers jointly reviewed MR images for anatomic sharpness, overall contrast, homogeneity, and absence of artifacts. The liver-to-lesion signal difference ratio (SDR) was measured. Paired sample Wilcoxon test and paired t-tests were used. Enhanced 3D GRE images performed better than centric 3D GRE images with respect to anatomic sharpness (P = 0.0156), overall contrast (P = 0.0195), homogeneity (P < 0.0001), and absence of artifacts (P = 0.0003) on precontrast images. For postcontrast MRI, enhanced 3D GRE images showed better quality in terms of overall contrast (P = 0.0195), homogeneity (P < 0.0001), and absence of artifacts (P = 0.009). Liver-to-lesion SDR on enhanced 3D GRE images (0.48 ± 0.13) was significantly higher than that of conventional 3D GRE images (0.40 ± 0.19, P = 0.0004) on postcontrast images, but not on precontrast images. The enhanced 3D GRE sequence available on our scanner provided better hepatic image quality than the centric variant, without compromising lesion contrast. Copyright © 2010 Wiley-Liss, Inc.
Neeman, Elias M.; Aviles Moreno, Juan-Ramon; Huet, T. R.
2016-06-01
Several monoterpenes and terpenoids are biogenic volatile organic compounds which are emitted in the atmosphere, where they react with OH, O_3 and NO_x etc. to give rise to several oxidation and degradation products. Their decomposition products are a major source of secondray organic aerosol (SOA). Spectroscopic information on these atmospheric species is still very scarce. The rotational spectrum of nopinone (C_9H14O) one of the major oxidation products of β-pinene, and of its water complexes were recorded in a supersonic jet expansion with a Fourier transform microwave spectrometer over the range 2-20 GHz. The structure of the unique stable conformer of the nopinone was optimized using density functional theory and ab initio calculations. Signals from the parent species and from the 13C and 18O isotopomers were observed in natural abundance. A magnetic hyperfine structure associated with the pairs of hydrogen nuclei in the methylene groups was observed and modeled. The structures of several conformers of the nopinone-water complexes with up to three molecules of water were optimized using density functional theory and ab initio calculations. The energetically most stable of calculated conformers were observed and anlyzed. The rotational and centrifugal distortion parameters were fitted to a Watson's Hamiltonian in the A-reduction. The present work provides the first spectroscopic characterization of nopinone and its water complexes in the gas phase. A. Calogirou, B.R. Larsen, and D. Kotzias, Atmospheric Environment, 33, 1423-1439, (1999) P. Paasonen et al., Nat. Geosci., 6, 438-442 (2013) D. Zhang and R. Zhang The Journal of Chemical Physics, 122, 114308, (2005) R. Winterhalter et al. Journal of Atmospheric Chemistry, 35, 165-197, (2000)
Fleming, Barry D; Zhang, Jie; Elton, Darrell; Bond, Alan M
2007-09-01
The analysis of dc cyclic voltammograms of surface-confined metalloproteins is complicated by large background currents, significant ohmic iRu drop, and frequency dispersion related to protein and electrode surface inhomogeneity. The use of large-amplitude Fourier transform ac voltammetry for the quantification of the electron-transfer properties of a thin film of redox-active protein azurin adsorbed onto edge-plane, basal-plane, and highly oriented pyrolytic graphite electrode surfaces has been evaluated and compared to results obtained by dc cyclic voltammetry. In principle, it has been established that fourth and higher harmonic sine-wave data are ideally suited for analysis of electron-transfer processes as they are almost completely devoid of background capacitance current contributions. However, uncompensated resistance has a higher impact on these components, as is the case with fast scan rate dc techniques, so strategies to include this term in the simulations have been investigated. Application of recommended strategies for the evaluation of the electron-transfer properties of azurin adsorbed onto three forms of graphite, each having different background or uncompensated resistance values, is described and compared to results obtained by traditionally used forms of cyclic voltammetry. The electron-transfer rate constant, k0', of azurin at a highly oriented pyrolytic graphite electrode surface was approximately 250 s(-1), compared with > or =1000 s(-1) at edge-plane and basal-plane graphite electrodes. The significantly lower k0' value found at the highly oriented pyrolytic graphite electrode was related to the relatively low level of edge-plane defect sites present at the surface of this electrode. However, analysis of high ac harmonics suggests that frequency dispersion is substantial at all electrode surfaces. Such effects in these diffusionless situations are significantly enhanced relative to solution-phase voltammetry, where overlay of diffusion
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.
Software safety analysis practice in installation phase
Energy Technology Data Exchange (ETDEWEB)
Huang, H. W.; Chen, M. H.; Shyu, S. S., E-mail: hwhwang@iner.gov.t [Institute of Nuclear Energy Research, No. 1000 Wenhua Road, Chiaan Village, Longtan Township, 32546 Taoyuan County, Taiwan (China)
2010-10-15
This work performed a software safety analysis in the installation phase of the Lung men nuclear power plant in Taiwan, under the cooperation of Institute of Nuclear Energy Research and Tpc. The US Nuclear Regulatory Commission requests licensee to perform software safety analysis and software verification and validation in each phase of software development life cycle with Branch Technical Position 7-14. In this work, 37 safety grade digital instrumentation and control systems were analyzed by failure mode and effects analysis, which is suggested by IEEE standard 7-4.3.2-2003. During the installation phase, skew tests for safety grade network and point to point tests were performed. The failure mode and effects analysis showed all the single failure modes can be resolved by the redundant means. Most of the common mode failures can be resolved by operator manual actions. (Author)
Bellisola, Giuseppe; Cinque, Gianfelice; Vezzalini, Marzia; Moratti, Elisabetta; Silvestri, Giovannino; Redaelli, Sara; Gambacorti Passerini, Carlo; Wehbe, Katia; Sorio, Claudio
2013-07-21
We tested the ability of Fourier Transform (FT) InfraRed (IR) microspectroscopy (microFTIR) in combination with unsupervised Hierarchical Cluster Analysis (HCA) in identifying drug-resistance/sensitivity in leukemic cells exposed to tyrosine kinase inhibitors (TKIs). Experiments were carried out in a well-established mouse model of human Chronic Myelogenous Leukemia (CML). Mouse-derived pro-B Ba/F3 cells transfected with and stably expressing the human p210(BCR-ABL) drug-sensitive wild-type BCR-ABL or the V299L or T315I p210(BCR-ABL) drug-resistant BCR-ABL mutants were exposed to imatinib-mesylate (IMA) or dasatinib (DAS). MicroFTIR was carried out at the Diamond IR beamline MIRIAM where the mid-IR absorbance spectra of individual Ba/F3 cells were acquired using the high brilliance IR synchrotron radiation (SR) via aperture of 15 × 15 μm(2) in sizes. A conventional IR source (globar) was used to compare average spectra over 15 cells or more. IR signatures of drug actions were identified by supervised analyses in the spectra of TKI-sensitive cells. Unsupervised HCA applied to selected intervals of wavenumber allowed us to classify the IR patterns of viable (drug-resistant) and apoptotic (drug-sensitive) cells with an accuracy of >95%. The results from microFTIR + HCA analysis were cross-validated with those obtained via immunochemical methods, i.e. immunoblotting and flow cytometry (FC) that resulted directly and significantly correlated. We conclude that this combined microFTIR + HCA method potentially represents a rapid, convenient and robust screening approach to study the impact of drugs in leukemic cells as well as in peripheral blasts from patients in clinical trials with new anti-leukemic drugs.
Montgomery, Hugh L
2015-01-01
Hugh Montgomery has written a book which both students and faculty should appreciate. I wish it had been written 15 years ago so I could have shared it with students. It is a gem. -Richard Askey, University of Wisconsin-Madison Montgomery has written an exquisite text combining basic material, exciting examples, advanced topics, wonderful historical notes, and excellent exercises. It is absolutely compelling and masterful! -John Benedetto, University of Maryland This nice book is likely to be especially successful. l feel that the author has managed admirably to bring to light both the beauty
Stevenson, Gareth P; Lee, Chong-Yong; Kennedy, Gareth F; Parkin, Alison; Baker, Ruth E; Gillow, Kathryn; Armstrong, Fraser A; Gavaghan, David J; Bond, Alan M
2012-06-26
A detailed analysis of the cooperative two-electron transfer of surface-confined cytochrome c peroxidase (CcP) in contact with pH 6.0 phosphate buffer solution has been undertaken. This investigation is prompted by the prospect of achieving a richer understanding of this biologically important system via the employment of kinetically sensitive, but background devoid, higher harmonic components available in the large-amplitude Fourier transform ac voltammetric method. Data obtained from the conventional dc cyclic voltammetric method are also provided for comparison. Theoretical considerations based on both ac and dc approaches are presented for cases where reversible or quasi-reversible cooperative two-electron transfer involves variation in the separation of their reversible potentials, including potential inversion (as described previously for solution phase studies), and reversibility of the electrode processes. Comparison is also made with respect to the case of a simultaneous two-electron transfer process that is unlikely to occur in the physiological situation. Theoretical analysis confirms that the ac higher harmonic components provide greater sensitivity to the various mechanistic nuances that can arise in two-electron surface-confined processes. Experimentally, the ac perturbation with amplitude and frequency of 200 mV and 3.88 Hz, respectively, was employed to detect the electron transfer when CcP is confined to the surface of a graphite electrode. Simulations based on cooperative two-electron transfer with the employment of reversible potentials of 0.745 ± 0.010 V, heterogeneous electron transfer rate constants of between 3 and 10 s(-1) and charge transfer coefficients of 0.5 for both processes fitted experimental data for the fifth to eighth ac harmonics. Imperfections in theory-experiment comparison are consistent with kinetic and thermodynamic dispersion and other nonidealities not included in the theory used to model the voltammetry of surface
Theoretical discussions on the geometrical phase analysis
Energy Technology Data Exchange (ETDEWEB)
Rouviere, J.L. [CEA-Grenoble, Departement de Recherche Fondamentale sur la Matiere Condensee, SP2M, 17 rue des Martyrs, 38054 Grenoble Cedex 9 (France)]. E-mail: rouvierej@cea.fr; Sarigiannidou, E. [CEA-Grenoble, Departement de Recherche Fondamentale sur la Matiere Condensee, SP2M, 17 rue des Martyrs, 38054 Grenoble Cedex 9 (France)
2005-12-15
The Geometrical phase analysis, which is a very efficient method to measure deformation from High resolution transmission electron microscopy images, is studied from a theoretical point of view. We point out that the basic property of this method is its ability to measure local reciprocal lattice parameters with a high level of accuracy. We attempt to provide some insights into (a) different formula used in the geometrical phase analysis such as the well-known relation between phase and displacement: P{sub g}(r)=-2{pi}g.u(r), (b) the two different definitions of strain, each of which corresponding to a different lattice reference and (c) the meaning of a continuous displacement in a dot-like high resolution image. The case of one-dimensional analysis is also presented. Finally, we show that the method is able to give the position of the dot that is nearest to a given pixel in the image.
A 2D Fourier tool for the analysis of photo-elastic effect in large granular assemblies
Leśniewska, Danuta
2017-06-01
Fourier transforms are the basic tool in constructing different types of image filters, mainly those reducing optical noise. Some DIC or PIV software also uses frequency space to obtain displacement fields from a series of digital images of a deforming body. The paper presents series of 2D Fourier transforms of photo-elastic transmission images, representing large pseudo 2D granular assembly, deforming under varying boundary conditions. The images related to different scales were acquired using the same image resolution, but taken at different distance from the sample. Fourier transforms of images, representing different stages of deformation, reveal characteristic features at the three (`macro-`, `meso-` and `micro-`) scales, which can serve as a data to study internal order-disorder transition within granular materials.
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
Transformadas Discretas de Fourier
Alpízar-Brenes, Geisel; Calderón-Arce, Cindy; Soto-Quirós, Juan Pablo
2015-01-01
Proyecto de Investigación (VIE-5402-1440-4301). Este proyecto presenta un marco matem atico-computacional para el desarrollo de un conjunto de de niciones derivadas de la transformada discreta de Fourier (TDF), que son la funci on discreta de ambig uedad, la transformada discreta de Zak, la transformada discreta de Fourier en tiempo corto, la transformada discreta chirp-Fourier, la transformada discreta de Fourier de quaterniones, la transformada discreta de Cohen, la transform...
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Riedel, Thomas; Dittmar, Thorsten
2014-08-19
Fourier Transform Ion Cyclotron Resonance mass spectra (FT-ICR-MS) of natural organic matter are complex and consist of several thousands of peaks. The corresponding mass to charge ratios (m/z) and signal intensities result from analytes and noise. The most commonly applied way of distinguishing between analyte and noise is a fixed signal-to-noise ratio below which a detected peak is considered noise. However, this procedure is problematic and can yield ambiguous results. For example, random noise peaks can occur slightly above the signal-to-noise threshold (false positives), while peaks of low abundance analytes may occasionally fall below the fixed threshold (false negatives). Thus, cumulative results from repeated measurements of the same sample contain more peaks than a single measurement. False positive and false negative signals are difficult to distinguish, which affects the reproducibility between replicates of a sample. To target this issue, we tested the feasibility of a method detection limit (MDL) for the analysis of natural organic matter to identify peaks that can reliably be distinguished from noise by estimating the uncertainty of the noise. We performed 556 replicate analyses of a dissolved organic matter sample from the deep North Pacific on a 15 T FT-ICR-MS; each of these replicate runs consisted of 500 cumulated broadband scans. To unambiguously identify analyte peaks in the mass spectra, the sample was also run at time-consuming high-sensitivity settings. The resulting data set was used to establish and thoroughly test a MDL. The new method is easy to establish with software help, does only require the additional analysis of replicate blanks (low time increase), and can implement all steps of sample preparation. Especially when analysis time does not allow for replicate runs, major merits of the MDL are reliable removal of false positive (noise) peaks and better reproducibility, while the risk of losing analytes with low signal intensities
Choe, E.; Meer, van der F.; Rossiter, D.; Salm, van der C.; Kim, K.W.
2010-01-01
This study aimed at examining effective sample treatments and spectral processing for an alternate method of soil nitrate determination using the attenuated total reflectance (ATR) of Fourier transform infrared (FTIR) spectroscopy. Prior to FTIR measurements, soil samples were prepared as paste to e
Shakib, Farzin; Hughes, Thomas J. R.
1991-01-01
A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.
Indian Academy of Sciences (India)
Pavitra Tandon; K Sunanda; M N Deo; M D Saksena; K N Uttam
2011-04-01
The emission spectra of $B^3 ^-_u (0^+_u) - X^3 ^-_g (0^+_g)$ transition of the isotopic species 80Se2, excited in an electrodeless discharge lamp by the 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.
Static Fourier transform infrared spectrometer.
Schardt, Michael; Murr, Patrik J; Rauscher, Markus S; Tremmel, Anton J; Wiesent, Benjamin R; Koch, Alexander W
2016-04-01
Fourier transform spectroscopy has established itself as the standard method for spectral analysis of infrared light. Here we present a robust and compact novel static Fourier transform spectrometer design without any moving parts. The design is well suited for measurements in the infrared as it works with extended light sources independent of their size. The design is experimentally evaluated in the mid-infrared wavelength region between 7.2 μm and 16 μm. Due to its large etendue, its low internal light loss, and its static design it enables high speed spectral analysis in the mid-infrared.
Phase Coherence Analysis of Insect Flight
Shchekinova, E Y
2009-01-01
During insect flight a high--frequency wing oscillatory motion is generated. Here we present analysis of kinematic data of tethered Drosophila melanogaster flight. For a reliable detection of specific regimes of frequency variation we propose phase coherence method. The approach is generic and can be applied to nonstationary biological signals that feature multi- scale frequency variations. Our analysis reveals existence of distinct oscillatory modes.
Nyakas, Adrien; Han, Jun; Peru, Kerry M; Headley, John V; Borchers, Christoph H
2013-05-07
Oil sands processed water (OSPW) is the main byproduct of the large-scale bitumen extraction activity in the Athabasca oil sands region (Alberta, Canada). We have investigated the acid-extractable fraction (AEF) of OSPW by extraction-only (EO) direct infusion (DI) negative-ion mode electrospray ionization (ESI) on a 12T-Fourier transform ion cyclotron resonance mass spectrometer (FTICR-MS), as well as by offline ultrahigh performance liquid chromatography (UHPLC) followed by DI-FTICR-MS. A preliminary offline UHPLC separation into 8 fractions using a reversed-phase C4 column led to approximately twice as many detected peaks and identified compounds (973 peaks versus 2231 peaks, of which 856 and 1734 peaks, respectively, could be assigned to chemical formulas based on accurate mass measurements). Conversion of these masses to the Kendrick mass scale allowed the straightforward recognition of homologues. Naphthenic (CnH2n+zO2) and oxy-naphthenic (CnH2n+zOx) acids represented the largest group of molecules with assigned formulas (64%), followed by sulfur-containing compounds (23%) and nitrogen-containing compounds (8%). Pooling of corresponding fractions from two consecutive offline UHPLC runs prior to MS analysis resulted in ~50% more assignments than a single injection, resulting in 3-fold increase of identifications compared to EO-DI-FTICR-MS using the same volume of starting material. Liquid-liquid extraction followed by offline UHPLC fractionation thus holds enormous potential for a more comprehensive profiling of OSPW, which may provide a deeper understanding of its chemical nature and environmental impact.
Discrete ambiguities in phase-shift analysis
Heemskerk, A.C.; Kok, L.P.; Roo, M. de
1975-01-01
In two practical examples (Î±-3He and Î±-Î± scattering) we investigate to what extent the elastic amplitude above the first inelastic threshold, determined from phase-shift analysis, is subject to ambiguity. We find that it is extremely difficult to determine the correct physical amplitude uniquely.
Signal Analysis from Fourier Transform to Wavelet Transform%信号分析从傅氏变换到小波变换
Institute of Scientific and Technical Information of China (English)
余小勇
2001-01-01
In this paper, the signal analysis methods are expounded from Fourier transform to wavelet transform in the aspect of development of the signal analysis, their respective advantages and shortcomings are analyzed and compared, and the inner development regularity of the signal analysis methods is uncovered.%从信号分析的发展着重阐述了从傅氏变换到小波变换的信号分析方法，分析并比较了各自的优缺点，揭示了信号分析方法发展的内在规律性。
Energy Technology Data Exchange (ETDEWEB)
Takeda, Kan; Maeda, Hisato; Yamaguchi, Nobuo; Nakamura, Kazuyoshi; Nakagawa, Tsuyoshi (Mie Univ., Tsu (Japan). School of Medicine)
1983-07-01
The ventricular emptying performance in patients with congenital heart disease with left to right (L-to-R) shunt was investigated by temporal Fourier analysis of multi-gated cardiac blood-pool data. Functional images are constructed with parameters of each pixel's phase angle and amplitude at fundamental frequency. Using global time-activity curves of both ventricles, phase angle and amplitude of left and right ventricles (LV and RV) were computed. Values of interventricular phase difference (D (phase)) and amplitude ratio of RV to LV (R (amp)) were calculated in individual cases. In 18 subjects with normal cardiac function, mean ( +- standard deviation) values of D (phase) was 1.7 +- 5.8 degree and that of R (amp) was 0.54 +- 0.20, respectively regardless of heart rate. In 22 patients of ventricular septal defect (VSD) with L-to-R shunt, D (phase) became larger in proportion to the ratio of pulmonary to systemic blood flow (Qp/Qs) (r = 0.899, p < 0.001). Especially, in those with large L-to-R shunt (Qp/ Qs < 2.0), significant RV phase lag over 18 degrees was recognized and types of VSD might be possible to be differentiated by phase images. In 9 patients with patent ductus arteriosus (PDA), no RV phase delay was seen. Mean value of R (amp) was considerably smaller in patients with PDA and significantly larger in 11 patients with atrial septal defect (ASD), as compared with that of subjects with normal cardiac functions. However, cases with VSD took the values within normal range. This method is highly valuable for pathophysiologic investigation and differential diagnosis of congenital heart disease with L-to-R shunt.
Teherani, James T
2013-01-01
We have developed a physically-intuitive method to calculate the local lattice constant as a function of position in a high-resolution transmission electron microscopy image by performing a two-dimensional fast Fourier transform. We apply a Gaussian filter with appropriate spatial full-width-half-max (FWHM) bandwidth to the image centered at the desired location to calculate the local lattice constant (as opposed to the average lattice constant). Fourier analysis of the filtered image yields the vertical and horizontal lattice constants at this location. The process is repeated by stepping the Gaussian filter across the image to produce a set of local lattice constants in the vertical and horizontal direction as a function of position in the image. The method has been implemented in a freely available tool on nanoHUB.
VOLMER, M; BOLCK, A; WOLTHERS, BG; DERUITER, AJ; DOORNBOS, DA; VANDERSLIK, W
1993-01-01
Quantitative assessment of urinary calculus (renal stone) constituents by infrared analysis (IR) is hampered by the need of expert knowledge for spectrum interpretation. Our laboratory performed a computerized search of several libraries, containing 235 reference spectra from various mixtures with d
Ushenko, A. G.; Dubolazov, O. V.; Ushenko, Vladimir A.; Ushenko, Yu. A.; Sakhnovskiy, M. Yu.; Prydiy, O. G.; Lakusta, I. I.; Novakovskaya, O. Yu.; Melenko, S. R.
2016-12-01
This research presents investigation results of diagnostic efficiency of a new azimuthally stable Mueller-matrix method of laser autofluorescence coordinate distributions analysis of dried polycrystalline films of uterine cavity peritoneal fluid. A new model of generalized optical anisotropy of biological tissues protein networks is proposed in order to define the processes of laser autofluorescence. The influence of complex mechanisms of both phase anisotropy (linear birefringence and optical activity) and linear (circular) dichroism is taken into account. The interconnections between the azimuthally stable Mueller-matrix elements characterizing laser autofluorescence and different mechanisms of optical anisotropy are determined. The statistic analysis of coordinate distributions of such Mueller-matrix rotation invariants is proposed. Thereupon the quantitative criteria (statistic moments of the 1st to the 4th order) of differentiation of dried polycrystalline films of peritoneal fluid - group 1 (healthy donors) and group 2 (uterus endometriosis patients) are estimated.
Motion-corrected Fourier ptychography
Bian, Liheng; Guo, Kaikai; Suo, Jinli; Yang, Changhuei; Chen, Feng; Dai, Qionghai
2016-01-01
Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the FP reconstruction and limits its practicability. In this paper, we propose a novel FP reconstruction method to efficiently correct for unknown sample motion. Specifically, we adaptively update the sample's Fourier spectrum from low spatial-frequency regions towards high spatial-frequency ones, with an additional motion recovery and phase-offset compensation procedure for each sub-spectrum. Benefiting from the phase retrieval redundancy theory, the required large overlap between adjacent sub-spectra offers an accurate guide for successful motion recovery. Experimental results on both simulated data and real captured data show that the proposed method can correct for unknown sample motion with its standard deviation being up to 10% of the field-of-view scale. We have released...
Directory of Open Access Journals (Sweden)
Yubo Wang
2017-06-01
Full Text Available It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC. In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976 ratio and outperforms existing methods such as short-time Fourier transfrom (STFT, continuous Wavelet transform (CWT and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Wang, Yubo; Veluvolu, Kalyana C
2017-06-14
It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Fourier analysis of non-Blazhko ab-type RR Lyrae stars observed with the Kepler space telescope
Nemec, J M; Benko, J M; Moskalik, P; Kolenberg, K; Szabo, R; Kurtz, D W; Bryson, S; Guggenberger, E; Chadid, M; Jeon, Y -B; Kunder, A; Layden, A C; Kinemuchi, K; Kiss, L L; Poretti, E; Christensen-Dalsgaard, J; Kjeldsen, H; Caldwell, D; Ripepi, V; Derekas, A; Nuspl, J; Mullally, F; Thompson, S E; Borucki, W J
2011-01-01
Nineteen of the ~40 RR Lyr stars in the Kepler field have been identified as candidate non-Blazhko (or unmodulated) stars. In this paper we present the results of Fourier decomposition of the time-series photometry of these stars acquired during the first 417 days of operation (Q0-Q5) of the Kepler telescope. Fourier parameters based on ~18400 long-cadence observations per star (and ~150000 short-cadence observations for FN Lyr and for AW Dra) are derived. None of the stars shows the recently discovered `period-doubling' effect seen in Blazhko variables; however, KIC 7021124 has been found to pulsate simultaneously in the fundamental and second overtone modes with a period ratio P2/P0 ~ 0.59305 and is similar to the double-mode star V350 Lyr. Period change rates are derived from O-C diagrams spanning, in some cases, over 100 years; these are compared with high-precision periods derived from the Kepler data alone. Extant Fourier correlations by Kovacs, Jurcsik et al. (with minor transformations from the V to t...
SFFT based phase demodulation for faster interference fringes analysis
Lee, Chen-Yu; Hsu, Kuan-Yu; Lee, Chih-Kung
2016-03-01
Try to take advantages of the high-resolution CCD/CMOS developed over the years for real-time three-dimensional deformation/geometry metrology system development, Fourier transform (FT) based algorithms have been integrated to convert interference fringes to wrapped phase maps and then to unwrapped phase maps. All of which led to easy implementation of the algorithms developed over the years to achieve extremely efficient FT computation. Sparse Fast Fourier Transform (SFFT) that only calculating the non-zero coefficient in frequency domain, includes calculations of imaginary part and log, was implemented to further accelerate the computation rate for the above-mentioned FT based operations. Coupling the SFFT accelerated phase map computation approach with Michelson interferometer and Electronic Speckle Pattern Interferometry (ESPI) for near real-time three-dimensional deformation measurement led to the newly developed system. The directions of object deformation are revealed by performing FT to the interference fringes obtained with pre-introduced spatial carrier frequency, which provides a way to retrieve the phase maps by using a single rather than several intensity maps. With only one image frame needed, the interference fringes caused by the deformation could be recorded for off-line phase maps computation if the computation efforts are longer than the recording frame rate. To apply the SFFT algorithm on phase retrieval, a conceptual framework was presented. The benefit of using SFFT as compared to FT was also demonstrated.
Fourier transformation for pedestrians
Butz, Tilman
2006-01-01
Meant to serve an "entertaining textbook," this book belongs to a rare genre. It is written for all students and practitioners who deal with Fourier transformation. Fourier series as well as continuous and discrete Fourier transformation are covered, and particular emphasis is placed on window functions. Many illustrations and easy-to-solve exercises make the book especially accessible, and its humorous style will add to the pleasure of learning from it.
A More Accurate Fourier Transform
Courtney, Elya
2015-01-01
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals (EI) that define Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric $\\mathrm{CO_2}$ concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT's FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability t...
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.
Samsir, Sri A'jilah; Bunawan, Hamidun; Yen, Choong Chee; Noor, Normah Mohd
2016-09-01
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 (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.
Fourier Series Operating Package
Charnow, Milton L.
1961-01-01
This report presents a computer program for multiplying, adding, differentiating, integrating, "barring" and scalarly multiplying "literal" Fourier series as such, and for extracting the coefficients of specified terms.
Note on Redshift Distortion in Fourier Space
Institute of Scientific and Technical Information of China (English)
Yan-Chuan Cai; Jun Pan
2007-01-01
We explore features of redshift distortion in Fourier analysis of N-body simulations.The phases of the Fourier modes of dark matter density fluctuation are generally shifted by the peculiar motion along the line of sight, the induced phase shift is stochastic and has a probability distribution function (PDF) that is symmetric about the peak at zero shift and whose exact shape depends on the wave vector, except on very large scales where phases are invariant by linear perturbation theory. Analysis of the phase shifts motivates our phenomenological models for the bispectrum in redshift space. Comparison with simulations shows that our toy models are very successful in modeling bispectrum of equilateral and isosceles triangles at large scales. In the second part we compare the monopole of the power spectrum and bispectrum in the radial and plane-parallel distortion to test the plane-parallel approximation.We confirm the results of Scoccimarro that difference of power spectrum is at the level of 10%, and, in the reduced bispectrum, the difference is as small as a few percent. However, on the plane perpendicular to the line of sight of kz = 0, the difference in power spectrum between the radial and plane-parallel approximation can be more than ～ 10%, and even worse on very small scales. Such difference is prominent for bispectrum, especially for configurations of tilted triangles. Non-Gaussian signals under the radial distortion on small scales are systematically biased downside than are in the plane-parallel approximation, with amplitudes depending on the opening angle of the sample point to the observer. This observation gives warning to the practice of using the power spectrum and bispectrum measured on the kz = 0 plane as estimates of the real space statistics.
Rummel, Julia L; McKenna, Amy M; Marshall, Alan G; Eyler, John R; Powell, David H
2010-03-01
Direct Analysis in Real Time (DART) is an ambient ionization technique for mass spectrometry that provides rapid and sensitive analyses with little or no sample preparation. DART has been reported primarily for mass analyzers of low to moderate resolving power such as quadrupole ion traps and time-of-flight (TOF) mass spectrometers. In the current work, a custom-built DART source has been successfully coupled to two different Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometers for the first time. Comparison of spectra of the isobaric compounds, diisopropyl methylphosphonate and theophylline, acquired by 4.7 T FT-ICR MS and TOF MS, demonstrates that the TOF resolving power can be insufficient for compositionally complex samples. 9.4 T FT-ICR MS yielded the highest mass resolving power yet reported with DART ionization for 1,2-benzanthracene and 9,10-diphenylanthracene. Polycyclic aromatic hydrocarbons exhibit a spatial dependence in ionization mechanisms between the DART source and the mass spectrometer. The feasibility of analyzing a variety of samples was established with the introduction and analysis of food products and crude oil samples. DART FT-ICR MS provides complex sample analysis that is rapid, highly selective and information-rich, but limited to relatively low-mass analytes.
基于分数阶傅里叶变换的振动信号分析%Vibration Signal Analysis Based on Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
高宇; 黄宜坚
2012-01-01
通过仿真实验验证了分数阶傅里叶变换可以抑制高斯噪声,检测出chirp信号.通过机械振动实验进一步验证了分数阶傅里叶变换不仅可以分析平稳振动信号,而且分析非平稳振动信号比传统傅里叶变换更客观地表达出信号的频谱,提取出非平稳成分.%Simulation results verify that the fractional fourier transform can suppress gaussian noise and detect the chirp signal. Mechanical vibration experiments further prove that the fractional fourier transform not only analyses stationary signals, but also is more objective to show the spectral characteristics of the signal than that by the traditional fourier transform for analysis of nonstationary signals, and extract non-stationary components.
Analysis of annular phased array transducers for ultrasonic guided wave mode control
Kannajosyula, H.; Lissenden, C. J.; Rose, J. L.
2013-08-01
Exact and asymptotic analyses of annular phased array transducers (PAT) for elastic guided wave mode selection are presented. For the purpose of analysis, the transducer-substrate interaction is formulated in terms of a three-dimensional analogy to filters as applied one-dimensionally in areas such as signal processing and control theory. This enables the deduction of most of the properties of the annular array purely from the Fourier analysis of any actuating function that represents the loading due to the transducer. A generalized mathematical model of the actuating function due to the annular PAT is constructed. The Fourier spectrum is analyzed for resonances in the wavenumber domain. Formulas for phase and time delays are presented. The phenomena of outgoing and incoming waves are also studied. Numerical analysis of the wavenumber spectrum for the annular PAT with a finite number of elements is performed to further illustrate the results deduced from exact and asymptotic analyses. Finite element simulations are presented to further verify the phenomena predicted through the wavenumber spectrum analysis.
Fractional Fourier processing of quantum light.
Sun, Yifan; Tao, Ran; Zhang, Xiangdong
2014-01-13
We have extended Fourier transform of quantum light to a fractional Fourier processing, and demonstrated that a classical optical fractional Fourier processor can be used for the shaping of quantum correlations between two or more photons. Comparing the present method with that of Fourier processing, we find that fractional Fourier processing for quantum light possesses many advantages. Based on such a method, not only quantum correlations can be shaped more rich, but also the initial states can be easily identified. Moreover, the twisted phase information can be recovered and quantum states are easily controlled in performing quantum information experiments. Our findings open up new avenues for the manipulation of correlations between photons in optical quantum information processing.
DEFF Research Database (Denmark)
Nørbygaard, Thomas; Berg, Rolf W.
2004-01-01
Fourier transform (FT) Raman spectroscopy is applied to a range of phthalate ester plasticizers in pure form as well as in poly(vinyl chloride) (PVC) samples. It is found that phthalate esters as a group can be identified by a set of six characteristic Raman bands. FT-Raman spectra of 22 phthalate...... esters are given. It is demonstrated that the presence of phthalate esters in PVC products is readily detectable by FT-Raman spectroscopy. By use of proper ref. samples quant. detn. of the phthalate ester content becomes possible as well....
Directory of Open Access Journals (Sweden)
T. Ge
1995-01-01
Full Text Available A semianalytical algorithm is proposed for the solutions and their stability of a piecewise nonlinear system. The conventional harmonic balance method is modified by the introduction of Toeplitz Jacobian matrices (TJM and by the alternative applications of fast Fourier transformation (FFT and its inverse. The TJM/FFT method substantially reduces the amount of computation and circumvents the necessary numerical differentiation for the Jacobian. An arc-length algorithm and a branch switching procedure are incorporated so that the secondary branches can be independently traced. Oscillators with piecewise nonlinear characteristics are taken as illustrative examples. Flip, fold, and Hopf bifurcations are of interest.
Wulstein, Devynn M; Regan, Kathryn E; Robertson-Anderson, Rae M; McGorty, Ryan
2016-09-01
Using light-sheet microscopy combined with digital Fourier methods we probe the dynamics of colloidal samples and DNA molecules. This combination, referred to as selective-plane illumination differential dynamic microscopy (SPIDDM), has the benefit of optical sectioning to study, with minimal photobleaching, thick samples allowing us to measure the diffusivity of colloidal particles at high volume fractions. Further, SPIDDM exploits the inherent spatially-varying thickness of Gaussian light-sheets. Where the excitation sheet is most focused, we capture high spatial frequency dynamics as the signal-to-background is high. In thicker regions, we capture the slower dynamics as diffusion out of the sheet takes longer.
DEFF Research Database (Denmark)
Nørbygaard, Thomas; Berg, Rolf W.
2004-01-01
Fourier transform (FT) Raman spectroscopy is applied to a range of phthalate ester plasticizers in pure form as well as in poly(vinyl chloride) (PVC) samples. It is found that phthalate esters as a group can be identified by a set of six characteristic Raman bands. FT-Raman spectra of 22 phthalate...... esters are given. It is demonstrated that the presence of phthalate esters in PVC products is readily detectable by FT-Raman spectroscopy. By use of proper ref. samples quant. detn. of the phthalate ester content becomes possible as well....
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
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
Bond, Alan M; Duffy, Noel W; Elton, Darrell M; Fleming, Barry D
2009-11-01
Under most experimental conditions, a distinctly nonlinear background current is encountered in all forms of voltammetry which arises from the potential dependence of the capacitance. The nonlinear background current has been successfully modeled under large amplitude sinusoidal ac voltammetric conditions with a fourth order polynomial. The model was applied to a dummy cell containing a nonideal ceramic capacitor and commonly used electrodes. The nonlinearity in behavior of the background capacitance is particularly significant when considering the discrimination between the Faradaic and background contributions in the higher order harmonics resolved in ac voltammetry by Fourier transform-inverse Fourier transform approaches and in the simulation of the background current and hence double-layer capacitance as a function of potential. Typically, measurable background current under large amplitude conditions is detectable in the dc and fundamental to fourth harmonic components in large amplitude ac voltammetry. For analytical purposes, this background current can be corrected on a per harmonic basis without the need for any model. Background correction has been successfully applied to the first four harmonics for the oxidation of ferrocenemonocarboxylic acid over the concentration range of 5-500 microM in aqueous 0.5 M NaCl solution.
Cross, William Murray
The adsorption of surfactants at mineral oxide surfaces was investigated by in situ Fourier transform infrared internal reflection spectroscopy (FT-IR/IRS), and contact angle goniometry. FT-IR/IRS was used to determine both adsorption isotherms and the enthalpy of adsorption. Furthermore, the conformation and orientation of the hydrocarbon chain of SDS adsorbed at a sapphire internal reflection element (IRE) were determined. Contact angle goniometry was used to measure the effect of the surface phase of the surfactant on the hydrophobic character of sapphire surfaces in aqueous solutions. For SDS adsorbed by sapphire, in situ FT-IR/IRS experiments indicate that a surface phase transition occurs at an adsorption density of 2 to 3 x 10-10 mol/cm2 for both pD 2.9 and 6.9. This transition is characterized by a two to four wavenumber shift in the position of the asymmetric -CH2 stretching band. Based on solution spectroscopy studies, the surface phase was found to be similar to solution phase micelles and liquid crystals for adsorption densities less than the adsorption density of the surface phase transition. Whereas for adsorption densities in excess of the adsorption density of the surface phase transition, the surface phase resembled a solution phase coagel species. It was also found that the contact angle of an air bubble at the sapphire surface exhibited a sharp decrease at the adsorption density corresponding to the surface phase transition The effect of temperature on adsorption and phase behavior of SDS at the sapphire IRE surface was also determined. It was shown that a surface phase transition similar to that discussed occurred at approximately 298 K. The adsorption reaction was found to be exothermic, with a heat of adsorption of --1.3 kcal/mole for adsorption densities less than the adsorption density of the surface phase transition at 298 K and --4.1 kcal/mole for adsorption densities greater than the adsorption density of the surface phase transition
Correia, Alexandre C M
2015-01-01
Here we show how to determine the orbital parameters of a system composed of a star and N companions (that can be planets, brown-dwarfs or other stars), using a simple Fourier analysis of the radial velocity data of the star. This method supposes that all objects in the system follow keplerian orbits around the star and gives better results for a large number of observational points. The orbital parameters may present some errors, but they are an excellent starting point for the traditional minimization methods such as the Levenberg-Marquardt algorithms.
Phase Difference Correction Method for Phase and Frequency in Spectral Analysis
Kang, D.; Ming, X.; Xiaofei, Z.
2000-09-01
A new method, phase difference corrections method is developed to correct the frequency and phase of spectrum peak. The continuous time-domain signal is separated into two segments and fast Fourier translation (FFT) is carried out for them, respectively. The frequency and phase are corrected using the phase difference of corresponding discrete spectral lines. Furthermore, the amplitude can also be rectified using the formula of window function spectrum. This method, with good adaptability, high speed and accuracy, is theoretically simple. It can resolve the frequency by means of phase difference directly without the formula of window function. Simulation shows that the single-component frequency, phase and amplitude of theoretical signal can be corrected satisfactorily, with frequency error less than 0.0002 frequency resolution, phase 0.1° and amplitude 0.0002. If the signal involves noise, the mean corrected errors are less than 0.001 frequency resolution, 1° for phase, and 0.01 for amplitude, respectively, and the maximum corrected errors of one segment are less than 0.01 frequency resolution, 1° and 0.03, respectively.
Energy Technology Data Exchange (ETDEWEB)
Santiago Buey, C. de
2011-07-01
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.
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Wavelet Analysis for Acoustic Phased Array
Kozlov, Inna; Zlotnick, Zvi
2003-03-01
Wavelet spectrum analysis is known to be one of the most powerful tools for exploring quasistationary signals. In this paper we use wavelet technique to develop a new Direction Finding (DF) Algorithm for the Acoustic Phased Array (APA) systems. Utilising multi-scale analysis of libraries of wavelets allows us to work with frequency bands instead of individual frequency of an acoustic source. These frequency bands could be regarded as features extracted from quasistationary signals emitted by a noisy object. For detection, tracing and identification of a sound source in a noisy environment we develop smart algorithm. The essential part of this algorithm is a special interacting procedure of the above-mentioned DF-algorithm and the wavelet-based Identification (ID) algorithm developed in [4]. Significant improvement of the basic properties of a receiving APA pattern is achieved.
Mathematica在Fourier级数分析中的应用%On the Application of Mathematica in Fourier series Analysis
Institute of Scientific and Technical Information of China (English)
张平; 张小华
2012-01-01
In order to make students have direct perception and sophisticated understanding of Fourier series, the article presents the means to convert abstract math ideas and complicated process into software so that mathematics can be understood easier and the students＇ interest and enthusiasm for advanced mathematics enhanced.%文章用Mathematica实现了函数展开成Fourier级数及其图形演示,将抽象的教学概念和复杂的过程用软件来实现,从而降低教学问题的难度,增强学生学习高等数学的兴趣和积极性.
Riedrich-Möller, Janine; Becher, Christoph
2010-01-01
We present the design of two-dimensional photonic crystal microcavities in thin diamond membranes well suited for coupling of color centers in diamond. By comparing simulated and ideal field distributions in Fourier and real space and by according modification of air hole positions and size, we optimize the cavity structure yielding high quality factors up to Q = 320000 with a modal volume of V = 0.35 (lambda/n)^3. Using the very same approach we also improve previous designs of a small modal volume microcavity in silicon, gaining a factor of 3 in cavity Q. In view of practical realization of photonic crystals in synthetic diamond films, it is necessary to investigate the influence of material absorption on the quality factor. We show that this influence can be predicted by a simple model, replacing time consuming simulations.
Multifractality and Network Analysis of Phase Transition
Li, Wei; Yang, Chunbin; Han, Jihui; Su, Zhu; Zou, Yijiang
2017-01-01
Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. PMID:28107414
Phase unwrapping work of photoelastic stress analysis
Huang, M. J.; Sung, P. C.; An, H. L.
2010-03-01
π Photoelasticity plays an important role in the field of stress analysis. Not only because it is a non-contact whole field optical method, but it provides isoclinic (principal stress direction) and isochomatic (principal stress difference) data as well, which serve as the two most important parameters in the field. But, unfortunately, the coupling between these two parameters induces phase ambiguity problem in the isochromatic data unless the isoclinic data have been correctly procured first. In this paper, a novel spatial phase unwrapping is first applied for retrieving the correct isoclinic data, which is then substituted into the isochromatic calculation to solve the 2 ambiguity problem conducted by wrapped isoclinic data. The result is checked with that from the theoretical analysis and shown to be with limited error. The same problem is solved in a different way - by the temporal approaches, load stepping or multiple wavelengths sourcing in advance. The intercomparison depicts that the spatial approach is more noise-immune than the temporal approach is. It is because that by the spatial approach the algorithm can check data not only of themselves but consult data also from their neighbors. As a result, any small localized error can be eliminated accordingly.
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…
Deng, Haiqiang; Huang, Xinjian; Wang, Lishi
2010-12-21
This paper describes a novel application of Fourier transformed large-amplitude square-wave voltammetry (FT-SWV) in combination with three-phase edge plane pyrolytic graphite (EPPG) electrode to investigate both the kinetics and thermodynamics of anion transfer across the liquid/liquid interface using a conventional three-electrode arrangement. The transfer of anion from aqueous phase to organic phase was electrochemically driven by reversible redox transformation of confined redox probe in the organic phase. The kinetics and thermodynamics of anion transfer were inspected by a so-called "quasi-reversible maximum" (QRM) emerged in the profile of even harmonic components of power spectrum obtained by Fourier transformation (FT) of time-domain total current response and formal potential E(f) of first harmonic voltammogram obtained by application of inverse FT on the power spectrum. Besides, a systematic study of patterns of behavior of a variety of anions at the same concentration and a specific anion at different concentrations on kinetics and thermodynamics and the effect of amplitude ΔE on QRM were also conducted, aiming to optimize the measurement conditions. The investigation mentioned above testified that the ion transfer across the liquid/liquid interface controls the kinetics of overall electrochemical process, regardless of either FT-SWV or traditional SWV investigation. Moreover, either the kinetic probe f(max) or the thermodynamic probe E(f) can be served as a way for analytical applications. Interestingly, a linear relationship between peak currents of the first harmonic components and concentrations of perchlorate anion in the aqueous solutions can be observed, which is somewhat in accordance with a finding obtained by Fourier transformed alternating current voltammetry (FT-ACV) [Bond, A. M.; Duffy, N. W.; Elton, D. M.; Fleming, B. D. Anal. Chem. 2009, 81, 8801-8808]. This may open a new door for analytical detection of a wide spectrum of
Fiber Optic Fourier Transform White-Light Interferometry
Institute of Scientific and Technical Information of China (English)
Yi Jiang; Cai-Jie Tang
2008-01-01
Fiber optic Fourier transform white-light inter-fereometry is presented to interrogate the absolute optical path difference of an Mach-Zehnder inter-ferometer. The phase change of the interferometer caused by scanning wavelength can be calculated by a Fourier transform-based phase demodulation technique. A linear output is achieved.
Hartsville data and analysis book: Phase I
Energy Technology Data Exchange (ETDEWEB)
Kerley, C.R.; Siegrist, C.
1978-09-01
A preconstruction data base is recorded for the impact area surrounding the Hartsville nuclear construction project. The objective is to document baseline information for socioeconomic characteristics that may be either temporarily or permanently altered by the project. The analysis suggests that the five counties surrounding the site make up a primary impact area, but some impacts may occur outside the area. The work force for the construction phase of the project is segregated into four components: (1) former residents of the site county, (2) former residents of other counties in the impact area, (3) in-movers to the site county, and (4) in-movers to other counties in the impact area. A theoretical model is developed to illustrate the contribution of each component to the spatial pattern of economic benefits and social costs in the impact area. A shift-share analysis of agricultural characteristics in the impact area shows that employment and farm numbers in the area have declined at a slightly faster rate than in the nation but at a slower rate than in the South. A population and construction project threshold analysis suggests that, given the project size and population base at Hartsville, significant social and economic constraints may be encountered in the public and private economic infrastructure. These include amenities such as housing, school space, medical and police protection.
Qualitative Analysis of Self Phase Modulation (SPM
Directory of Open Access Journals (Sweden)
Ruby Verma
2013-03-01
Full Text Available Optical fiber changed the way of communication. In comparison with wireless communication, optical fiber communication is very fast and reliable. It is more secure but costly. Optical fiber uses the principle of total internal reflection for transmission. Optical fiber has core and cladding with different refractive index and major portion of the signal goes through the core. But due macro and micro bending, chromatic dispersion is observed.In this paper, we have analyzed self phase modulation in an optical fiber system and discussed how it causes dispersion in input signal. These effects are simulated using OPTISYSTEM tool at a bit rate of 10Gbps and analysed using eye pattern method with respect to bit error rate and Q factor. Simulation results from the OPTISYSTEM tool are also compared with the numerical analysis of nonlinear Schrodinger equation, which is simulated in MATLAB
Berry phase and band structure analysis of the Weyl semimetal NbP
Sergelius, Philip; Gooth, Johannes; Bäßler, Svenja; Zierold, Robert; Wiegand, Christoph; Niemann, Anna; Reith, Heiko; Shekhar, Chandra; Felser, Claudia; Yan, Binghai; Nielsch, Kornelius
2016-01-01
Weyl semimetals are often considered the 3D-analogon of graphene or topological insulators. The evaluation of quantum oscillations in these systems remains challenging because there are often multiple conduction bands. We observe de Haas-van Alphen oscillations with several frequencies in a single crystal of the Weyl semimetal niobium phosphide. For each fundamental crystal axis, we can fit the raw data to a superposition of sinusoidal functions, which enables us to calculate the characteristic parameters of all individual bulk conduction bands using Fourier transform with an analysis of the temperature and magnetic field-dependent oscillation amplitude decay. Our experimental results indicate that the band structure consists of Dirac bands with low cyclotron mass, a non-trivial Berry phase and parabolic bands with a higher effective mass and trivial Berry phase. PMID:27667203
Li, Yin-long
2016-01-01
The objective of this study was to investigate the spectra characteristics (SC) at wavelengths of 400~1000 nm and 2.5~15.5 μm of pure moxa stick (MS) during its 25-minute burning process using new spectral imaging techniques. Spectral images were collected for the burning pure MS at 5, 10, 15, 20, and 25 min using hyperspectral imaging (HSI) and Fourier transform infrared spectroscopy (FTIR) for the first time. The results showed that, at wavelengths of 400~1000 nm, the spectral range of the cross section of MS burning was 750~980 nm; the peak position was 860 nm. At wavelengths of 2.5~15.5 μm, the spectral range of the cross section of MS burning was 3.0~4.0 μm; the peak position was approximately 3.5 μm. The radiation spectra of MS burning include litter red and amount of infrared (but mainly near infrared) wavelengths. The temperature, blood perfusion, and oxygen saturation increase of Shenshu (BL23) after moxibustion radiation were observed too. According to mechanism of photobiological effects and moxibustion biological effects, it was inferred that moxibustion effects should be linked with moxibustion SC. This study provided new data and means for physical properties of moxibustion research.
Valtchanov, Ivan; Polehampton, Edward; Benielli, Dominique; Fulton, Trevor; Imhof, Peter; Konopczynski, Tomasz; Lim, Tanya; Lu, Nanyao; Marchili, Nicola; Naylor, David; Swinyard, Bruce
2014-01-01
We present a method to derive the relative pointing offsets for SPIRE Fourier-Transform Spectrometer (FTS) solar system object (SSO) calibration targets, which were observed regularly throughout the Herschel mission. We construct ratios of the spectra for all observations of a given source with respect to a reference. The reference observation is selected iteratively to be the one with the highest observed continuum. Assuming that any pointing offset leads to an overall shift of the continuum level, then these ratios represent the relative flux loss due to mispointing. The mispointing effects are more pronounced for a smaller beam, so we consider only the FTS short wavelength array (SSW, 958-1546 GHz) to derive a pointing correction. We obtain the relative pointing offset by comparing the ratio to a grid of expected losses for a model source at different distances from the centre of the beam, under the assumption that the SSW FTS beam can be well approximated by a Gaussian. In order to avoid dependency on the...
Melin, A M; Perromat, A; Deleris, G
2001-09-01
We investigated the sensitivity of rat heart microsomes to free radical attack using Fourier transform infrared (FT-IR) spectroscopy. This physico-chemical method seemed a valuable technique: quite sensitive to changes in the vibrational spectra. The spectral variations observed between normal and treated rats were in great part due to reactive oxygen species that led to changes in protein conformation involving beta-sheets, aggregation of proteins, and modification of protein synthesis. Carrageenan-induced inflammation slightly enhanced the total lipid content; rearrangement of acyl chains and accumulation of cholesterol esters and phospholipids also occurred in the treated rats. Carbon tetrachloride induced a decrease in both lipid and protein contents. The level of glucidic substrates was diminished with carbon tetrachloride and enhanced with carrageenan; these changes were due to metabolic interactions between cell components and drugs. FT-IR spectroscopy provided an accurate means to monitor, in rat heart, the in vivo effects of inflammatory and peroxidative damages, to discriminate and classify the affected cells, and to correlate the findings with known physiological and biochemical data in close relationship with metabolic disruptions induced by the two xenobiotics.
Taradolsirithitikul, Panchita; Sirisomboon, Panmanas; Dachoupakan Sirisomboon, Cheewanun
2017-03-01
Ochratoxin A (OTA) contamination is highly prevalent in a variety of agricultural products including the commercially important coffee bean. As such, rapid and accurate detection methods are considered necessary for the identification of OTA in green coffee beans. The goal of this research was to apply Fourier transform near infrared spectroscopy to detect and classify OTA contamination in green coffee beans in both a quantitative and qualitative manner. PLSR models were generated using pretreated spectroscopic data to predict the OTA concentration. The best model displayed a correlation coefficient (r) of 0.814, a standard error of prediction (SEP and bias of 1.965 µg kg(-1) and 0.358 µg kg(-1) , respectively. Additionally, a PLS-DA model was also generated, displaying a classification accuracy of 96.83% for a non-OTA contaminated model and 80.95% for an OTA contaminated model, with an overall classification accuracy of 88.89%. The results demonstrate that the developed model could be used for detecting OTA contamination in green coffee beans in either a quantitative or qualitative manner. © 2016 Society of Chemical Industry. © 2016 Society of Chemical Industry.
Courtiol, Alexandre; Ferdy, Jean Baptiste; Godelle, Bernard; Raymond, Michel; Claude, Julien
2010-05-01
Many studies use representations of human body outlines to study how individual characteristics, such as height and body mass, affect perception of body shape. These typically involve reality-based stimuli (e.g., pictures) or manipulated stimuli (e.g., drawings). These two classes of stimuli have important drawbacks that limit result interpretations. Realistic stimuli vary in terms of traits that are correlated, which makes it impossible to assess the effect of a single trait independently. In addition, manipulated stimuli usually do not represent realistic morphologies. We describe and examine a method based on elliptic Fourier descriptors to automatically predict and represent body outlines for a given set of predicted variables (e.g., sex, height, and body mass). We first estimate whether these predictive variables are significantly related to human outlines. We find that height and body mass significantly influence body shape. Unlike height, the effect of body mass on shape differs between sexes. Then, we show that we can easily build a regression model that creates hypothetical outlines for an arbitrary set of covariates. These statistically computed outlines are quite realistic and may be used as stimuli in future studies.
Energy Technology Data Exchange (ETDEWEB)
Takeda, K.
1983-09-01
Using global time-activity curves, the phase and amplitude at fundamental frequency were calculated, and emptying patterns of the right and left ventricles (RV, LV) were evaluated by phase difference and RV/LV amplitude ratio. In 21 subjects with normal cardiac function, D(phase) was minimal (mean 2.2 +- 6.1/sup 0/), regardless of heart rate, and R(amp) was distributed from 0.31 to 0.92 (mean 0.57 +- 0.20). In 19 patients of ventricular septal defect (VSD), R(amp) remained within the normal range, whereas D(phase) became larger in proportion to the ratio of pulmonary-to-systemic blood flow, Qp/Qs (p < 0.001). Especially, cases with Qp/Qs over 2.0 showed a significant RV phase lag. By contrast, nine patients with patent ductus arteriosus (PDA), showed no RV phase lag, but - particularly in cases with Qp/Qs > 2.0 - R(amp) was smaller than normal (p < 0.001). Thus this method is valuable for pathophysiologic investigation of diseases with L-to-R shunt, and can help in the noninvasive differential diagnosis between VSD and PDA.
Application of Fast Fourier Transform in Frequency and Spectrum Analysis%快速傅里叶变换在频谱分析中的应用
Institute of Scientific and Technical Information of China (English)
胡丽莹; 肖蓬
2011-01-01
在快速傅里叶变换原理和Cooley-Tukey快速傅里叶变换算法的基础上,给出一个新的应用于数字信号处理(DSP)的频谱分析方法,并分析该方法的运算效率和存储空间开销.实例证明,本方法的复数乘法运算量与存储空间开销均较小,符合DSP信号处理器的特点,适合应用于采用高性能DSP的MP3/MP4或手机等消费电子产品.%Based on fast Fourier transform principle and Cooley-Tukey fast Fourier transform algorithm, a new method of frequency and spectrum analysis which applies in digital signal processing (DSP) is presented, and the operational efficiency and memory space of the method are analyzed. Example shows that the new method have less amount of complex multiplication and small memory space which is fit for DSP. So the method is very suitable for MP3/MP4 or mobile phone and other consumer electronic products which use high-performance DSP.
Chadeau, Elise; Dumas, Emilie; Adt, Isabelle; Degraeve, Pascal; Noël, Claude; Girodet, Christophe; Oulahal, Nadia
2012-12-01
Polyhexamethylene biguanide (PHMB) is a cationic biocide. The antibacterial mode of action of PHMB (at concentrations not exceeding its minimal inhibitory concentration) upon Listeria innocua LRGIA 01 was investigated by Fourier transformed infrared spectroscopy and fluorescence anisotropy analysis. Fourier transformed infrared spectra of bacteria treated with or without PHMB presented some differences in the lipids region: the CH(2)/CH(3) (2924 cm(-1)/2960 cm(-1)) band areas ratio significantly increased in the presence of PHMB. Since this ratio generally reflects membrane phospholipids and membrane microenvironment of the cells, these results suggest that PHMB molecules interact with membrane phospholipids and, thus, affect membrane fluidity and conformation. To assess the hypothesis of PHMB interaction with L. innocua membrane phospholipids and to clarify the PHMB mode of action, we performed fluorescence anisotropy experiments. Two probes, 1,6-diphenyl-1,3,5-hexatriene (DPH) and its derivative 1-[4-(trimethyl-amino)-phenyl]-6-phenylhexa-1,3,5-triene (TMA-DPH), were used. DPH and TMA-DPH incorporate inside and at the surface of the cytoplasmic membrane, respectively. When PHMB was added, an increase of TMA-DPH fluorescence anisotropy was observed, but no changes of DPH fluorescence anisotropy occurred. These results are consistent with the hypothesis that PHMB molecules perturb L. innocua LRGIA 01 cytoplasmic membrane by interacting with the first layer of the membrane lipid bilayer.
Lin, Yulan; Smith, Pieter E. S.; Zhang, Zhiyong; Frydman, Lucio
2017-01-01
Multidimensional Nuclear Magnetic Resonance (NMR) provides a unique window into structure and dynamics at an atomic level. Traditionally, given the scan-by-scan time modulation involved in these experiments, the duration of nD NMR increases exponentially with spectral dimensionality. In addition, acquisition times increase as the number of spectral elements being sought in each indirect domain - given by the ratio between the spectral bandwidth being targeted and the resolution desired. These long sampling times can be substantially reduced by exploiting information that is often available from lower-dimensionality acquisitions. This work presents a novel approach that exploits previous 2D information to speed up the acquisition of 3D spectra, based on what we denote as a Time-Optimized FouriEr Encoding (TOFEE) of pre-targeted peaks. Such 3D TOFEE experiments, which present points in common with Hadamard-encoded 3D acquisitions, do not necessarily require more scans than their 2D counterparts. This is here demonstrated based on extensions of 2D Heteronuclear Single-quantum Coherence (HSQC) experiments, to 3D HSQC-TOCSY or 3D HSQC-NOESY acquisitions. The theoretical basis of this new approach is given, and experimental demonstrations are presented on small molecule and protein-based model systems.
Directory of Open Access Journals (Sweden)
O. D. Mrachkovskyi
2015-06-01
Full Text Available Introduction. This article contain short introduction to history of complicated signals and list of common sequences, used in spectrum spreading. Method of creating Kasami sequences. In this article is shown sequence creation method, based on method of creating maximum length sequence. Creating of the structural schema of Kasami sequences generator. Principles of construction of Kasami sequence generator are shown in this article. Example of generator for sequence with length 63 symbols, which are created using method, mentioned in previous article, is also shown. Spectrum of Kasami sequences. This article contain amplitude and phase spectrum of two Kasami sequences with lengths of 1023 and 255 symbols. Theoretical formulas are created using Discrete Fourier Transform operation, and graphics are plotted using Fast Fourier Transform operation. Phase spectrum data are also been changed by unwrap operation for better visibility. Conclusion. This article contain analysis of characteristics of previously shown spectrum. Several conclusions are made about correlation between sequence and spectrum characteristics. These conclusions include that made about amplitude spectrum form dependence of sequence length, type and basic impulse characteristics.
Multi-wavelength fibril dynamics and oscillations above sunspot - Fourier decomposition
Mumpuni, Emanuel Sungging; Herdiwijaya, Dhani; Djamal, Mitra; Djamaluddin, Thomas
2015-09-01
In this work we continue our previous work on wave propagation analysis using multi-wavelength images from Dutch Open Telescope from exceptional data observed of Active Region 10789, 2005 July, 13th. By Fourier analysis we study the layer by layer interaction of the Solar atmosphere represented by multi-wavelength, consist of Hα both line center & the blue wing, Ca II H, and the G Band. By Fourier decomposition from power, coherence and phase-difference along the fibril we try to discuss the possible mechanism in the area under investigation.
Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
Salo, Raimo A; Miettinen, Tuukka; Laitinen, Teemu; Gröhn, Olli; Sierra, Alejandra
2017-03-04
Imaging markers for monitoring disease progression, recovery, and treatment efficacy are a major unmet need for many neurological diseases, including epilepsy. Recent evidence suggests that diffusion tensor imaging (DTI) provides high microstructural contrast even outside major white matter tracts. We hypothesized that in vivo DTI could detect progressive microstructural changes in the dentate gyrus and the hippocampal CA3bc in the rat brain after status epilepticus (SE). To test this hypothesis, we induced SE with systemic kainic acid or pilocarpine in adult male Wistar rats and subsequently scanned them using in vivo DTI at five time-points: prior to SE, and 10, 20, 34, and 79 days post SE. In order to tie the DTI findings to changes in the tissue microstructure, myelin- and glial fibrillary acidic protein (GFAP)-stained sections from the same animals underwent Fourier analysis. We compared the Fourier analysis parameters, anisotropy index and angle of myelinated axons or astrocyte processes, to corresponding DTI parameters, fractional anisotropy (FA) and the orientation angle of the principal eigenvector. We found progressive detectable changes in DTI parameters in both the dentate gyrus (FA, axial diffusivity [D||], linear anisotropy [CL] and spherical anisotropy [CS], pmixed-effects model [LMEM]) and the CA3bc (FA, D||, CS, and angle, p<0.001, LMEM; CL and planar anisotropy [CP], p<0.01, LMEM) post SE. The Fourier analysis revealed that both myelinated axons and astrocyte processes played a role in the water diffusion anisotropy changes detected by DTI in individual portions of the dentate gyrus (suprapyramidal blade, mid-portion, and infrapyramidal blade). In the whole dentate gyrus, myelinated axons markedly contributed to the water diffusion changes. In CA3bc as well as in CA3b and CA3c, both myelinated axons and astrocyte processes contributed to water diffusion anisotropy and orientation. Our study revealed that DTI is a promising method for noninvasive
Directory of Open Access Journals (Sweden)
Hong-Wei Deng
2014-11-01
Full Text Available AIM: To detect the macular ganglion cell complex thickness in monocular strabismus amblyopia patients, in order to explore the relationship between the degree of amblyopia and retinal ganglion cell complex thickness, and found out whether there is abnormal macular ganglion cell structure in strabismic amblyopia. METHODS: Using a fourier-domain optical coherence tomography(FD-OCTinstrument iVue®(Optovue Inc, Fremont, CA, Macular ganglion cell complex(mGCCthickness was measured and statistical the relation rate with the best vision acuity correction was compared Gman among 26 patients(52 eyesincluded in this study. RESULTS: The mean thickness of the mGCC in macular was investigated into three parts: centrial, inner circle(3mmand outer circle(6mm. The mean thicknesses of mGCC in central, inner and outer circle was 50.74±21.51μm, 101.4±8.51μm, 114.2±9.455μm in the strabismic amblyopia eyes(SAE, and 43.79±11.92μm,92.47±25.01μm, 113.3±12.88μm in the contralateral sound eyes(CSErespectively. There was no statistically significant difference among the eyes(P>0.05. But the best corrected vision acuity had a good correlation rate between mGcc thicknesses, which was better relative for the lower part than the upper part.CONCLUSION:There is a relationship between the amblyopia vision acuity and the mGCC thickness. Although there has not statistically significant difference of the mGCC thickness compared with the SAE and CSE. To measure the macular center mGCC thickness in clinic may understand the degree of amblyopia.
Maeda, A.; Sasaki, J.; Shichida, Y.; Yoshizawa, T.; Chang, M.; Ni, B.; Needleman, R.; Lanyi, J. K.
1992-01-01
The light-induced difference Fourier transform infrared spectrum between the L or N intermediate minus light-adapted bacteriorhodopsin (BR) was measured in order to examine the protonated states and the changes in the interactions of carboxylic acids of Asp-96 and Asp-115 in these intermediates. Vibrational bands due to the protonated and unprotonated carboxylic acid were identified by isotope shift and band depletion upon substitution of Asp-96 or -115 by asparagine. While the signal due to the deprotonation of Asp-96 was clearly observed in the N intermediate, this residue remained protonated in L. Asp-115 was partially deprotonated in L. The C = O stretching vibration of protonated Asp-96 of L showed almost no shift upon 2H2O substitution, in contrast to the corresponding band of Asp-96 or Asp-115 of BR, which shifted by 9-12 cm-1 under the same conditions. In the model system of acetic acid in organic solvents, such an absence of the shift of the C = O stretching vibration of the protonated carboxylic acid upon 2H2O substitution was seen only when the O-H of acetic acid is hydrogen-bonded. The non-hydrogen-bonded monomer showed the 2H2O-dependent shift. Thus, the O-H bond of Asp-96 enters into hydrogen bonding upon conversion of BR to L. Its increased hydrogen bonding in L is consistent with the observed downshift of the O-H stretching vibration of the carboxylic acid of Asp-96.
Kumar, Dinesh; Singh, Surjan; Rai, K. N.
2016-06-01
In this paper, the temperature distribution in a finite biological tissue in presence of metabolic and external heat source when the surface subjected to different type of boundary conditions is studied. Classical Fourier, single-phase-lag (SPL) and dual-phase-lag (DPL) models were developed for bio-heat transfer in biological tissues. The analytical solution obtained for all the three models using Laplace transform technique and results are compared. The effect of the variability of different parameters such as relaxation time, metabolic heat source, spatial heat source, different type boundary conditions on temperature distribution in different type of the tissues like muscle, tumor, fat, dermis and subcutaneous based on three models are analyzed and discussed in detail. The result obtained in three models is compared with experimental observation of Stolwijk and Hardy (Pflug Arch 291:129-162, 1966). It has been observe that the DPL bio-heat transfer model provides better result in comparison of other two models. The value of metabolic and spatial heat source in boundary condition of first, second and third kind for different type of thermal therapies are evaluated.
Fourier transforms in radar and signal processing
Brandwood, David
2011-01-01
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit
Harmonic functions on groups and Fourier algebras
Chu, Cho-Ho
2002-01-01
This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
Schrader, W; Geiger, J; Hoffmann, T; Klockow, D; Korte, E H
1999-12-24
The gas phase reaction of alpha-pinene with the atmospheric oxidant ozone was investigated by using the capabilities of both gas chromatography-cryocondensation-Fourier transform infrared spectroscopy (GC-FT-IR) and gas chromatography-mass spectrometry (GC-MS), for the identification of the reaction products formed. The reaction was carried out in a flow reaction chamber from where the compounds were sampled on Tenax-containing adsorption cartridges. The reaction mixture was injected onto the column after thermodesorption and analyzed using both GC-IR and GC-MS. Twenty compounds could be detected, including the reactant alpha-pinene and it's impurities tricyclene and camphene. Eleven compounds were identified by spectra comparison with either reference data or spectra obtained from commercial standards. Four compounds were tentatively identified from their IR and MS spectra, while from the remaining two compounds the nature of basic functional groups could be established.
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.
Causin, Valerio; Casamassima, Rosario; Marega, Carla; Maida, Pietro; Schiavone, Sergio; Marigo, Antonio; Villari, Antonino
2008-11-01
The knowledge of the discriminating power of analytical techniques used for the differentiation of writing inks can be useful when interpreting results. Ultraviolet-visible (UV-VIS) spectrophotometry, thin layer chromatography (TLC), and diffuse reflectance Fourier transform infrared spectroscopy (FT-IR) were used to examine a population of 21 black and 12 blue ballpoint writing inks. Based on corroborative results of these methods, the discrimination power for UV-VIS, TLC, and FT-IR was determined to be 100% and 98% for the black and blue inks, respectively. Generally, TLC and UV-VIS can be used to differentiate the colorant components (i.e., dyes and some pigments) found in inks. As FT-IR can be utilized to identify some of the noncolorant components, it was determined to be an excellent complementary technique that can be implemented into an analytical scheme for ink analysis.
Directory of Open Access Journals (Sweden)
Mohammad Mohadasi
2014-09-01
Full Text Available Study of phenotypic diversity among populations can help better understanding of diversification of species within ecosystems and intraspecific diversification in fishes. A geometric morphometric study was carried out using the Elliptic Fourier analysis to demonstrate the effect of habitat type on morphological features of shemaya (Alburnus chalcoides populations. Populations were sampled from three rivers and one lagoon, from the southern part of Caspian Sea. Significant differences in body shape were found among the populations. Differences in shapes of the riverine populations were minute compared to those of lagoon one in terms of size and shape. Shemaya is an anaderemus fish and its populations have a common origin, therefore, observed differences could be as result of environmental factors. In addition, this study suggest that the amount of curvature i.e. fusiform body shape of this species could be independent form environmental condition.
Shim, J Y; Cho, I K; Khurana, H K; Li, Q X; Jun, S
2008-06-01
Fourier transform infrared (FTIR) spectroscopy was investigated as a method for analysis of acesulfame-K content after a simple extraction procedure for certain commercial diet food samples. Partial least squares (PLS) models were developed for prediction of acesulfame-K using select spectral ranges on the basis of relevant IR absorption bands associated with acesulfame-K. The acesulfame-K content of test food samples was predicted accurately in the fingerprint region between 1100 and 1300 cm(-1) with a maximum prediction error of 9.82% when compared with conventional HPLC method. The PLS was found to be a consistently better predictor when both PLS and principal component regression (PCR) analyses were used for quantification of acesulfame-K. The developed procedure was further validated by comparing with HPLC results as well as recovery studies. As a quick tool, the method developed is expected to be used for routine estimation of acesulfame-K in commercial products.
Habibi, Neda
2015-02-05
The preparation and characterization of functional biocompatible magnetite-cellulose nano-composite fibrous material is described. Magnetite-cellulose nano-composite was prepared by a combination of the solution-based formation of magnetic nano-particles and subsequent coating with amino celluloses. Characterization was accomplished using X-ray powder diffraction (XRD), fourier transformed infrared (FTIR) and field emission scanning electron microscopy (FESEM) analysis. The peaks of Fe3O4 in the XRD pattern of nanocomposite confirm existence of the nanoparticles in the amino cellulose matrix. Magnetite-cellulose particles exhibit an average diameter of roughly 33nm as demonstrated by field emission scanning electron microscopy. Magnetite nanoparticles were irregular spheres dispersed in the cellulose matrix. The vibration corresponding to the NCH3 functional group about 2850cm(-1) is assigned in the FTIR spectra. Functionalized magnetite-cellulose nano-composite polymers have a potential range of application as targeted drug delivery system in biomedical field.
Analysis of the High-Resolution Fourier Spectrum of the ν6 Band of the cis-C2h2d2 Molecule
Konov, I. A.; Chertavskikh, Yu. V.; Fomchenko, A. L.; Aslapovskaya, Yu. S.; Zhdanovich, S. A.; Sydow, C.
2016-03-01
The spectrum of the ν6 band of the cis-ethylene-d2 molecule (cis-C2H2D2) is recorded with a Bruker IFS 125 HR Fourier spectrometer in the range 580-1210 cm-1 with resolution of 0.0021 cm-1. An analysis of the experimental spectrum allows more than 1500 transitions belonging to this band to be assigned that by more than 2.5 times greater than it has been known in the literature so far. The obtained experimental data are then used to determine the model parameters of the molecule (the effective Hamiltonian in the A-reduction and I'- representation). Strong resonance interaction with the band ν4 forbidden in absorption by the symmetry of a molecule is taken into account. 10 parameters of the Hamiltonian obtained by solving inverse spectroscopic problem reproduce 427 initial experimental energies (more than 1500 transitions) with accuracy close to the experimental uncertainty.
Prokai, Laszlo; Stevens, Stanley M
2016-01-16
Direct analysis in real time (DART) is a recently developed ambient ionization technique for mass spectrometry to enable rapid and sensitive analyses with little or no sample preparation. After swab-based field sampling, the organothiophosphate malathion was analyzed using DART-Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry (MS) and tandem mass spectrometry (MS/MS). Mass resolution was documented to be over 800,000 in full-scan MS mode and over 1,000,000 for an MS/MS product ion produced by collision-induced dissociation of the protonated analyte. Mass measurement accuracy below 1 ppm was obtained for all DART-generated ions that belonged to the test compound in the mass spectra acquired using only external mass calibration. This high mass measurement accuracy, achievable at present only through FTMS, was required for unequivocal identification of the corresponding molecular formulae.
Tiwari, Saumya; Zong, Xinying; Holton, Sarah E.; Prasanth, K. V.; Bhargava, Rohit
2015-03-01
Determination of neoplasia is largely dependent on the state of cell growth. Infrared (IR) spectroscopy has the potential to measure differences between normal and cancerous cells. When analyzing biopsy sections using IR spectroscopy, careful analyses become important since biochemical variations may be misinterpreted due to variations in cell cycle. Processes like DNA replication, transcription and translation to produce proteins are important in determining if the cells are actively dividing but no studies on this aspect using IR spectroscopy have been conducted on isolated cell nuclei. Nuclei hold critical information about the phase of cell and its capacity to divide, but IR spectra of nuclei are often confounded by cytoplasmic signals during data acquisition from intact cells and tissues. Therefore, we sought to separate nuclear signals from cytoplasmic signals and identify spectral differences that characterize different phases of the cell cycle. Both cells and isolated nuclei were analyzed to assess the effect of the cytoplasmic background and to identify spectral changes in nuclei in different phases of cell cycle. We observed that signals of DNA could be obtained when imaging nuclei isolated from cells in different phases of cell cycle, which is in contrast to the oft-cited case in cells wherein nuclear contributions are obscured. The differences across cell cycle phases were more pronounced in nucleic acid regions of the spectra, showing that the use of nuclear spectrum can provide additional information on cellular state. These results can aid in developing computational models that extract nuclear spectra from whole cells and tissues for more accurate assessment of biochemical variations.