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
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 ...
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...
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...
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.
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.
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 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.
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)
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.
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...
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.
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...
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.
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.
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.
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.
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...
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.
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.
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....
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.
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...
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 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.
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.
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.
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).
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.
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.
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.
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...
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.
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.
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.
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.
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.
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.
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.
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...
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
2011-02-01
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.
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.
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...
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...
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
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.
[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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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 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.
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
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.
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.
Interpreting the Phase Spectrum in Fourier Analysis of Partial Ranking Data
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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.
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
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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.
A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations
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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.
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.
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.
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.
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.
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.
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.
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.
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.
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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.
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.
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.
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.
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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.
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
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.
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.
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 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.
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 ...
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.
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...
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.
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.
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.
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
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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
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.
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.
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.
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 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.
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.
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)
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.
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.
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.
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.
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)
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.
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.
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 ...
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.
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.
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.
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.
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%.
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
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.
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
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 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 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.
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.
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...
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
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.
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).
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.
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.
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.
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.
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.
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.
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.
[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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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)
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.
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…
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Mackie, David M; Jahnke, Justin P; Benyamin, Marcus S; Sumner, James J
2016-01-01
The standard methodologies for quantitative analysis (QA) of mixtures using Fourier transform infrared (FTIR) instruments have evolved until they are now more complicated than necessary for many users' purposes. We present a simpler methodology, suitable for widespread adoption of FTIR QA as a standard laboratory technique across disciplines by occasional users.•Algorithm is straightforward and intuitive, yet it is also fast, accurate, and robust.•Relies on component spectra, minimization of errors, and local adaptive mesh refinement.•Tested successfully on real mixtures of up to nine components. We show that our methodology is robust to challenging experimental conditions such as similar substances, component percentages differing by three orders of magnitude, and imperfect (noisy) spectra. As examples, we analyze biological, chemical, and physical aspects of bio-hybrid fuel cells.
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
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.
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.).
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.
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
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.
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
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
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.
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.
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...
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.
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.
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.…
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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 ...
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...
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.
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.
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
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.
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。
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
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 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...
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.
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.
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.
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....
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
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…
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.
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.
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.
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.
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…
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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
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.
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.
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.
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.
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.
Graichen, Uwe; Eichardt, Roland; Fiedler, Patrique; Strohmeier, Daniel; Zanow, Frank; Haueisen, Jens
2015-01-01
Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.
Bilinear Fourier restriction theorems
Demeter, Ciprian
2012-01-01
We provide a general scheme for proving $L^p$ estimates for certain bilinear Fourier restrictions outside the locally $L^2$ setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior approaches, our argument avoids any use of the Rubio de Francia Littlewood--Paley inequality.
Fast Fourier Orthogonalization
Ducas, L.; Prest, T.; Abramov, S.A.; Zima, E.V.; Gao, X-S.
2016-01-01
The classical fast Fourier transform (FFT) allows to compute in quasi-linear time the product of two polynomials, in the {\\em circular convolution ring} R[x]/(x^d−1) --- a task that naively requires quadratic time. Equivalently, it allows to accelerate matrix-vector products when the matrix is *circ
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 spectr...
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.
Fourier-Bessel rotational invariant eigenimages.
Zhao, Zhizhen; Singer, Amit
2013-05-01
We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-dimensional images and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are essentially band limited in the Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel-based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.
DEFF Research Database (Denmark)
Batina, N.; Reyna-Cordova, A.; Trinidad-Reyes, Y.;
2005-01-01
indicated that the surface of the thin films of the oil samples prepared for AFM is oxidized. Oil samples of different origin show different degrees of oxidation seen by the development of carboxylic acid vibrations at 1750 cm-1 as well as vibrations in the 1300−1100 cm-1 region. The relative degree...... 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....
Generic Quantum Fourier Transforms
Moore, Cristopher; Russell, A; Moore, Cristopher; Rockmore, Daniel; Russell, Alexander
2003-01-01
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the separation of variables technique that has been so successful in the study of classical Fourier transform computations. Specifically, this framework applies the existence of computable Bratteli diagrams, adapted factorizations, and Gel'fand-Tsetlin bases to offer efficient quantum circuits for the QFT over a wide variety a finite Abelian and non-Abelian groups, including all group families for which efficient QFTs are currently known and many new group families. Moreover, the method gives rise to the first subexponential-size quantum circuits for the QFT over the linear groups GL_k(q), SL_k(q), and the finite groups of Lie type, for any fixed prime power q.
Directory of Open Access Journals (Sweden)
Juliana Aparecida de Almeida Chaves Piva
Full Text Available Introduction The colorectal cancer is a major health problem worldwide. Histology is considered the gold standard for differential diagnosis. However, it depends on the observer's experience, which can lead to discrepancies and poor results. Spectroscopic imaging by Fourier transform infrared (FTIR is a technique that may be able to improve the diagnosis, because it is based on biochemical differences of the structural constituents of tissue. Therefore, the main goal of this study was to explore the use of FTIR imaging technique in normal colon tissue, colorectal adenoma, and adenocarcinoma in order to correlate their morphological structures with their biochemical imaging. Methods Samples were collected from normal (n = 4, adenoma (n = 4, and adenocarcinoma human colorectal tissue (n = 4 from patients undergoing colonoscopy or surgical resection of colon lesions. The samples were sectioned with a cryostat in sequential sections; the first slice was placed on CaF2 slide and the second slice was placed on glass slide for histological analysis (HE staining. The cluster analyses were performed by the software Cytospec (1.4.02®. Results In normal samples, biochemical analysis classified six different structures, namely the lamina propria of mucous glands (epithelial cells and goblet cells, central lumen of the gland, mucin, and conjunctive tissue. In samples with adenoma and adenocarcinoma, altered regions could also be identified with high sensitivity and specificity. Conclusion The results of this study demonstrate the potential and viability of using infrared spectroscopy to identify and classify colorectal tissues.
Daood, Umer; Swee Heng, Chan; Neo Chiew Lian, Jennifer; Fawzy, Amr S
2015-06-26
To modify two-step experimental etch-and-rinse dentin adhesive with different concentrations of riboflavin and to study its effect on the bond strength, degree of conversion, along with resin infiltration within the demineralized dentin substrate, an experimental adhesive-system was modified with different concentrations of riboflavin (m/m, 0, 1%, 3%, 5% and 10%). Dentin surfaces were etched with 37% phosphoric acid, bonded with respective adhesives, restored with restorative composite-resin, and sectioned into resin-dentin slabs and beams to be stored for 24 h or 9 months in artificial saliva. Micro-tensile bond testing was performed with scanning electron microscopy to analyse the failure of debonded beams. The degree of conversion was evaluated with Fourier transform infrared spectroscopy (FTIR) at different time points along with micro-Raman spectroscopy analysis. Data was analyzed with one-way and two-way analysis of variance followed by Tukey's for pair-wise comparison. Modification with 1% and 3% riboflavin increased the micro-tensile bond strength compared to the control at 24 h and 9-month storage with no significant differences in degree of conversion (Pbond strengths and bond durability after 9-month storage in artificial saliva without adversely affecting the degree of conversion of the adhesive monomers and resin infiltration.
Somogyi, Árpád; Thissen, Roland; Orthous-Daunay, Francois-Régis; Vuitton, Véronique
2016-03-24
It is an important but also a challenging analytical problem to understand the chemical composition and structure of prebiotic organic matter that is present in extraterrestrial materials. Its formation, evolution and content in the building blocks ("seeds") for more complex molecules, such as proteins and DNA, are key questions in the field of exobiology. Ultrahigh resolution mass spectrometry is one of the best analytical techniques that can be applied because it provides reliable information on the chemical composition and structure of individual components of complex organic mixtures. Prebiotic organic material is delivered to Earth by meteorites or generated in laboratories in simulation (model) experiments that mimic space or atmospheric conditions. Recent representative examples for ultrahigh resolution mass spectrometry studies using Fourier-transform (FT) mass spectrometers such as Orbitrap and ion cyclotron resonance (ICR) mass spectrometers are shown and discussed in the present article, including: (i) the analysis of organic matter of meteorites; (ii) modeling atmospheric processes in ICR cells; and (iii) the structural analysis of laboratory made tholins that might be present in the atmosphere and surface of Saturn's largest moon, Titan.
Gudi, Gennadi; Krähmer, Andrea; Krüger, Hans; Schulz, Hartwig
2015-10-01
Sage (Salvia officinalis L.) is cultivated worldwide for its aromatic leaves, which are used as herbal spice, and for phytopharmaceutical applications. Fast analytical strategies for essential oil analysis, performed directly on plant material, would reduce the delay between sampling and analytical results. This would enhance product quality by improving technical control of cultivation. The attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) method described here provides a reliable calibration model for quantification of essential oil components [EOCs; R(2) = 0.96; root-mean-square error of cross-validation (RMSECV) = 0.249 mL 100 g(-1) of dry matter (DM); and range = 1.115-5.280 mL 100 g(-1) of DM] and main constituents [e.g., α-thujone/β-thujone; R(2) = 0.97/0.86; RMSECV = 0.0581/0.0856 mL 100 g(-1) of DM; and range = 0.010-1.252/0.005-0.893 mL 100 g(-1) of DM] directly on dried intact leaves of sage. Except for drying, no further sample preparation is required for ATR-FTIR, and the measurement time of less than 5 min per sample contrasts with the most common alternative of hydrodistillation followed by gas chromatography analysis, which can take several hours per sample.
Energy Technology Data Exchange (ETDEWEB)
Akyuz, Sevim, E-mail: s.akyuz@iku.edu.tr [Physics Department, Science and Letters Faculty, Istanbul Kultur University, Atakoy Campus, Bakirkoy 34156, Istanbul (Turkey); Akyuz, Tanil [Physics Department, Science and Letters Faculty, Istanbul Kultur University, Atakoy Campus, Bakirkoy 34156, Istanbul (Turkey); Mukhamedshina, Nuranya M.; Mirsagatova, A. Adiba [Institute of Nuclear Physics, Uzbek Academy of Sciences, 702132, Ulugbek, Tashkent (Uzbekistan); Basaran, Sait; Cakan, Banu [Department of Restoration and Conservation of Artefacts, Letters Faculty, Istanbul University, Vezneciler, Istanbul (Turkey)
2012-05-15
Ancient glass fragments excavated in the archaeological district Enez (Ancient Ainos)-Turkey were investigated by combined Instrumental Neutron Activation Analysis (INAA) and Fourier Transform Infrared (FTIR) spectrometry techniques. Multi-elemental contents of 15 glass fragments that belong to Hellenistic, Roman, Byzantine, and Ottoman Periods, were determined by INAA. The concentrations of twenty six elements (Na, K, Ca, Sc, Cr, Mn, Fe, Co, Cu, Zn, As, Rb, Sr, Sb, Cs, Ba, Ce, Sm, Eu, Tb, Yb, Lu, Hf, Ta, Au and Th), which might be present in the samples as flux, stabilizers, colorants or opacifiers, and impurities, were examined. Chemometric treatment of the INAA data was performed and principle component analysis revealed presence of 3 distinct groups. The thermal history of the glass samples was determined by FTIR spectrometry. - Highlights: Black-Right-Pointing-Pointer INAA was performed to determine elemental compositions of ancient glass fragments. Black-Right-Pointing-Pointer Basic, coloring/discoloring elements and impurities have been determined. Black-Right-Pointing-Pointer PCA discriminated the glasses depending on their chronological order. Black-Right-Pointing-Pointer The thermal history of the glass samples was determined by FTIR spectrometry.
Li, Tao; He, Xuan
2016-01-01
A nondestructive, efficient, and rapid method for quantitative analysis of two bioactive components (salidroside and p-tyrosol) in Rhodiola crenulata, a traditional Tibetan medicine, by Fourier transform near-infrared (FT-NIR) spectroscopy was developed. Near-infrared diffuse reflectance spectra in the range of 4000 to 10000 cm(-1) of 50 samples of Rhodiola crenulata with different sources were measured. To get a satisfying result, partial least squares regression (PLSR) was used to establish NIR models for salidroside and p-tyrosol content determination. Different preprocessing methods, including smoothing, taking a second derivative, standard normal variate (SNV) transformation, and multiplicative scatter correction (MSC), were investigated to improve the model accuracy of PLSR. The performance of the two final models (salidroside model and p-tyrosol model) was evaluated by factors such as the values of correlation coefficient (R(2)), root mean square error of prediction (RMSEP), and root mean square error of calibration (RMSEC). The optimal results of the PLSR model of salidroside showed that R(2), RMSEP and RMSEC were 0.99572, 0.0294 and 0.0309, respectively. Meanwhile, in the optimization model of p-tyrosol, the R(2), RMSEP and RMSEC were 0.99714, 0.0154 and 0.0168, respectively. These results demonstrate that FT-NIR spectroscopy not only provides a precise, rapid method for quantitative analysis of major effective constituents in Rhodiola crenulata, but can also be applied to the quality control of Rhodiola crenulata.
Institute of Scientific and Technical Information of China (English)
Wang Wei; Liu Yingrong; Liu Zelong; Tian Songbai
2015-01-01
Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) has become a powerful tool for ana-lyzing the detailed composition of petroleum samples. However, the correlation between the numerous peaks obtained by FT-ICR MS and bulk properties of petroleum samples is still a challenge. In this study, the internal standard method was applied for the quantitative analysis of four straight-run vacuum gas oils (VGO) by atmospheric pressure photoionization (APPI) FT-ICR MS. The heteroatom class distribution of these VGO samples turned to be different when the concentration changed. Linear relationship between the normalized abundance and the concentration of VGO samples was identiifed for the total aromatic compounds, aromatic hydrocarbons, S1 and N1 species. The differences of the response factors were also discussed. The sulfur contents of a series of crude oils were proved to be linear with the FT-ICR MS data calibrated by the response factor of S1 species. This study demonstrated the feasibility of the internal standard method in quantitative analysis with APPI FT-ICR MS, and the bulk properties of petroleum samples could be correlated directly with the FT-ICR MS data.
Directory of Open Access Journals (Sweden)
Árpád Somogyi
2016-03-01
Full Text Available It is an important but also a challenging analytical problem to understand the chemical composition and structure of prebiotic organic matter that is present in extraterrestrial materials. Its formation, evolution and content in the building blocks (“seeds” for more complex molecules, such as proteins and DNA, are key questions in the field of exobiology. Ultrahigh resolution mass spectrometry is one of the best analytical techniques that can be applied because it provides reliable information on the chemical composition and structure of individual components of complex organic mixtures. Prebiotic organic material is delivered to Earth by meteorites or generated in laboratories in simulation (model experiments that mimic space or atmospheric conditions. Recent representative examples for ultrahigh resolution mass spectrometry studies using Fourier-transform (FT mass spectrometers such as Orbitrap and ion cyclotron resonance (ICR mass spectrometers are shown and discussed in the present article, including: (i the analysis of organic matter of meteorites; (ii modeling atmospheric processes in ICR cells; and (iii the structural analysis of laboratory made tholins that might be present in the atmosphere and surface of Saturn’s largest moon, Titan.
Directory of Open Access Journals (Sweden)
Siong Fong Sim
2012-11-01
Full Text Available A computational approach was used to analyze the FTIR spectra of a wide range of treated and untreated lignocellulosic biomass (coconut husk, banana trunk, sago hampas, rice husk, and empty fruit bunch. The biomass was treated with strong sulphuric acid and NaOH, respectively. A total of 87 spectra were obtained in which the absorption bands were de-convoluted automatically, generating a peak table of 87 rows and 60 columns. Square roots were taken of the peak values, with further standardization prior to Principal Component Analysis (PCA for data exploration. In a scores plot, the treated and untreated biomass were distinguishable along the two main axes, PC1 and PC2. Examining the absorption bands corresponding to lignocellulosic components indicated that the acid pretreatment had resulted in dissolution and degradation of hemicelluloses and lignin, confirmed typically by disappearance of bands. The alkali treatment however was not as rigorous as the acid treatment, as some characteristic bands of hemicelluloses and lignin were enhanced, suggesting condensation of the degraded polysaccharides. The computer-assisted analysis of the FTIR spectra allowed efficient and simultaneous comparisons of lignocellulosic compositions present in various treated and untreated biomass. This represents an improvement relative to the conventional methods, since a large dataset can be handled efficiently and individual peaks can be examined.
Local properties of Fourier series
Hüseyin Bor
2000-01-01
A theorem on local property of |N¯,pn|k summability of factored Fourier series, which generalizes some known results, and also a general theorem concerning the |N¯,pn|k summability factors of Fourier series have been proved.
Schaub, Tanner M; Hendrickson, Christopher L; Qian, Kuangnan; Quinn, John P; Marshall, Alan G
2003-05-01
We report the first field desorption ionization broadband high-resolution (m/Deltam(50%) approximately 65 000) mass spectra. We have interfaced a field ionization/field desorption source to a home-built 9.4-T FT-ICR mass spectrometer. The instrumental configuration employs convenient sample introduction (in-source liquid injection) and external ion accumulation. We demonstrate the utility of this configuration by generating high-resolution positive-ion mass spectra of C(60) and a midboiling crude oil distillate. The latter contains species not accessible by common soft-ionization methods, for example, low-voltage electron ionization, electrospray ionization, and matrix-assisted laser desorption/ionization. The present work demonstrates significant advantages of FI/FD FT-ICR MS for analysis of nonpolar molecules in complex mixtures.
Directory of Open Access Journals (Sweden)
Sagar T. Cholake
2014-05-01
Full Text Available This article informs the essence of major work done by a number of researchers on the analysis of two-step curing mechanism of diglycidyl ether of bisphenol A (DGEBA epoxy resin in presence of amine curing agents using near- and mid-IR technology. Various peaks used as a marker for resin formation are discussed and their implementation is comprehensively studied. In addition to this, a wide range of information about the importance of reference peaks in both near-IR (NIR and mid-IR (MIR regions are congregated and their accuracy is audited. Also discrepancies observed by researchers in epoxy conversion (α in NIR and MIR regions are reviewed to highlight the comparative advantages of both regions, one over the other.Defence Science Journal, Vol. 64, No. 3, May 2014, pp. 314-321, DOI:http://dx.doi.org/10.14429/dsj.64.7326
Directory of Open Access Journals (Sweden)
Javid Ali
2015-06-01
Full Text Available Objective: To compare the proximate composition, mineral contents, antimicrobial, phytochemical and Fourier transforms infrared (FTIR spectroscopy analysis of bark, stem and seed of Hippophae rhamnoides. Methods: Proximate composition was determined according to the described methods. Mineral analysis was carried out by atomic absorption spectroscopy and flame photometer. Antimicrobial activities were evaluated according to the agar well diffusion method. Phytochemical qualitative analysis was carried out according to the described methods and functional groups were determined by FTIR Prestige-21 Shimadzu Japan. Results: The proximate analysis showed high content of protein and fiber in stem and bark. High content of Na (900 mg/L and K (670 mg/L was found in bark powder, while in seed, high contents of Ca (800 mg/L, Mg (725 mg/L, Fe (250 mg/L Zn (90 mg/L and Mn (65 mg/L were found compared to stem and bark. Phenols, flavonoids and tannins showed high contents in stem and bark of all extracts. The bark aqueous extract showed high zone of inhibition against Staphylococcus aureus (21 mm and Escherichia coli (20 mm, while methanol extract of stem showed high zone of inhibition (14 mm and 13 mm against Enterococcus faecalis and Escherichia coli respectively. The aqueous extract of bark documented high zone of inhibition against Aspergillus niger (21 mm and Aspergillus parasiticus (20 mm. FTIR spectra revealed the presence of OH, C-O and C=O functional groups. Conclusions: The study concludes that bark, stem and seed extracts will be useful guideline for the new syntheses of feed, food supplements and herb drugs with various combination, which can be used for the treatment of many diseases at global level especially in tropical regions as well as the male nutrition problems in these areas.
Musingarabwi, Davirai M; Nieuwoudt, Hélène H; Young, Philip R; Eyéghè-Bickong, Hans A; Vivier, Melané A
2016-01-01
Fourier transform (FT) near-infrared (NIR) and attenuated total reflection (ATR) FT mid-infrared (MIR) spectroscopy were used to qualitatively and quantitatively analyse Vitis vinifera L. cv Sauvignon blanc grape berries. FT-NIR and ATR FT-MIR spectroscopy, coupled with spectral preprocessing and multivariate data analysis (MVDA), provided reliable methods to qualitatively assess berry samples at five distinct developmental stages: green, pre-véraison, véraison, post-véraison and ripe (harvest), without any prior metabolite extraction. Compared to NIR spectra, MIR spectra provided more reliable discrimination between the berry samples from the different developmental stages. Interestingly, ATR FT-MIR spectra from fresh homogenized berry samples proved more discriminatory than spectra from frozen homogenized berry samples. Different developmental stages were discriminated by principal component analysis (PCA) and orthogonal partial least squares discriminant analysis (OPLS-DA). In order to generate partial least squares (PLS) models from the MIR/NIR spectral datasets; the major sugars (glucose and fructose) and organic acids (malic acid, succinic acid and tartaric acid) were separated and quantified by high performance liquid chromatography (HPLC) and the data used as a reference dataset. PLS regression was used to develop calibration models to predict the concentration of the major sugars and organic acids in the berry samples from different developmental stages. Our data show that infrared (IR) spectroscopy could provide a rapid, reproducible and cost-effective alternative to the chromatographic analysis of the sugar and organic acid composition of grape berries at various developmental stages, using small sample volumes and requiring limited sample preparation. This provides scope and support for the possible development of hand-held devices to assess quality parameters in field-settings in real-time and non-destructively using IR technologies.
Institute of Scientific and Technical Information of China (English)
Javid Ali; Bashir Ahmad; Said Hassan; Muhammad Siddique; Farrah Gul; Shafaat Ullah
2015-01-01
Objective: To compare the proximate composition, mineral contents, antimicrobial, phytochemical and Fourier transforms infrared (FTIR) spectroscopy analysis of bark, stem and seed of Hippophae rhamnoides. Methods: Proximate composition was determined according to the described methods. Mineral analysis was carried out by atomic absorption spectroscopy and flame photometer. Antimicrobial activities were evaluated according to the agar well diffusion method. Phytochemical qualitative analysis was carried out according to the described methods and functional groups were determined by FTIR Prestige-21 Shimadzu Japan. Results:The proximate analysis showed high content of protein and fiber in stem and bark. High content of Na (900 mg/L) and K (670 mg/L) was found in bark powder, while in seed, high contents of Ca (800 mg/L), Mg (725 mg/L), Fe (250 mg/L) Zn (90 mg/L) and Mn (65 mg/L) were found compared to stem and bark. Phenols, flavonoids and tannins showed high contents in stem and bark of all extracts. The bark aqueous extract showed high zone of inhibition against Staphylococcus aureus (21 mm) and Escherichia coli (20 mm), while methanol extract of stem showed high zone of inhibition (14 mm and 13 mm) against Enterococcus faecalis and Escherichia coli respectively. The aqueous extract of bark documented high zone of inhibition against Aspergillus niger (21 mm) and Aspergillus parasiticus (20 mm). FTIR spectra revealed the presence of OH, C-O and C=O functional groups. Conclusions:The study concludes that bark, stem and seed extracts will be useful guideline for the new syntheses of feed, food supplements and herb drugs with various combination, which can be used for the treatment of many diseases at global level especially in tropical regions as well as the male nutrition problems in these areas.
Fourier transforms principles and applications
Hansen, Eric W
2014-01-01
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.
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
Guo, Yizhen; Lv, Beiran; Wang, Jingjuan; Liu, Yang; Sun, Suqin; Xiao, Yao; Lu, Lina; Xiang, Li; Yang, Yanfang; Qu, Lei; Meng, Qinghong
2016-01-01
As complicated mixture systems, active components of Chuanxiong Rhizoma are very difficult to identify and discriminate. In this paper, the macroscopic IR fingerprint method including Fourier transform infrared spectroscopy (FT-IR), the second derivative infrared spectroscopy (SD-IR) and two-dimensional correlation infrared spectroscopy (2DCOS-IR), was applied to study and identify Chuanxiong raw materials and its different segmented production of HPD-100 macroporous resin. Chuanxiong Rhizoma is rich in sucrose. In the FT-IR spectra, water eluate is more similar to sucrose than the powder and the decoction. Their second derivative spectra amplified the differences and revealed the potentially characteristic IR absorption bands and combined with the correlation coefficient, concluding that 50% ethanol eluate had more ligustilide than other eluates. Finally, it can be found from 2DCOS-IR spectra that proteins were extracted by ethanol from Chuanxiong decoction by HPD-100 macroporous resin. It was demonstrated that the above three-step infrared spectroscopy could be applicable for quick, non-destructive and effective analysis and identification of very complicated and similar mixture systems of traditional Chinese medicines.
Zhang, Pudun; Unger, Miriam; Pfeifer, Frank; Siesler, Heinz W.
2016-11-01
Variable-temperature Fourier-transform infrared (FT-IR) spectra of a predominantly amorphous and a semi-crystalline poly(L-lactic acid) (PLLA) film were measured between 30 °C and 170 °C in order to investigate their temperature-dependent structural changes as a function of the initial state of order. For an in-depth analysis of the spectral variations in the carbonyl stretching band region (1803-1722 cm-1) two-dimensional correlation spectroscopy (2DCOS) and perturbation-correlation moving-window two-dimensional (PCMW2D) analyses were applied. Significant spectral changes were observed during heating of the amorphous PLLA sample whereas the semi-crystalline specimen showed only slight band shifts as a function of the external perturbation. The PCMW2D results suggested that for efficient 2DCOS analyses the heating process should be split up in two temperature intervals. These analyses then provided information on the recrystallization of the amorphous regions, the presence of an intermediate state of order and a sequence scenario for the observed spectral changes.
Bouvier, A. J.; Inard, D.; Veyret, V.; Bussery, B.; Bacis, R.; Churassy, S.; Brion, J.; Malicet, J.; Judge, R. H.
1998-08-01
The analysis of the rotational structure of the high-resolution Fourier transform 000absorption spectrum of the3A2←X1A1band system of the "Wulf" transition of the isotopomer16O3of ozone is reported for the first time. With a near pure case (b) coupling model for the upper triplet state, we have assigned a significant portion of the spectrum, mainly theF1(J=N+ 1) andF2(J=N) spin components, primarily in the lower frequency region of the band. The lines corresponding to theF3(J=N- 1) component are weak at lower frequencies and heavily congested in the central and higher frequency regions of the spectrum. Perturbations and predissociation phenomena have reduced the effective lifetime of the metastable3A2state and have also limited the number of transitions included in the least-squares fit of the band. Approximately 100 lines have been assigned in the range from 9100-9550 cm-1. Three rotational, three centrifugal distortion, three spin-rotation, and one spin-spin constant were varied. The geometry of the molecule in the3A2state, as determined from these constants, isr= 1.345 Å and θ = 98.9°, in good agreement withab initioresults.
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
Institute of Scientific and Technical Information of China (English)
Umer Daood; Chan Swee Heng; Jennifer Neo Chiew Lian; Amr S Fawzy
2015-01-01
To modify two-step experimental etch-and-rinse dentin adhesive with different concentrations of riboflavin and to study its effect on the bond strength, degree of conversion, along with resin infiltration within the demineralized dentin substrate, an experimental adhesive-system was modified with different concentrations of riboflavin (m/m, 0, 1%, 3%, 5%and 10%). Dentin surfaces were etched with 37%phosphoric acid, bonded with respective adhesives, restored with restorative composite–resin, and sectioned into resin–dentin slabs and beams to be stored for 24 h or 9 months in artificial saliva. Micro-tensile bond testing was performed with scanning electron microscopy to analyse the failure of debonded beams. The degree of conversion was evaluated with Fourier transform infrared spectroscopy (FTIR) at different time points along with micro-Raman spectroscopy analysis. Data was analyzed with one-way and two-way analysis of variance followed by Tukey’s for pair-wise comparison. Modification with 1%and 3%riboflavin increased the micro-tensile bond strength compared to the control at 24 h and 9-month storage with no significant differences in degree of conversion (P,0.05). The most predominant failure mode was the mixed fracture among all specimens except 10%riboflavin-modified adhesive specimens where cohesive failure was predominant. Raman analysis revealed that 1%and 3%riboflavin adhesives specimens showed relatively higher resin infiltration. The incorporation of riboflavin in the experimental two-step etch-and-rinse adhesive at 3%(m/m) improved the immediate bond strengths and bond durability after 9-month storage in artificial saliva without adversely affecting the degree of conversion of the adhesive monomers and resin infiltration.
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
Sayet, G; Sinegre, M; Ben Reguiga, M
2014-01-01
Antibiotic Lock technique maintains catheters' sterility in high-risk patients with long-term parenteral nutrition. In our institution, vancomycin, teicoplanin, amikacin and gentamicin locks are prepared in the pharmaceutical department. In order to insure patient safety and to comply to regulatory requirements, antibiotic locks are submitted to qualitative and quantitative assays prior to their release. The aim of this study was to develop an alternative quantitation technique for each of these 4 antibiotics, using a Fourier transform infrared (FTIR) coupled to UV-Visible spectroscopy and to compare results to HPLC or Immunochemistry assays. Prevalidation studies permitted to assess spectroscopic conditions used for antibiotic locks quantitation: FTIR/UV combinations were used for amikacin (1091-1115cm(-1) and 208-224nm), vancomycin (1222-1240cm(-1) and 276-280nm), and teicoplanin (1226-1230cm(-1) and 278-282nm). Gentamicin was quantified with FTIR only (1045-1169cm(-1) and 2715-2850cm(-1)) due to interferences in UV domain of parabens, preservatives present in the commercial brand used to prepare locks. For all AL, the method was linear (R(2)=0.996 to 0.999), accurate, repeatable (intraday RSD%: from 2.9 to 7.1% and inter-days RSD%: 2.9 to 5.1%) and precise. Compared to the reference methods, the FTIR/UV method appeared tightly correlated (Pearson factor: 97.4 to 99.9%) and did not show significant difference in recovery determinations. We developed a new simple reliable analysis technique for antibiotics quantitation in locks using an original association of FTIR and UV analysis, allowing a short time analysis to identify and quantify the studied antibiotics.
Fourier transforms in spectroscopy
Kauppinen, Jyrki
2000-01-01
This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
Budevska, Boiana O
2009-09-01
Target partial least squares (PLS) is applied to Fourier transform infrared-attenuated total reflection (FT-IR-ATR) hyperspectral images of plant leaf surface treated with crop protection products. Detection of active ingredient is demonstrated at application rates of 50 g active ingredient per hectare. This sensitivity could not be achieved without the application of multivariate analysis. Quantitative information appears to be easily recovered through analysis of combined images with known and unknown amounts of active ingredient.
Energy Technology Data Exchange (ETDEWEB)
Krapez, J.C.; Spagnolo, L. [Politechnique di Bari (Italy); Friess, M. [Deutsches Luft- und Raumfahrtzentrum eV (DLR), Stuttgart (Germany); Maier, H.P. [Stuttgart Univ., MPA (Germany); Neuer, G. [Institut fur Kernenergetik und Energiesysteme, Universitat Stuttgart (Germany)
2003-07-01
The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an homogeneous and extended source is used to irradiate the surface and a thermographic camera is used to monitor the temperature evolution of the opposite side, a map of the through-thickness thermal diffusivity can be obtained in a single experiment and without any contact with the sample under inspection. In order to measure the in-plane thermal diffusivity of a plate-like sample or in one of the principal directions of its plane, a thermal gradient across the plane of the material has to be settled. The ratio of the Fourier transform of temperature at two different spatial frequencies is an exponential function of time multiplied by the diffusivity in the considered principal direction. This can be used to evaluate the diffusivity in an homogenous material. In order to maximize the signal-to-noise ratio, it is better if heat is absorbed over a series of periodic parallel strips (grid flash method). When the material presents a transverse gradient of conductivity, we propose, as a first approach, to perform the Fourier analysis over a sliding window corresponding to one period of the grid pattern. This method allowed us to quantify in situ the diffusivity decrease in a tensile composite sample due to the stress-induced density increase of transverse microcracks. We finally analysed a more rigorous method for transverse conductivity profile inversion. It is based on a perturbation method. The analytical expression of the 'transfer function' between the Fourier transform of the temperature contrast and the Fourier transform of conductivity was established. We validated the proposed inverse technique on simulated and noise-corrupted thermograms. The approach is robust and the simulated profiles are very well resolved. (authors)
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
Qu, Lei; Chen, Jian-bo; Zhou, Qun; Zhang, Gui-jun; Sun, Su-qin; Guo, Yi-zhen
2016-11-01
As a kind of expensive perfume and valuable herb, the commercial Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy and two-dimensional (2D) correlation analysis are employed to establish a simple and quick identification method for the authentic and adulterated ALR. In the conventional infrared spectra, the standard ALR has a strong peak at 1658 cm-1 referring to the conjugated carbonyl of resin, while this peak is absent in the adulterated samples. The position, intensity, and shape of the auto-peaks and cross-peaks of the authentic and adulterated ALR are much different in the synchronous 2D correlation spectra with thermal perturbation. In the range of 1700-1500 cm-1, the standard ALR has four obvious auto-peaks, while the strongest one is at 1659 cm-1. The adulterated sample w-1 has three obvious auto-peaks and the strongest one is at 1647 cm-1. The adulterated sample w-2 has three obvious auto-peaks and the strongest one is at 1519 cm-1. The adulterated sample w-3 has four obvious auto-peaks and the strongest one is at 1690 cm-1. The above auto-peaks confirm that the standard ALR contains a certain content of resin compounds, while the three counterfeits contain little or different resins. The results show the potential of FT-IR spectroscopy and 2D correlation analysis in the simple and quick identification of authentic and adulterated ALR.
Hackel, L.A.; Hermann, M.R.; Dane, C.B.; Tiszauer, D.H.
1995-12-12
A solid state laser is frequency tripled to 0.3 {micro}m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only about 1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power. 1 fig.
Fast Fourier transform telescope
Tegmark, Max; Zaldarriaga, Matias
2009-04-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore’s law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog2N rather than N2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Hackel, Lloyd A.; Hermann, Mark R.; Dane, C. Brent; Tiszauer, Detlev H.
1995-01-01
A solid state laser is frequency tripled to 0.3 .mu.m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only .about.1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power.
Fourier Analysis in Introductory Physics
Huggins, Elisha
2007-01-01
In an after-dinner talk at the fall 2005 meeting of the New England chapter of the AAPT, Professor Robert Arns drew an analogy between classical physics and Classic Coke. To generations of physics teachers and textbook writers, classical physics was the real thing. Modern physics, which in introductory textbooks "appears in one or more extra…
Masked object registration in the Fourier domain.
Padfield, Dirk
2012-05-01
Registration is one of the most common tasks of image analysis and computer vision applications. The requirements of most registration algorithms include large capture range and fast computation so that the algorithms are robust to different scenarios and can be computed in a reasonable amount of time. For these purposes, registration in the Fourier domain using normalized cross-correlation is well suited and has been extensively studied in the literature. Another common requirement is masking, which is necessary for applications where certain regions of the image that would adversely affect the registration result should be ignored. To address these requirements, we have derived a mathematical model that describes an exact form for embedding the masking step fully into the Fourier domain so that all steps of translation registration can be computed efficiently using Fast Fourier Transforms. We provide algorithms and implementation details that demonstrate the correctness of our derivations. We also demonstrate how this masked FFT registration approach can be applied to improve the Fourier-Mellin algorithm that calculates translation, rotation, and scale in the Fourier domain. We demonstrate the computational efficiency, advantages, and correctness of our algorithm on a number of images from real-world applications. Our framework enables fast, global, parameter-free registration of images with masked regions.
Alps, K.; Kruzins, A.; Tamanis, M.; Ferber, R.; Pazyuk, E. A.; Stolyarov, A. V.
2016-04-01
Fourier-transform A1Σ+ - b3Π → X1Σ+ laser-induced fluorescence spectra were recorded for the natural mixture of 39,41K85,87Rb isotopologues produced in a heatpipe oven. Overall 4200 rovibronic term values of the spin-orbit coupled A1Σ+ and b3Π states were determined with an uncertainty of about 0.01 cm-1 in the energy range [10 850, 14 200] cm-1 covering rotational quantum numbers J' ∈ [3, 280]. Direct deperturbation analysis of the A ˜ b complex performed within the framework of the A1Σ+ ˜ b3ΠΩ=0,1,2 coupled-channel approach reproduced experimental data with a standard deviation of 0.004 cm-1. Initial parameters of the internuclear potentials and spin-orbit coupling functions along with the relevant transition dipole moments were obtained by performing the quasi-relativistic electronic structure calculations. The mass-invariant molecular parameters obtained from the fit were used to predict energy and radiative properties of the A ˜ b complex for low J levels of 39K85Rb as well as for 41K87Rb isotopologues, allowing us to identify the most reasonable candidates for the stimulated Raman transitions between the initial uppermost vibrational levels of the a3Σ+ and X1Σ+ states, the intermediate levels of the A ˜ b complex, and the lowest absolute ground X1Σ+(v = 0, J = 0) state.
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.
Seigneur, A; Hou, S; Shaw, R A; McClure, Jt; Gelens, H; Riley, C B
2015-01-15
Deficiency in immunoglobulin G (IgG) is associated with an increased susceptibility to infections in humans and animals, and changes in IgG levels occur in many disease states. In companion animals, failure of transfer of passive immunity is uncommonly diagnosed but mortality rates in puppies are high and more than 30% of these deaths are secondary to septicemia. Currently, radial immunodiffusion (RID) and enzyme-linked immunosorbent assays are the most commonly used methods for quantitative measurement of IgG in dogs. In this study, a Fourier-transform infrared spectroscopy (FTIR) assay for canine serum IgG was developed and compared to the RID assay as the reference standard. Basic signalment data and health status of the dogs were also analyzed to determine if they correlated with serum IgG concentrations based on RID results. Serum samples were collected from 207 dogs during routine hematological evaluation, and IgG concentrations determined by RID. The FTIR assay was developed using partial least squares regression analysis and its performance evaluated using RID assay as the reference test. The concordance correlation coefficient was 0.91 for the calibration model data set and 0.85 for the prediction set. A Bland-Altman plot showed a mean difference of -89 mg/dL and no systematic bias. The modified mean coefficient of variation (CV) for RID was 6.67%, and for FTIR was 18.76%. The mean serum IgG concentration using RID was 1943 ± 880 mg/dL based on the 193 dogs with complete signalment and health data. When age class, gender, breed size and disease status were analyzed by multivariable ANOVA, dogs < 2 years of age (p = 0.0004) and those classified as diseased (p = 0.03) were found to have significantly lower IgG concentrations than older and healthy dogs, respectively.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hang, E-mail: hangwang@sjtu.edu.cn [Instrumental Analysis Center, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240 (China); Dai, Bona [Instrumental Analysis Center, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240 (China); Liu, Bin [Key Laboratory of Kidney Disease Pathogenesis and Intervention of Hubei Province, College of Medicine, Hubei Polytechnic University, Huangshi, Hubei 435003 (China); Lu, Han [Department of Anesthesiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine (SJTU-SM), 197, Rui Jin Er Road, Shanghai 200025 (China)
2015-07-02
Highlights: • Coumarins were used as new MALDI matrices. • Coumarins were used for MALDI-FT ICR MS detection of hydrophobic compounds. • DCA had improvement in detection sensitivity, stability, selectivity and reproducibility. • DCA was applied to sterols detection in yeast cells. - Abstract: Hydrophobic compounds with hydroxyl, aldehyde or ketone groups are generally difficult to detect using matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS), because these compounds have low proton affinity and are poorly ionized by MALDI. Herein, coumarins have been used as new matrices for MALDI-MS analysis of a variety of hydrophobic compounds with low ionization efficiency, including steroids, coenzyme Q10, a cyclic lipopeptide and cholesterol oleate. Five coumarins, including coumarin, umbelliferone, esculetin, 7-hydroxycoumarin-3-carboxylic acid (HCA) and 6,7-dihydroxycoumarin-3-carboxylic acid (DCA), were compared with the conventional matrices of 2,5-dihydroxybenzoic acid (DHB) and α-cyano-4-hydroxycinnamic acid (CHCA). Coumarins with hydroxyl or carboxylic acid groups enabled detection. Taking DCA as an example, this matrix proved to be superior to DHB or CHCA in detection sensitivity, stability, spot-to-spot and sample-to-sample reproducibility, and accuracy. DCA increased the stability of the target compounds and decreased the loss of water. The [M + Na]{sup +} peaks were observed for all target compounds by adding NaCl as an additive, and the [M − H{sub 2}O + H]{sup +} and [M + H]{sup +} peaks decreased. DCA was selected for the identification of sterols in yeast cells, and thirteen sterols were detected by Fourier transform ion cyclotron resonance (FT ICR) mass spectrometry. This work demonstrates the potential of DCA as a new matrix for detection of hydrophobic molecules by MALDI-MS and provides an alternative tool for screening sterols in antifungal research.
Ron, Izhar; Zaltsman, Amalia; Kendler, Shai
2013-12-01
On-site identification of organic compounds in the presence of interfering materials using a field-portable attenuated total reflection Fourier transform infrared (ATR FT-IR) spectrometer is presented. Identification is based on an algorithm that compares the analyte's infrared absorption spectrum with the reference spectra. The comparison is performed at several predetermined frequencies, and a similarity value (distance) between the measured and the reference spectra is calculated either at each frequency individually, or, alternatively, the average distance for all frequencies is calculated. The examined frequencies are selected to give the best contrast between the target materials of interest. In this study, the algorithm was optimized to identify three common chemical warfare agents (CWAs): O-ethyl S-[2-(diisopropylamino)ethyl] methylphosphonothioic acid (VX), sarin (GB), and sulfur mustard (bis(2-chloroethyl) sulfide) (HD), in the presence of field-related interfering materials (fuels, water, and dust). Receiver operating characteristics analysis was performed in order to determine the probabilities for detection (PD) and for false alerts (PF). Challenging the algorithm with a set of data that contains mixtures of CWAs and interfering materials resulted in PD of 90% and PF of 0%, 0%, and 1% for VX, GB, and HD, respectively, using the average distance approach, which was found to be much more effective than analyzing each frequency individually. This finding was validated for all possible combinations of 2-7 peaks per material. It is suggested that this algorithm provides a reliable mean for the identification of a predetermined set of target analytes and interfering materials.
Fourier transform infrared spectrometery: an undergraduate experiment
Lerner, L.
2016-11-01
Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory.
Fourier Transform Spectrometer System
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Projective Fourier duality and Weyl quantization
Energy Technology Data Exchange (ETDEWEB)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Applying Quaternion Fourier Transforms for Enhancing Color Images
Directory of Open Access Journals (Sweden)
M.I. Khalil
2012-03-01
Full Text Available The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.
Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
P. Neelakantan; S. Sharma; H. Shemesh; P.R. Wesselink
2015-01-01
Introduction There is a lack of evidence on the chemical interaction between sealers and dentin. The influence of irrigation on the chemical interaction between root canal sealers and dentin was analyzed by using Fourier transform infrared spectroscopy (FTIRS) and measurement of dislocation resistan
Kamleh, A.; Barrett, M. P.; Wildridge, D.; Burchmore, R. J. S.; Scheltema, R. A.; Watson, D. G.
2008-01-01
It was shown that coupling hydrophilic interaction chromatography (HILIC) to Orbitrap Fourier transform mass spectrometery (FT-MS) provided an excellent tool for metabolic profiling, principally due to rapid elution of lipids in advance of most metabolites entering the mass spectrometer. We used in
The use of Fourier Transform-Infrared Spectroscopy (FT-IR) in conjunction with Artificial Neural Network software, NeuroDeveloper™ was examined for the rapid identification and classification of Listeria species and serotyping of Listeria monocytogenes. A spectral library was created for 245 strains...
Reconstruction in Fourier space
Burden, A.; Percival, W. J.; Howlett, C.
2015-10-01
We present a fast iterative fast Fourier transform (FFT) based reconstruction algorithm that allows for non-parallel redshift-space distortions (RSDs). We test our algorithm on both N-body dark matter simulations and mock distributions of galaxies designed to replicate galaxy survey conditions. We compare solenoidal and irrotational components of the redshift distortion and show that an approximation of this distortion leads to a better estimate of the real-space potential (and therefore faster convergence) than ignoring the RSD when estimating the displacement field. Our iterative reconstruction scheme converges in two iterations for the mock samples corresponding to Baryon Oscillation Spectroscopic Survey CMASS Data Release 11 when we start with an approximation of the RSD. The scheme takes six iterations when the initial estimate, measured from the redshift-space overdensity, has no RSD correction. Slower convergence would be expected for surveys covering a larger angle on the sky. We show that this FFT based method provides a better estimate of the real-space displacement field than a configuration space method that uses finite difference routines to compute the potential for the same grid resolution. Finally, we show that a lognormal transform of the overdensity, used as a proxy for the linear overdensity, is beneficial in estimating the full displacement field from a dense sample of tracers. However, the lognormal transform of the overdensity does not perform well when estimating the displacements from sparser simulations with a more realistic galaxy density.
Reflective Fourier ptychography.
Pacheco, Shaun; Zheng, Guoan; Liang, Rongguang
2016-02-01
The Fourier ptychography technique in reflection mode has great potential applications in tissue imaging and optical inspection, but the current configuration either has a limitation on cut-off frequency or is not practical. By placing the imaging aperture stop outside the illumination path, the illumination numerical aperture (NA) can be greater than the imaging NA of the objective lens. Thus, the cut-off frequency achieved in the proposed optical system is greater than twice the objective's NA divided by the wavelength (2NAobj/λ ), which is the diffraction limit for the cut-off frequency in an incoherent epi-illumination configuration. We experimentally demonstrated that the synthesized NA is increased by a factor of 4.5 using the proposed optical concept. The key advantage of the proposed system is that it can achieve high-resolution imaging over a large field of view with a simple objective. It will have a great potential for applications in endoscopy, biomedical imaging, surface metrology, and industrial inspection.
POINTWISE FOURIER INVERSION OF DISTRIBUTIONS
Institute of Scientific and Technical Information of China (English)
F.J.González Vieli
2008-01-01
We show that,given a tempered distribution T whose Fourier transform is a function of polynomial growth and a point x in Rn at which T has the value τ(in the sense of Lojasiewicz),the Fourier integral of T at x is summable in Bochner-Riesz means to τ.
García-González, Diego L; Sedman, Jacqueline; van de Voort, Frederik R
2013-04-01
Spectral reconstitution (SR) is a dilution technique developed to facilitate the rapid, automated, and quantitative analysis of viscous oil samples by Fourier transform infrared spectroscopy (FT-IR). This technique involves determining the dilution factor through measurement of an absorption band of a suitable spectral marker added to the diluent, and then spectrally removing the diluent from the sample and multiplying the resulting spectrum to compensate for the effect of dilution on the band intensities. The facsimile spectrum of the neat oil thus obtained can then be qualitatively or quantitatively analyzed for the parameter(s) of interest. The quantitative performance of the SR technique was examined with two transition-metal carbonyl complexes as spectral markers, chromium hexacarbonyl and methylcyclopentadienyl manganese tricarbonyl. The estimation of the volume fraction (VF) of the diluent in a model system, consisting of canola oil diluted to various extents with odorless mineral spirits, served as the basis for assessment of these markers. The relationship between the VF estimates and the true volume fraction (VF(t)) was found to be strongly dependent on the dilution ratio and also depended, to a lesser extent, on the spectral resolution. These dependences are attributable to the effect of changes in matrix polarity on the bandwidth of the ν(CO) marker bands. Excellent VF(t) estimates were obtained by making a polarity correction devised with a variance-spectrum-delineated correction equation. In the absence of such a correction, SR was shown to introduce only a minor and constant bias, provided that polarity differences among all the diluted samples analyzed were minimal. This bias can be built into the calibration of a quantitative FT-IR analytical method by subjecting appropriate calibration standards to the same SR procedure as the samples to be analyzed. The primary purpose of the SR technique is to simplify preparation of diluted samples such that
Analysis of DC Arc Feature Based on Fractional Fourier Transform%基于分数阶傅里叶变换的直流电弧特征分析
Institute of Scientific and Technical Information of China (English)
魏渠渠; 王莉
2015-01-01
For the shortcomings of detecting the arc fault simply with time domain or frequency domain methods,an analysis method of arc time-frequency feature was proposed based on fractional Fourier transform (FRFT).DC serial and parallel arc faults under different load were carried out and the arc fault data was obtained from the experiment.Based on the analysis of the data,the feature of the arc on the fractional Fourier domain is more obvious than the frequency domain by changing the transform order p and makes the feature extracting more easier. Then,the influence on the fractional Fourier domain of different types of load and arc was analyzed.Finally,the algorithm complexity and real-time property were compared between(FRFT)and fast Fourier transform.%针对单纯从时域或频域方面检测电弧故障的缺陷，提出了采用分数阶傅里叶变换分析电弧的时频特征。通过试验模拟不同负载时直流串行与并行电弧故障，发现改变变换阶次使得电弧分数阶傅里叶域的特征比频域特征更加明显，有利于提取电弧特征。同时比较了负载性质及电弧类型对电弧分数阶傅里叶域特征的影响，及在线检测电弧故障时分数阶傅里叶变换和快速傅里叶变换算法复杂度与实时性。
Vibration analysis of reciprocating cutter based on Fourier series%基于傅里叶级数的往复式切割器振动分析
Institute of Scientific and Technical Information of China (English)
严帅
2013-01-01
本文对曲柄连杆往复式切割器工作特性进行了分析，利用傅里叶级数将切割器周期激励分解为简谐收敛级数，以特征值为插值结点对傅里叶级数的待定系数进行了求解，并利用叠加原理求出切割器振动系统的稳态响应。%This paper analyzed the characteristics of the crank and connecting rod reciprocating cutter, decomposed the cutter periodic excitation into the harmonic convergenc series using the Fourier series, undetermined coefficients of Fourier series are solved with the eigenvalues for the interpolation nodes, and by using the principle of superposition to calculate the steady-state vibration response of system.
Romanolo, K. F.; Gorski, L; Wang, S.; C R Lauzon
2015-01-01
The use of Fourier Transform-Infrared Spectroscopy (FT-IR) in conjunction with Artificial Neural Network software NeuroDeveloper™ was examined for the rapid identification and classification of Listeria species and serotyping of Listeria monocytogenes. A spectral library was created for 245 strains of Listeria spp. to give a biochemical fingerprint from which identification of unknown samples were made. This technology was able to accurately distinguish the Listeria species with 99.03% accura...
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.
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.
Institute of Scientific and Technical Information of China (English)
杨天鸣; 马雯婷; 付海燕; 郑岸冰; 吴燕
2012-01-01
采用粉末X-射线衍射法对7个不同厂家的银杏叶片进行分析,获得了各样品的粉末X-射线衍射Fourier指纹图谱.根据银杏叶提取物的粉末X-射线衍射Fourier图谱的几何拓扑图形和32个特征共有峰,研究了银杏叶片的粉末X-射线衍射Fourier指纹图谱的图形几何拓扑规律,并计算了其特征共有峰的比例,为银杏叶片的质量鉴定提供了参考依据.%Powder X-ray diffraction analysis was used to analyze tablets of Ginkgo biloba L. from different manufacturers. The powder X-ray diffraction Fourier fingerprint patterns of these samples were obtained. Based on the geometry topology of powder X-ray diffraction Fourier fingerprint pattern and 32 characteristic peaks of the extract of Ginkgo biloba L. , the geometry topology law of powder X-ray diffraction Fourier fingerprint pattern of the tablets of Ginkgo biloba L. was studied,and the proportions of characteristic peaks were calculated. It could be used as reference for the quality identification of the tablets of Ginkgo biloba L..
Image restoration based on the discrete fraction Fourier transform
Yan, Peimin; Mo, Yu L.; Liu, Hong
2001-09-01
The fractional Fourier transform is the powerful tool for time-variant signal analysis. For space-variant degradation and non-stationary processes the filtering in fractional Fourier domains permits reduction of the error compared with ordinary Fourier domain filtering. In this paper the concept of filtering in fractional Fourier domains is applied to the problem of estimating degraded images. Efficient digital implementation using discrete Hermite eigenvectors can provide similar results to match the continuous outputs. Expressions for the 2D optimal filter function in fractional domains will be given for transform domains characterized by the two rotation angle parameters of the 2D fractional Fourier transform. The proposed method is used to restore images that have several degradations in the experiments. The results show that the method presented in this paper is valid.
Embolic Doppler ultrasound signal detection via fractional Fourier transform.
Gençer, Merve; Bilgin, Gökhan; Aydın, Nizamettin
2013-01-01
Computerized analysis of Doppler ultrasound signals can aid early detection of asymptomatic circulating emboli. For analysis, physicians use informative features extracted from Doppler ultrasound signals. Time -frequency analysis methods are useful tools to exploit the transient like signals such as Embolic signals. Detection of discriminative features would be the first step toward automated analysis of embolic Doppler ultrasound signals. The most problematic part of setting up emboli detection system is to differentiate embolic signals from confusing similar wave-like patterns such as Doppler speckle and artifacts caused by tissue movement, probe tapping, speaking etc. In this study, discrete version of fractional Fourier transform is presented as a solution in the detection of emboli in digitized Doppler ultrasound signals. An accurate set of parameters are extracted using short time Fourier transform and fractional Fourier transform and the results are compared to reveal detection quality. Experimental results prove the efficiency of fractional Fourier transform in which discriminative features becomes more evident.
Bittante, G; Cecchinato, A
2013-09-01
Fourier-transform infrared (FTIR) spectra are used to predict the fat, protein, casein, and lactose contents of milk. These estimates are currently used to predict the individual estimated breeding values of animals. The objective of the present study was to estimate the genetic variation and heritabilities of the milk transmittance spectrum at each individual FTIR wave. Milk was sampled once per cow from a total of 1,064 Italian Brown Swiss cows from 30 herds, sired by 50 artificial insemination sires. The FTIR spectra of all samples were collected within 3 h of sampling from 25 mL of milk. The obtained spectral range comprised wavenumbers 5,000 to 930×cm(-1), corresponding to wavelengths 2.00 to 10.76 μm and frequencies from 149.9 to 27.9 THz, for a total of 1,056 waves. These were acquired using a MilkoScan FT120 FTIR interferometer (Foss Electric A/S, Hillerød, Denmark). Each spectral data point was treated as a single trait and analyzed using an animal model REML method. The results indicated that the transmittance of the bovine milk FTIR spectrum was heritable for most individual waves in the wavenumber interval from 5,000 to 930×cm(-1). Moreover, the transmittance of contiguous FTIR waves was much more highly correlated in terms of the average value and phenotypic variation, compared with genetic variation. In the present study, we characterized 5 regions of the FTIR spectrum that were relevant to the analysis of milk; 2 regions, one in the transition area between the short-wavelength infrared (SWIR) and mid-wavelength infrared (MWIR) divisions of the electromagnetic spectrum (SWIR-MWIR region) and another very short region in the MWIR division (MWIR-2 region), were characterized by very high phenotypic variability in the transmittance of individual milk samples within each wave. This was caused by the absorption peaks of water, which can mask the effects of other important milk components. These regions also showed high genetic variability in
Directory of Open Access Journals (Sweden)
Mariele Regina Pinheiro
2011-03-01
Full Text Available Este trabalho foi realizado utilizando dados coletados em uma Floresta de Transição, em uma área pertencente à Fazenda Maracaí no Noroeste de Sinop, MT, com dados micrometeorológicos obtidos com o sistema de correlação de vórtices turbulentos (Eddy Covarience instalado numa torre de 40 metros. Teve como objetivo principal estudar as potencialidades da análise de Fourier aplicada a dados de fluxo de Calor Latente (LE, Calor Sensível (H e Temperatura (T. Para os cálculos foram feitas médias de 3 em 3 horas para cada mês, ao longo do período de 1999 a 2005, para as variáveis estudadas. Os períodos dominantes encontrados foram de 24; 12; 4 e 3,4 horas. Os dois primeiros são atribuíveis ao movimento de rotação da Terra, ou seja, à periodicidade dia/noite. Quanto aos dois períodos menores, há indícios que estão relacionados com a dinâmica de abertura dos estômatos. Assim sendo, os resultados deste trabalho indicam que os fatores que influenciam predominantemente as variáveis microclimatológicas durante o dia (freqüências entre 10-5 a 10-4 Hz são a radiação solar e a dinâmica de abertura dos estômatos, um resultado que destaca as potencialidades da aplicação do método de Fourier no estudo da dinâmica de microclimas em ecossistemas.In this work, we employed data collected in a transition forest, on the Maracaí farm, northwest of Sinop, MT, Brazil. The data was obtained by the eddy covariance method, using equipment installed on a 42m high tower. Its main purpose was to study the potentialities of Fourier analysis applied to data of latent (H and sensible (Le heat flux and the air temperature (T. We investigated the main frequencies presented by the data, and obtained mean values for the variables corresponding to every 3 hours, between 1999 and 2005. The main periods obtained with the Fourier method were 24; 12; 4 and 3.4 hours. The first two are attributed to the solar radiation and to the Earth rotation. The
DEFF Research Database (Denmark)
Renfrow, MB; Mackay, CL; Chalmers, MJ;
2007-01-01
IgA nephropathy (IgAN) is the most common form of primary glomerulonephritis. In IgAN, IgA1 molecules with incompletely galactosylated O-linked glycans in the hinge region (HR) are present in mesangial immunodeposits and in circulating immune complexes. It is not known whether the galactose...... deficiency in IgA1 proteins occurs randomly or preferentially at specific sites. We have previously demonstrated the first direct localization of multiple O-glycosylation sites on a single IgA1 myeloma protein by use of activated ion-electron capture dissociation (AI-ECD) Fourier transform ion cyclotron...
Introduction to partial differential equations from Fourier series to boundary-value problems
Broman, Arne
2010-01-01
This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.
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.
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 Transform Fabry-Perot Interferometer
Snell, Hilary E.; Hays, Paul B.
1992-01-01
We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.
Directory of Open Access Journals (Sweden)
Luiz G. de Carvalho
2005-12-01
Full Text Available O objetivo deste trabalho foi obter um modelo de previsão de produtividade para a cultura do café, em sete municípios do Estado de Minas Gerais. Submeteram-se à análise harmônica por séries de Fourier, séries de produtividades representativas de cada município, das quais se extraíram os coeficientes até o sétimo harmônico, submetendo-os à regressão linear múltipla nos três primeiros componentes principais de um conjunto de 33 variáveis inerentes à produção cafeeira. Essas variáveis foram médias de 15 anos correspondentes aos mesmos anos das produtividades e subdivididos em quatro períodos trimestrais, ao longo do ciclo produtivo da cultura (julho a junho. O modelo mostrou-se inconsistente, apresentando erros das estimativas bastante discrepantes, evidenciando a complexidade de modelagem de previsão de safras para a cultura do café.The objective of this work was to obtain a forecast model of coffee crop productivity in seven municipal districts of Minas Gerais State, Brazil. The harmonic analysis in Fourier series was applied on productivity series to each location. The obtained coefficients until the harmonic seventh were submitted to multiple linear regression in the first three principal components of a group of 33 inherent variables of coffee production. These variables were averages of 15 years corresponding to the same years of productivity and subdivided in four quarterly periods during the agricultural year (July to June. The model did not prove adequate, since the results presented errors of estimatives with great discrepancies evidencing the complexity of yield forecast of coffee crop.
Yang, Fan; Voelkel, Jacob E; Dearden, David V
2012-06-01
We demonstrate a technique for determining molecular collision cross sections via measuring the variation of Fourier transform ion cyclotron resonance (FTICR) line width with background damping gas pressure, under conditions where the length of the FTICR transient is pressure limited. Key features of our method include monoisotopic isolation of ions, the pulsed introduction of damping gas to a constant pressure using a pulsed leak valve, short excitation events to minimize collisions during the excitation, and proper choice of damping gas (Xe is superior to He). The measurements are reproducible within a few percent, which is sufficient for distinguishing between many structural possibilities and is comparable to the uncertainty in cross sections calculated from computed molecular structures. These techniques complement drift ion mobility measurements obtained on dedicated instruments. They do not require a specialized instrument, but should be easily performed on any FTICR mass spectrometer equipped with a pulsed leak valve.
Energy Technology Data Exchange (ETDEWEB)
Manso, M. [Centro de Fisica Atomica, Universidade de Lisboa, Faculdade de Ciencias, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal); Valadas, S. [Chemistry Department, Evora Chemistry Centre and HERCULES Centre, University of Evora, Rua Romao Ramalho, 59 Evora (Portugal); Pessanha, S.; Guilherme, A. [Centro de Fisica Atomica, Universidade de Lisboa, Faculdade de Ciencias, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal); Queralt, I. [Laboratory of X-ray Analytical Applications, Institute of Earth Sciences ' Jaume Almera' , CSIC, Sole Sabaris s/n. 08028 Barcelona (Spain); Candeias, A.E. [Chemistry Department, Evora Chemistry Centre and HERCULES Centre, University of Evora, Rua Romao Ramalho, 59 Evora (Portugal); Carvalho, M.L., E-mail: luisa@cii.fc.ul.p [Centro de Fisica Atomica, Universidade de Lisboa, Faculdade de Ciencias, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal)
2010-04-15
This work comprises the use of energy dispersive X-ray fluorescence (EDXRF), X-ray diffraction (XRD) and Fourier transformed infrared (FTIR) techniques for the study of the composition of twentieth century traditional Japanese color sticks. By using the combination of analytical techniques it was possible to obtain information on inorganic and organic pigments, binders and fillers present in the sticks. The colorant materials identified in the sticks were zinc and titanium white, chrome yellow, yellow and red ochre, vermillion, alizarin, indigo, Prussian and synthetic ultramarine blue. The results also showed that calcite and barite were used as inorganic mineral fillers while Arabic gum was the medium used. EDXRF offered great potential for such investigations since it allowed the identification of the elements present in the sample preserving its integrity. However, this information alone was not enough to clearly identify some of the materials in study and therefore it was necessary to use XRD and FTIR techniques.
Fourier-transform spectroscopy of 13C17O and deperturbation analysis of the A1Π (υ=0-3) levels
Hakalla, R.; Niu, M. L.; Field, R. W.; Heays, A. N.; Salumbides, E. J.; Stark, G.; Lyons, J. R.; Eidelsberg, M.; Lemaire, J. L.; Federman, S. R.; de Oliveira, N.; Ubachs, W.
2017-03-01
The high-resolution B1Σ+→A1Π (0, 0) and (0, 3) emission bands of the less-abundant 13C17O isotopologue have been investigated by Fourier-transform spectroscopy in the visible region using a Bruker IFS 125HR spectrometer at an accuracy 0.003 cm-1. These spectra are combined with high-resolution photoabsorption measurements of the 13C17O B1Σ+←X1Σ+ (0, 0), B1Σ+←X1Σ+ (1, 0) and C1Σ+←X1Σ+ (0, 0) bands recorded with an accuracy of 0.01 cm-1 using the vacuum ultraviolet Fourier-transform spectrometer, installed on the DESIRS beamline at the SOLEIL synchrotron. In the studied 17,950-22,500 cm-1 and 86,800-92,100 cm-1 regions, 480 transitions have been measured. These new experimental data were combined with data from the C→A and B→A systems, previously analyzed in 13C17O. The frequencies of 1003 transitions derived from 12 bands were used to analyze the perturbations between the A1Π (υ=0-3) levels and rovibrational levels of the d3Δi, e3Σ-, a'3Σ+, I1Σ- and D1Δ states as well as to a preliminary investigation of weak irregularities that appear in the B1Σ+ (υ=0) level. Deperturbed molecular constants and term values of the A1Π state were obtained. The spin-orbit and L-uncoupling interaction parameters as well as isotopologue-independent spin-orbit and rotation-electronic perturbation parameters were derived.
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.
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.
Institute of Scientific and Technical Information of China (English)
周业勤; 龙敏
2015-01-01
According to the properties of fractional Fourier transform, a kind of fractional Fourier transform image encryp-tion algorithm is analyzed. The key is not sensitive and the deciphering diagram is of great distortion, when with the naked eye on results chart to judge and extract the image data for comparison. Theoretical analysis and experimental results show that the algorithm is not sensitive to the key when the fractional Fourier transform is directly applied to image encryption. The introduction of RGB mapping to realize the cipher image display and transmission, result a great distortion in pixels.%从分数阶傅里叶变换的性质出发，对一类分数阶傅里叶变换图像加密算法进行分析。对原有算法结果图进行肉眼判断，提取图像中间结果数据进行对比分析，可知算法的密钥具有不敏感性，并且解密图具有很大失真。对分数傅里叶变换进行理论上的分析和讨论。分析及实验结果表明，直接使用分数阶傅里叶变换进行加密的算法对密钥并不敏感，存在安全隐患。为实现密文图像的显示和传输而引入的RGB映射将导致解密图像像素值失真。
Dong, Kyung-Rae; Goo, Eun-Hoe; Lee, Jae-Seung; Chung, Woon-Kwan
2013-01-01
A consecutive series of 50 patients (28 males and 22 females) who underwent hepatic magnetic resonance imaging (MRI) from August to December 2011 were enrolled in this study. The appropriate parameters for abdominal MRI scans were determined by comparing the images (TE = 90 and 128 msec) produced using the half-Fourier acquisition single-shot turbo spin-echo (HASTE) technique at different signal acquisition times. The patients consisted of 15 normal patients, 25 patients with a hepatoma and 10 patients with a hemangioma. The TE in a single patient was set to either 90 msec or 128 msec. This was followed by measurements using the four normal rendering methods of the biliary tract system and the background signal intensity using the maximal signal intensity techniques in the liver, spleen, pancreas, gallbladder, fat, muscles and hemangioma. The signal-to-noise and the contrast-to-noise ratios were obtained. The image quality was assessed subjectively, and the results were compared. The signal-to-noise and the contrast-to-noise ratios were significantly higher at TE = 128 msec than at TE = 90 when diseases of the liver, spleen, pancreas, gallbladder, and fat and muscles, hepatocellular carcinomas and hemangiomas, and rendering the hepatobiliary tract system based on the maximum signal intensity technique were involved (p < 0.05). In addition, the presence of artifacts, the image clarity and the overall image quality were excellent at TE = 128 msec (p < 0.05). In abdominal MRI, the breath-hold half-Fourier acquisition single-shot turbo spin-echo (HASTE) was found to be effective in illustrating the abdominal organs for TE = 128 msec. Overall, the image quality at TE = 128 msec was better than that at TE = 90 msec due to the improved signal-to-noise (SNR) and contrast-to-noise (CNR) ratios. Overall, the HASTE technique for abdominal MRI based on a high-magnetic field (3.0 T) at a TE of 128 msec can provide useful data.
A Borderline Random Fourier Series
Talagrand, Michel
1995-01-01
Consider a mean zero random variable $X$, and an independent sequence $(X_n)$ distributed like $X$. We show that the random Fourier series $\\sum_{n\\geq 1} n^{-1} X_n \\exp(2i\\pi nt)$ converges uniformly almost surely if and only if $E(|X|\\log\\log(\\max(e^e, |X|))) < \\infty$.
Fourier Series and Elliptic Functions
Fay, Temple H.
2003-01-01
Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…
Fourier Lucas-Kanade algorithm.
Lucey, Simon; Navarathna, Rajitha; Ashraf, Ahmed Bilal; Sridharan, Sridha
2013-06-01
In this paper, we propose a framework for both gradient descent image and object alignment in the Fourier domain. Our method centers upon the classical Lucas & Kanade (LK) algorithm where we represent the source and template/model in the complex 2D Fourier domain rather than in the spatial 2D domain. We refer to our approach as the Fourier LK (FLK) algorithm. The FLK formulation is advantageous when one preprocesses the source image and template/model with a bank of filters (e.g., oriented edges, Gabor, etc.) as 1) it can handle substantial illumination variations, 2) the inefficient preprocessing filter bank step can be subsumed within the FLK algorithm as a sparse diagonal weighting matrix, 3) unlike traditional LK, the computational cost is invariant to the number of filters and as a result is far more efficient, and 4) this approach can be extended to the Inverse Compositional (IC) form of the LK algorithm where nearly all steps (including Fourier transform and filter bank preprocessing) can be precomputed, leading to an extremely efficient and robust approach to gradient descent image matching. Further, these computational savings translate to nonrigid object alignment tasks that are considered extensions of the LK algorithm, such as those found in Active Appearance Models (AAMs).
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.
Carlsohn, Elisabet; Ångström, Jonas; Emmett, Mark R.; Marshall, Alan G.; Nilsson, Carol L.
2004-05-01
Chemical cross-linking of proteins is a well-established method for structural mapping of small protein complexes. When combined with mass spectrometry, cross-linking can reveal protein topology and identify contact sites between the peptide surfaces. When applied to surface-exposed proteins from pathogenic organisms, the method can reveal structural details that are useful in vaccine design. In order to investigate the possibilities of applying cross-linking on larger protein complexes, we selected the urease enzyme from Helicobacter pylori as a model. This membrane-associated protein complex consists of two subunits: [alpha] (26.5 kDa) and [beta] (61.7 kDa). Three ([alpha][beta]) heterodimers form a trimeric ([alpha][beta])3 assembly which further associates into a unique dodecameric 1.1 MDa complex composed of four ([alpha][beta])3 units. Cross-linked peptides from trypsin-digested urease complex were analyzed by Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) and molecular modeling. Two potential cross-linked peptides (present in the cross-linked sample but undetectable in [alpha], [beta], and native complex) were assigned. Molecular modeling of urease [alpha][beta] complex and trimeric urease units ([alpha][beta])3 revealed a linkage site between the [alpha]-subunit and the [beta]-subunit, and an internal cross-linkage in the [beta]-subunit.
Zumbühl, Stefan; Scherrer, Nadim C; Eggenberger, Urs
2014-01-01
The interpretation of standard Fourier transform infrared spectra (FT-IR) on oil-based paint samples often suffers from interfering bands of the different compounds, namely, binder, oxidative aging products, carboxylates formed during aging, and several pigments and fillers. The distinction of the aging products such as ketone and carboxylic acid functional groups pose the next problem, as these interfere with the triglyceride esters of the oil. A sample preparation and derivatization technique using gaseous sulfur tetrafluoride (SF4), was thus developed with the aim to discriminate overlapping signals and achieve a signal enhancement on superposed compounds. Of particular interest in this context is the signal elimination of the broad carboxylate bands of the typical reaction products developing during the aging processes in oil-based paints, as well as signal interference originating from several typical pigments in this spectral range. Furthermore, it is possible to distinguish the different carbonyl-containing functional groups upon selective alteration. The derivatization treatment can be applied to both microsamples and polished cross sections. It increases the selectivity of the infrared spectroscopy technique in a fundamental manner and permits the identification and two-dimensional (2D) localization of binder components in aged paint samples at the micrometer scale. The combination of SF4 derivatization with high-resolution 2D FT-IR focal plane array (FPA) imaging delivers considerable advances to the study of micro-morphological processes involving organic compounds.
Energy Technology Data Exchange (ETDEWEB)
Tang, Yinjie; Pingitore, Francesco; Mukhopadhyay, Aindrila; Phan,Richard; Hazen, Terry C.; Keasling, Jay D.
2007-03-15
Flux distribution in central metabolic pathways ofDesulfovibrio vulgaris Hildenborough was examined using 13C tracerexperiments. Consistent with the current genome annotation andindependent evidence from enzyme activity assays, the isotopomer resultsfrom both GC-MS and Fourier Transform-Ion Cyclotron Resonance massspectrometry (FT-ICR MS) indicate the lack of oxidatively functional TCAcycle and an incomplete pentose phosphate pathway. Results from thisstudy suggest that fluxes through both pathways are limited tobiosynthesis. The data also indicate that>80 percent of the lactatewas converted to acetate and the reactions involved are the primary routeof energy production (NAD(P)H and ATP production). Independent of the TCAcycle, direct cleavage of acetyl-CoA to CO and 5,10-methyl-THF also leadsto production of NADH and ATP. Although the genome annotation implicatesa ferredoxin-dependentoxoglutarate synthase, isotopic evidence does notsupport flux through this reaction in either the oxidative or reductivemode; therefore, the TCA cycle is incomplete. FT-ICR MS was used tolocate the labeled carbon distribution in aspartate and glutamate andconfirmed the presence of an atypical enzyme for citrate formationsuggested in previous reports (the citrate synthesized by this enzyme isthe isotopic antipode of the citrate synthesized by the (S)-citratesynthase). These findings enable a better understanding of the relationbetween genome annotation and actual metabolic pathways in D. vulgaris,and also demonstrate FT-ICR MS as a powerful tool for isotopomeranalysis, overcoming problems in both GC-MS and NMRspectroscopy.
Methods of theme presentation "The Fourier transform of impulse functions"
Directory of Open Access Journals (Sweden)
Faniya Ahmetova
2016-09-01
Full Text Available The paper considers the Fourier transform of impulse functions, which is the mathematical basis of the tasks associated with the theory of reception and signal conversion in optoelectronic system. The method of calculating of two functions convolution, its Fourier image and the image of the Fourier-Bessel axisymmetric functions are demonstrated in details. A table, which summarizes the analytical expression for the shifted impulse functions and records their Fourier transforms, is provided. A wide range of examples of solving tasks, containing the graphic illustration, is analyzed. A structured approach to the presentation of the material, which combines basic theoretical information and analysis of typical tasks, will help second-year students of optoelectronic specialty in their independent work and homework.
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...
Walker, Amanda M; Yu, Peiqiang; Christensen, Colleen R; Christensen, David A; McKinnon, John J
2009-08-12
The objectives of this study were to use Fourier transform infrared microspectroscopy (FTIRM) to determine structural makeup (features) of cereal grain endosperm tissue and to reveal and identify differences in protein and carbohydrate structural makeup between different cereal types (corn vs barley) and between different varieties within a grain (barley CDC Bold, CDC Dolly, Harrington, and Valier). Another objective was to investigate how these structural features relate to rumen degradation kinetics. The items assessed included (1) structural differences in protein amide I to nonstructural carbohydrate (NSC, starch) intensity and ratio within cellular dimensions; (2) molecular structural differences in the secondary structure profile of protein, alpha-helix, beta-sheet, and their ratio; (3) structural differences in NSC to amide I ratio profile. From the results, it was observed that (1) comparison between grain types [corn (cv. Pioneer 39P78) vs barley (cv. Harrington)] showed significant differences in structural makeup in terms of NSC, amide I to NSC ratio, and rumen degradation kinetics (degradation ratio, effective degradability of dry matter, protein and NSC) (P degradation kinetics (effective degradability of dry matter, protein, and NSC) (P degradation kinetics in terms of the degradation rate (R = 0.91, P = 0.086) and effective degradability of dry matter (R = 0.93, P = 0.071). The results suggest that with the FTIRM technique, the structural makeup differences between cereal types and between different varieties within a type of grain could be revealed. These structural makeup differences were related to the rate and extent of rumen degradation.
Sasaki, K M; Aoki, A; Masuno, H; Ichinose, S; Yamada, S; Ishikawa, I
2002-02-01
The present study examines the dental root after Er:YAG laser irradiation, compared with CO2 lased and non-treated surfaces, using Fourier Transformed Infrared (FTIR) spectroscopy. Freshly extracted human teeth were irradiated by Er:YAG laser at an energy output of 40 mJ/pulse, 10 Hz (0.4 watts), with or without water coolant, and by CO2 laser at an energy output of 0.5 watts in continuous wave mode without coolant. The surfaces were chalky and smooth after irradiation by Er:YAG laser with water coolant, were charred and irregular after irradiation by Er:YAG laser without water coolant, and were completely carbonized after CO2 laser irradiation. The FTIR profiles from samples of the surfaces that were irradiated by Er:YAG laser with water coolant were similar to those from non-treated samples, except for a slight decrease on the OH and amide bands, which are mainly related to organic components. This decrease was observed to be extreme after CO2 laser irradiation and moderate after Er:YAG laser irradiation without coolant. The formation of new bands showing toxic substances was observed to a large extent after CO2 laser irradiation and to a smaller extent after Er:YAG laser irradiation without water coolant. In contrast, no such bands were detected after Er:YAG laser irradiation with water coolant. The present results show that these laser treatments selectively ablated more organic components than inorganic components and that Er:YAG laser irradiation with water coolant did not cause major compositional changes or chemically deleterious changes in either root cementum or dentin.
Gajjar, Ketan; Trevisan, Júlio; Owens, Gemma; Keating, Patrick J; Wood, Nicholas J; Stringfellow, Helen F; Martin-Hirsch, Pierre L; Martin, Francis L
2013-07-21
Currently available screening tests do not deliver the required sensitivity and specificity for accurate diagnosis of ovarian or endometrial cancer. Infrared (IR) spectroscopy of blood plasma or serum is a rapid, versatile, and relatively non-invasive approach which could characterize biomolecular alterations due to cancer and has potential to be utilized as a screening or diagnostic tool. In the past, no such approach has been investigated for its applicability in screening and/or diagnosis of gynaecological cancers. We set out to determine whether attenuated total reflection Fourier-transform IR (ATR-FTIR) spectroscopy coupled with a proposed classification machine could be applied to IR spectra obtained from plasma and serum for accurate class prediction (cancer vs. normal). Plasma and serum samples were obtained from ovarian cancer cases (n = 30), endometrial cancer cases (n = 30) and non-cancer controls (n = 30), and subjected to ATR-FTIR spectroscopy. Four derived datasets were processed to estimate the real-world diagnosis of ovarian and endometrial cancer. Classification results for ovarian cancer were remarkable (up to 96.7%), whereas endometrial cancer was classified with a relatively high accuracy (up to 81.7%). The results from different combinations of feature extraction and classification methods, and also classifier ensembles, were compared. No single classification system performed best for all different datasets. This demonstrates the need for a framework that can accommodate a diverse set of analytical methods in order to be adaptable to different datasets. This pilot study suggests that ATR-FTIR spectroscopy of blood is a robust tool for accurate diagnosis, and carries the potential to be utilized as a screening test for ovarian cancer in primary care settings. The proposed classification machine is a powerful tool which could be applied to classify the vibrational spectroscopy data of different biological systems (e.g., tissue, urine, saliva
Picollo, Marcello; Bartolozzi, Giovanni; Cucci, Costanza; Galeotti, Monica; Marchiafava, Veronica; Pizzo, Benedetto
2014-01-01
This study was completed within the framework of two research projects dealing with the conservation of contemporary artworks. The first is the Seventh Framework Project (FP7) of the European Union, Preservation of Plastic ARTefacts in Museum Collections (POPART), spanning years 2008-2012, and the second is the Italian project funded by the Tuscan Region, Preventive Conservation of Contemporary Art (Conservazione Preventiva dell'Arte Contemporanea (COPAC)), spanning 2011-2013. Both of these programs pointed out the great importance of having noninvasive and portable analytical techniques that can be used to investigate and characterize modern and contemporary artworks, especially those consisting of synthetic polymers. Indeed, despite the extensive presence of plastics in museum collections, there is still a lack of analytical tools for identifying, characterizing, and setting up adequate conservation strategies for these materials. In this work, the potentials of in situ and noninvasive Fourier transform infrared (FT-IR) spectroscopy, implemented by means of portable devices that operate in reflection mode, are investigated with a view to applying the results in large-scale surveys of plastic objects in museums. To this end, an essential prerequisite are the reliability of spectral data acquired in situ and the availability of spectral databases acquired from reference materials. A collection of polymeric samples, which are available commercially as ResinKit, was analyzed to create a reference spectral archive. All the spectra were recorded using three FT-IR configurations: transmission (trans), attenuated total reflection (ATR), and total reflection (TR). A comparative evaluation of the data acquired using the three instrumental configurations is presented, together with an evaluation of the similarity percentages and a discussion of the critical cases.
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...
Fourier's Law in Quantum Mechanics
Seligman, Thomas H
2010-01-01
We derive Fourier's law for a completely coherent quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the length of the system.
Subharmonic Fourier domain mode locking.
Eigenwillig, Christoph M; Wieser, Wolfgang; Biedermann, Benjamin R; Huber, Robert
2009-03-15
We demonstrate a subharmonically Fourier domain mode-locked wavelength-swept laser source with a substantially reduced cavity fiber length. In contrast to a standard Fourier domain mode-locked configuration, light is recirculated repetitively in the delay line with the optical bandpass filter used as switch. The laser has a fundamental optical round trip frequency of 285 kHz and can be operated at integer fractions thereof (subharmonics). Sweep ranges up to 95 nm full width centred at 1317 nm are achieved at the 1/5th subharmonic. A maximum sensitivity of 116 dB and an axial resolution of 12 microm in air are measured at an average sweep power of 12 mW. A sensitivity roll-off of 11 dB over 4 mm and 25 dB over 10 mm is observed and optical coherence tomography imaging is demonstrated. Besides the advantage of a reduced fiber length, subharmonic Fourier domain mode locking (shFDML) enables simple scaling of the sweep speed by extracting light from the delay part of the resonator. A sweep rate of 570 kHz is achieved. Characteristic features of shFDML operation, such as power leakage during fly-back and cw breakthrough, are investigated.
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...
Institute of Scientific and Technical Information of China (English)
王祝文; 向旻; 刘菁华; 王晓丽; 张雪昂; 杨闯
2012-01-01
目前,阵列声波测井信号处理大多在时间域或频率域中进行.但是,单纯的时间域或频率域方法有很大的局限性.为了打破这些局限性,笔者将分数阶Fourier变换方法用于阵列声波测井信号的分析之中,研究了不同性质储集层中信号幅度随分数阶Fourier变换阶数变化的规律.实验结果表明:在干层,幅度呈“1”型分布；在水层,幅度呈“Y”型分布,“Y”的两支开口较小,在阶数大于0.3的区域中,幅度较大；在油层,幅度呈“Y”型分布,“Y”的两支开口较大,在阶数大于0.6的区域中,幅度较大.因此,分数阶Fourier变换在提取阵列声波测井蕴含的储集层流体性质信息方面具有很好的前景.%As we knew, most of the process techniques for array acoustic logging data still use the analysis methods only in either time domain or frequency domain, but these methods all have obvious limitation for signal analysis. In order to break these limitations, the authors used the fratal Fourier for analysing the array acoustic logging signals and researching the law of signal amplitude variation with the order of the fratal Fourier transform variation in different kinds of reservoirs. As the results, in the dry formation, amplitude shows "1" type distribution; In water formation, amplitude shows "Y" type distribution, two branch of "Y" open narrow and in area of order greater than 0. 3, amplitude is larger; In oil formation, amplitude shows "Y" type distribution, two branch of "Y" open wide and in area of order greater than 0. 6, amplitude is larger. So the fratal Fourier transform have very good prospect for extracting the reservoir liquid properties information embedded in the array acoustic logging data.
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
Brooke, Heather; Perkins, David L; Setlow, Barbara; Setlow, Peter; Bronk, Burt V; Myrick, Michael L
2008-08-01
A study was conducted to determine the concentration dependency of the mid-infrared (MIR) absorbance of bacterial spores. A range of concentrations of Bacillus subtilis endospores filtered across gold-coated filter membranes were analyzed by Fourier transform infrared (FT-IR) reflectance microscopy. Calibration curves were derived from the peak absorbances associated with Amide A, Amide I, and Amide II vibrational frequencies by automatic baseline fitting to remove most of the scattering contribution. Linear relationships (R2 >or= 0.99) were observed between the concentrations of spores and the baseline-corrected peak absorbance for each frequency studied. Detection limits for our sampled area of 100 x100 microm2 were determined to be 79, 39, and 184 spores (or 7.92 x 10(5), 3.92 x 10(5), and 1.84 x 10(6) spores/cm2) for the Amide A, Amide I, and Amide II peaks, respectively. Absorbance increased linearly above the scattering baseline with particle surface concentration up to 0.9 monolayer (ML) coverage, with the monolayer density calculated to be approximately 1.17 x 10(8) spores/cm2. Scattering as a function of surface concentration, as estimated from extinction values at wavelengths exhibiting low absorbance, becomes nonlinear at a much lower surface concentration. The apparent scattering cross-section per spore decreased monotonically as concentrations increased toward 1.2 ML, while the absolute scattering decreased between 0.9 ML and 1.2 ML coverage. Calculations suggest that transverse spatial coherence effects are the origin of this nonlinearity, while the onset of nonlinearity in the baseline-corrected absorption is probably due to multiple scattering effects, which appear at a high surface concentration. Absorption cross-sections at peaks of the three bands were measured to be (2.15 +/- 0.05) x 10(-9), (1.48 +/- 0.03) x 10(-9), and (0.805 +/- 0.023) x 10(-9) cm2, respectively. These values are smaller by a factor of 2-4 than expected from the literature
The Formalization of Discrete Fourier Transform in HOL
Directory of Open Access Journals (Sweden)
Zhiping Shi
2015-01-01
Full Text Available Traditionally, Discrete Fourier Transform (DFT is performed with numerical or symbolic computation, which cannot guarantee 100% accurate analysis which may be necessary for safety-critical applications. Machine theorem proving is one of the formal methods that perform accurate analysis with completeness to some extent. This paper proposes the formalization of DFT in a higher-order logic theorem prover named HOL. We propose the formal definition of DFT and verify the fundamental properties of DFT. Two case studies are presented to illustrate usefulness and correctness of the formalized DFT, including formal verifications of Fast Fourier Transform (FFT and cosine frequency shift.
Fourier-transform optical microsystems
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
Novel Micro Fourier Transform Spectrometers
Institute of Scientific and Technical Information of China (English)
KONG Yan-mei; LIANG Jing-qiu; LIANG Zhong-zhu; WANG-Bo; ZHANG Jun
2008-01-01
The miniaturization of spectrometer opens a new application area with real-time and on-site measurements. The Fourier transform spectrometer(FTS) is much attractive considering its particular advantages among the approaches. This paper reviews the current status of micro FTS in worldwide and describes its developments; In addition, analyzed are the key problems in designing and fabricating FTS to be settled during the miniaturization. Finally, a novel model of micro FTS with no moving parts is proposed and analyzed, which may provide new concepts for the design of spectrometers.
Aperture scanning Fourier ptychographic microscopy
Ou, Xiaoze; Chung, Jaebum; Horstmeyer, Roarke; Yang, Changhuei
2016-01-01
Fourier ptychographic microscopy (FPM) is implemented through aperture scanning by an LCOS spatial light modulator at the back focal plane of the objective lens. This FPM configuration enables the capturing of the complex scattered field for a 3D sample both in the transmissive mode and the reflective mode. We further show that by combining with the compressive sensing theory, the reconstructed 2D complex scattered field can be used to recover the 3D sample scattering density. This implementation expands the scope of application for FPM and can be beneficial for areas such as tissue imaging and wafer inspection. PMID:27570705
JPL Fourier transform ultraviolet spectrometer
Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.
1994-01-01
The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.
Fourier-Transform Infrared Spectrometer
Schindler, R. A.
1986-01-01
Fourier-transform spectrometer provides approximately hundredfold increase in luminosity at detector plane over that achievable with older instruments of this type. Used to analyze such weak sources as pollutants and other low-concentration substances in atmosphere. Interferometer creates fringe patterns on two distinct arrays of light detectors, which observe different wavelength bands. Objective lens focuses scene on image plane, which contains optical chopper. To make instrument less susceptible to variations in scene under observation, field and detector lenses focus entrance aperture, rather that image, onto detector array.
Fourier Transform Methods. Chapter 4
Kaplan, Simon G.; Quijada, Manuel A.
2015-01-01
This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
Faye; Kou; Farrenq; Guelachvili
1999-10-01
The extension of high-resolution observation of the electronic emission spectrum of (14)N(2) toward the infrared domain is presented. To date, rotational analysis of the widely investigated spectrum of the N(2) molecule was done in a spectral domain ranging from 2500 cm(-1) to the UV. We have recorded for the first time the infrared part of the (14)N(2) spectrum from 1250 to 2250 cm(-1), using the Fourier transform spectrometer of Laboratoire de Photophysique Moléculaire (LPPM) at an unapodized resolution of 0.0043 cm(-1). A complete rotational analysis is performed for the (1 --> 0), (2 --> 1), (0 <-- 1), (1 <-- 2) bands of the B(3)Pi(g)-W(3)Delta(u) system, not included in any previous analysis. Spectroscopic parameters for the v = 0, v = 1, v = 2 levels of the B(3)Pi(g) and the W(3)Delta(u) states, consistent with those previously reported but with improved accuracy, are obtained from the experimental wavenumbers by a nonlinear least-squares procedure. Copyright 1999 Academic Press.
Faye, A.; Kou, Q.; Farrenq, R.; Guelachvili, G.
1999-10-01
The extension of high-resolution observation of the electronic emission spectrum of 14N2 toward the infrared domain is presented. To date, rotational analysis of the widely investigated spectrum of the N2 molecule was done in a spectral domain ranging from 2500 cm-1 to the UV. We have recorded for the first time the infrared part of the 14N2 spectrum from 1250 to 2250 cm-1, using the Fourier transform spectrometer of Laboratoire de Photophysique Moléculaire (LPPM) at an unapodized resolution of 0.0043 cm-1. A complete rotational analysis is performed for the (1 → 0), (2 → 1), (0 ← 1), (1 ← 2) bands of the B3Πg-W3Δu system, not included in any previous analysis. Spectroscopic parameters for the v = 0, v = 1, v = 2 levels of the B3Πg and the W3Δu states, consistent with those previously reported but with improved accuracy, are obtained from the experimental wavenumbers by a nonlinear least-squares procedure.
Institute of Scientific and Technical Information of China (English)
任重; 董明; 吴立远; 任明; 司文荣
2013-01-01
为了分析冲击电压下GIS腔体内局部放电信号的特征,将一种时频变换理论即二次型短时傅立叶变换应用于局放脉冲序列的分析,得到信号在时频平面的能量分布和变化规律.通过对含噪声局放脉冲序列时频变换的仿真研究,有效地提取了放电脉冲.另外,在实验室对220 kV GIS母线段进行了尖刺缺陷模型的安装和冲击耐压下局放检测,对实测数据进行了时频分析,验证了二次型短时傅里叶变换在局放信号处理中的有效性,得到了信号时频谱图在不同长度窗函数处理下的变化规律.%In order to analyze the characteristics of signals of partial discharge (PD) in GIS under the impulse voltage, a kind of time-frequency transform theory called the quadratic short-time Fourier transform was applied in analysis of the PD pulse sequence to get the distribution of energy and variation law of signals in the time-frequency plane. In this research, the time-frequency transform of a kind of typical PD pulse sequence containing noise was simulated, which showed that PD pulse could be extracted efficiently. Besides, a kind of spikes defect model was installed in the bus segment of 220 kV GIS and the PD of GIS under impulse voltage was detected. By time-frequency analysis of experiment data, it can be found that the theory of quadratic short-time Fourier transform can be applied in analysis of PD signals efficiently and the variation law of time-frequency spectrogram was affected by the length of window function.
Gravemeier, Volker; Kronbichler, Martin; Gee, Michael W.; Wall, Wolfgang A.
2011-02-01
This article studies three aspects of the recently proposed algebraic variational multiscale-multigrid method for large-eddy simulation of turbulent flow. First, the method is integrated into a second-order-accurate generalized-α time-stepping scheme. Second, a Fourier analysis of a simplified model problem is performed to assess the impact of scale separation on the overall performance of the method. The analysis reveals that scale separation implemented by projective operators provides modeling effects very close to an ideal small-scale subgrid viscosity, that is, it preserves low frequencies, in contrast to non-projective scale separations. Third, the algebraic variational multiscale-multigrid method is applied to turbulent flow past a square-section cylinder. The computational results obtained with the method reveal, on the one hand, the good accuracy achievable for this challenging test case already at a rather coarse discretization and, on the other hand, the superior computing efficiency, e.g., compared to a traditional dynamic Smagorinsky modeling approach.
Unger, Miriam; Siesler, Heinz W
2009-12-01
In the present study, the orientation of a poly(3-hydroxybutyrate) (PHB)/poly(epsilon-caprolactone) (PCL) blend was monitored during uniaxial elongation by rheo-optical Fourier transform infrared (FT-IR) spectroscopy and analyzed by generalized two-dimensional correlation spectroscopy (2D-COS). The dichroism of the delta(CH(2)) absorption bands of PHB and PCL was employed to determine the polymer chain orientation in the PHB/PCL blend during the elongation up to 267% strain. From the PHB and PCL specific orientation functions it was derived that the PCL chains orient into the drawing direction while the PHB chains orient predominantly perpendicular to the applied strain. To extract more detailed information about the polymer orientation during uniaxial elongation, 2D-COS analysis was employed for the dichroic difference of the polarization spectra recorded during the drawing process. In the corresponding synchronous and asynchronous 2D correlation plots, absorption bands characteristic of the crystalline and amorphous regions of PHB and PCL were separated. Furthermore, the 2D-COS analysis revealed that during the mechanical treatment the PCL domains orient before the PHB domains.
American Society for Testing and Materials. Philadelphia
2004-01-01
1.1 This test method covers determining the concentrations of refrigerant-114, other carbon-containing and fluorine-containing compounds, hydrocarbons, and partially or completely substituted halohydrocarbons that may be impurities in uranium hexafluoride. The two options are outlined for this test method. They are designated as Part A and Part B. 1.1.1 To provide instructions for performing Fourier-Transform Infrared (FTIR) spectroscopic analysis for the possible presence of Refrigerant-114 impurity in a gaseous sample of uranium hexafluoride, collected in a "2S" container or equivalent at room temperature. The all gas procedure applies to the analysis of possible Refrigerant-114 impurity in uranium hexafluoride, and to the gas manifold system used for FTIR applications. The pressure and temperatures must be controlled to maintain a gaseous sample. The concentration units are in mole percent. This is Part A. 1.2 Part B involves a high pressure liquid sample of uranium hexafluoride. This method can be appli...
Pilatti, Fernanda Kokowicz; Ramlov, Fernanda; Schmidt, Eder Carlos; Costa, Christopher; Oliveira, Eva Regina de; Bauer, Claudia M; Rocha, Miguel; Bouzon, Zenilda Laurita; Maraschin, Marcelo
2017-01-30
Fossil fuels, e.g. gasoline and diesel oil, account for substantial share of the pollution that affects marine ecosystems. Environmental metabolomics is an emerging field that may help unravel the effect of these xenobiotics on seaweeds and provide methodologies for biomonitoring coastal ecosystems. In the present study, FTIR and multivariate analysis were used to discriminate metabolic profiles of Ulva lactuca after in vitro exposure to diesel oil and gasoline, in combinations of concentrations (0.001%, 0.01%, 0.1%, and 1.0% - v/v) and times of exposure (30min, 1h, 12h, and 24h). PCA and HCA performed on entire mid-infrared spectral window were able to discriminate diesel oil-exposed thalli from the gasoline-exposed ones. HCA performed on spectral window related to the protein absorbance (1700-1500cm(-1)) enabled the best discrimination between gasoline-exposed samples regarding the time of exposure, and between diesel oil-exposed samples according to the concentration. The results indicate that the combination of FTIR with multivariate analysis is a simple and efficient methodology for metabolic profiling with potential use for biomonitoring strategies.
Kwon, Yong-Kook; Jie, Eun Yee; Sartie, Alieu; Kim, Dong Jin; Liu, Jang Ryol; Min, Byung Whan; Kim, Suk Weon
2015-01-01
To determine whether or not FT-IR spectroscopy could be used for taxonomic and metabolic discrimination of African yam lines, tuber samples from African and Asian yam species were subjected to FT-IR. Most remarkable spectral differences between African and Asian yams were found in the 1750-1700 cm(-1) region, polysaccharide (1200-900 cm(-1)) and protein/amide I and II (1700-1500 cm(-1)) regions of FT-IR spectra. A hierarchical dendrogram based on partial least square-discriminant analysis (PLS-DA) of FT-IR data from 7 African yam species show phylogenetic relationship. In addition, the content of dioscin, a steroidal saponin found in yam tuber, was predicted using a PLS regression model with regression coefficient R(2)=0.7208 indicated that prediction model had average accuracy. Thus, considering these results we suggest that FT-IR combined with multivariate analysis could be applied as a novel tool for metabolic evaluation and high-throughput screening of African yam lines with higher content of dioscin.
A VLSI architecture for simplified arithmetic Fourier transform algorithm
Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.
1992-01-01
The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.
AN ASYMPTOTIC ORDER OF FOURIER TRANSFORM ON SL(2,R)
Institute of Scientific and Technical Information of China (English)
Wang Xinsong; Zheng Weixing
2003-01-01
In this paper, a better asymptotic order of Fourier transform on SL(2 ,R) is obtained by using classicalanalysis and Lie analysis comparing with that of [5]、 [6], and the Plancherel theorem on Cc2 (SL (2, R)) isalso obtained as an application.
On Fourier series of fuzzy-valued functions.
Kadak, Uğur; Başar, Feyzi
2014-01-01
Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We derive uniform convergence of a fuzzy-valued function sequences and series with level sets. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, Fourier series of periodic fuzzy-valued functions is defined and its complex form is given via sine and cosine fuzzy coefficients with an illustrative example. Finally, by using the Dirichlet kernel and its properties, we especially examine the convergence of Fourier series of fuzzy-valued functions at each point of discontinuity, where one-sided limits exist.
Quantum Fourier transform in computational basis
Zhou, S. S.; Loke, T.; Izaac, J. A.; Wang, J. B.
2017-03-01
The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ɛ for each Fourier coefficient. Its time complexity depends polynomially on log (N), where N is the problem size, and linearly on 1/δ and 1/ɛ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
The multiple-parameter fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
LANG Jun; TAO Ran; RAN QiWen; WANG Yue
2008-01-01
The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in frac-tional operator. A new source for the multiplicity of the weight-type fractional Fou-rier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters MN,∈ZM. Therefore a generalized frac-tional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.
The Fourier Transform on Quantum Euclidean Space
Directory of Open Access Journals (Sweden)
Kevin Coulembier
2011-05-01
Full Text Available We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.
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.
Lee, Chong-Yong; Fleming, Barry D; Zhang, Jie; Guo, Si-Xuan; Elton, Darrell M; Bond, Alan M
2009-10-12
A systematic approach to quantifying the electrode kinetics of surface-confined proteins and identifying the impact of surface heterogeneity is presented. The evaluation approach is based on analysis of individual harmonics derived from Fourier transformed large-amplitude ac voltammetry, and their peak current magnitude, I(p)(nomegat) versus frequency, f, relationships. Effectively, variability in the time-scale of each harmonic is expected, and advantage is taken of the fact that each individual harmonic displays a different level of sensitivity with respect to the kinetic evaluation. The data strategy protocols have been examined for the azurin Cu(II)/Cu(I) process when this metalloprotein is immobilized on gold electrodes modified alkanethiols having different chain lengths, using both pure and mixed thiol systems. I(p)(nomegat) versusf relationships also offer the advantage of the ability to detect and allow for the ohmic IR(u) drop effect and allow analyses that are independent of protein surface coverage. Estimation of an electron transfer rate is achievable from this form of analysis. However, experimentally observed waveshapes for each individual harmonic are consistently broader than that deduced theoretically on the basis of their rate constants because of kinetic and/or thermodynamic dispersion. In the mixed thiol systems, and with use of the ac method, kinetic discrimination is achieved for fast processes. This systematic study based on a model protein indicates that a more comprehensive level of evaluation of electrode kinetics can be derived from analysis of the ac harmonics available in large-amplitude ac voltammetry, by initially using I(p)(nomegat)-f data to evaluate the electrode kinetics followed by waveshape analysis to detect heterogeneity effects that give rise to kinetic or thermodynamic dispersion.
Energy Technology Data Exchange (ETDEWEB)
Lee, Chong-Yong; Fleming, Barry D.; Zhang Jie; Guo Sixuan [School of Chemistry, Monash University, Clayton, Victoria 3800 (Australia); Elton, Darrell M. [Department of Electronic Engineering, La Trobe University, Bundoora, Victoria 3086 (Australia); Bond, Alan M., E-mail: alan.bond@sci.monash.edu.au [School of Chemistry, Monash University, Clayton, Victoria 3800 (Australia)
2009-10-12
A systematic approach to quantifying the electrode kinetics of surface-confined proteins and identifying the impact of surface heterogeneity is presented. The evaluation approach is based on analysis of individual harmonics derived from Fourier transformed large-amplitude ac voltammetry, and their peak current magnitude, I{sub p}(n{omega}t) versus frequency, f, relationships. Effectively, variability in the time-scale of each harmonic is expected, and advantage is taken of the fact that each individual harmonic displays a different level of sensitivity with respect to the kinetic evaluation. The data strategy protocols have been examined for the azurin Cu(II)/Cu(I) process when this metalloprotein is immobilized on gold electrodes modified alkanethiols having different chain lengths, using both pure and mixed thiol systems. I{sub p}(n{omega}t) versusf relationships also offer the advantage of the ability to detect and allow for the ohmic IR{sub u} drop effect and allow analyses that are independent of protein surface coverage. Estimation of an electron transfer rate is achievable from this form of analysis. However, experimentally observed waveshapes for each individual harmonic are consistently broader than that deduced theoretically on the basis of their rate constants because of kinetic and/or thermodynamic dispersion. In the mixed thiol systems, and with use of the ac method, kinetic discrimination is achieved for fast processes. This systematic study based on a model protein indicates that a more comprehensive level of evaluation of electrode kinetics can be derived from analysis of the ac harmonics available in large-amplitude ac voltammetry, by initially using I{sub p}(n{omega}t)-f data to evaluate the electrode kinetics followed by waveshape analysis to detect heterogeneity effects that give rise to kinetic or thermodynamic dispersion.
Zhao, Gong-Bo; Saito, Shun; Wang, Dandan; Ross, Ashley J; Beutler, Florian; Grieb, Jan Niklas; Chuang, Chia-Hsun; Kitaura, Francisco-Shu; Rodriguez-Torres, Sergio; Percival, Will J; Brownstein, Joel R; Cuesta, Antonio J; Eisenstein, Daniel J; Gil-Marín, Héctor; Kneib, Jean-Paul; Nichol, Robert C; Olmstead, Matthew D; Prada, Francisco; Rossi, Graziano; Salazar-Albornoz, Salvador; Samushia, Lado; Sánchez, Ariel G; Thomas, Daniel; Tinker, Jeremy L; Tojeiro, Rita; Weinberg, David H; Zhu, Fangzhou
2016-01-01
We perform a tomographic baryon acoustic oscillations (BAO) analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum measured from the pre-reconstructed combined galaxy sample of the completed Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release (DR)12 covering the redshift range of $0.20
Zhang, Ray Ruichong; King, Robert; Olson, Larry; Xu, You-Lin
2005-08-01
This paper presents the implementation of a method for nonlinear, nonstationary data processing, namely the Hilbert-Huang transform (HHT) in traditional vibration-based approaches to characterizing structural damage and shows the frequency signature of local structural damage in nonstationary vibration recordings. In particular, following the review of traditional approaches to characterizing structural damage from nonstationary vibration recordings, this study first offers the justifications of the HHT as an alternative and complementary data process in addressing the nonstationarity of the vibration. With the use of recordings from controlled field vibration tests of substructures in the Trinity River Relief Bridge in Texas in its intact, minor- and severe-damage pile states, this study then shows that the HHT-based approach can single out some natural frequencies of the structure from a mixed frequency content in recordings that also contain the time-dependent excitation and noise frequencies. Subsequently, this study exposes that the frequency downshift for the damaged pile relative to the undamaged one is an indicative index for the damage extent. The above results are also validated by an ANSYS model-based analysis. Finally, a comprehensive HHT-based characterization of structural damage is discussed, and the potential use for cost-effective, efficient structural damage diagnosis procedures and health-monitoring systems is provided.
Energy Technology Data Exchange (ETDEWEB)
Tang, Yinjie; Pingitore, Francesco; Mukhopadhyay, Aindrila; Phan,Richard; Hazen, Terry C.; Keasling, Jay D.
2006-07-11
It has been proposed that during growth under anaerobic oroxygen-limited conditions Shewanella oneidensis MR-1 uses theserine-isocitrate lyase pathway common to many methylotrophic anaerobes,in which formaldehyde produced from pyruvate is condensed with glycine toform serine. The serine is then transformed through hydroxypyruvate andglycerate to enter central metabolism at phosphoglycerate. To examine itsuse of the serine-isocitrate lyase pathway under anaerobic conditions, wegrew S. oneidensis MR-1 on [1-13C]lactate as the sole carbon source witheither trimethylamine N-oxide (TMAO) or fumarate as an electron acceptor.Analysis of cellular metabolites indicates that a large percentage(>75 percent) of lactate was partially oxidized to either acetate orpyruvate. The 13C isotope distributions in amino acids and other keymetabolites indicate that, under anaerobic conditions, a complete serinepathway is not present, and lactate is oxidized via a highly reversibleserine degradation pathway. The labeling data also suggest significantactivity in the anaplerotic (malic enzyme and phosphoenolpyruvatecarboxylase) and glyoxylate shunt (isocitrate lyase and malate synthase)reactions. Although the tricarboxylic acid (TCA) cycle is often observedto be incomplete in many other anaerobes (absence of 2-oxoglutaratedehydrogenase activity), isotopic labeling supports the existence of acomplete TCA cycle in S. oneidensis MR-1 under TMAO reductioncondition.
Zhao, Gong-Bo; Wang, Yuting; Saito, Shun; Wang, Dandan; Ross, Ashley J.; Beutler, Florian; Grieb, Jan Niklas; Chuang, Chia-Hsun; Kitaura, Francisco-Shu; Rodriguez-Torres, Sergio; Percival, Will J.; Brownstein, Joel R.; Cuesta, Antonio J.; Eisenstein, Daniel J.; Gil-Marín, Héctor; Kneib, Jean-Paul; Nichol, Robert C.; Olmstead, Matthew D.; Prada, Francisco; Rossi, Graziano; Salazar-Albornoz, Salvador; Samushia, Lado; Sánchez, Ariel G.; Thomas, Daniel; Tinker, Jeremy L.; Tojeiro, Rita; Weinberg, David H.; Zhu, Fangzhou
2017-04-01
We perform a tomographic baryon acoustic oscillations (BAO) analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum measured from the pre-reconstructed combined galaxy sample of the completed Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (BOSS) Data Release12 covering the redshift range of 0.20 < z < 0.75. By allowing for overlap between neighbouring redshift slices, we successfully obtained the isotropic and anisotropic BAO distance measurements within nine redshift slices to a precision of 1.5-3.4 per cent for DV/rd, 1.8-4.2 per cent for DA/rd and 3.7-7.5 per cent for H rd, depending on effective redshifts. We provide our BAO measurement of DA/rd and H rd with the full covariance matrix, which can be used for cosmological implications. Our measurements are consistent with those presented in Alam et al., in which the BAO distances are measured at three effective redshifts. We constrain dark energy parameters using our measurements and find an improvement of the Figure-of-Merit of dark energy in general due to the temporal BAO information resolved. This paper is a part of a set that analyses the final galaxy clustering data set from BOSS.
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 nonFourier 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.``
Ariosa, D.; Berger, H.; Schmauder, T.; Pavuna, D.; Margaritondo, G.; Christensen, S.; Kelley, R. J.; Onellion, M.
2001-04-01
We report on a distortion of Bi 2Sr 2Ca nCu n+1O 6+2n+x ( n=0,1) single crystals, perpendicular to the CuO 2 planes (the c-axis), for non-stoichiometric samples containing an excess of Bi. The distortion involves two parts: (a) symmetric displacements in the SrO and CuO 2 planes along the c-axis, and (b) an antisymmetric longitudinal compressive wave. The latter is revealed by observing odd harmonics in the X-ray diffraction (XRD) data. Such odd harmonics are typically extinguished for the I4/mmm space group of the exact stoichiometric phase. The antisymmetric compressive wave is reported for both BSCCO-2201 and BSCCO-2212 Bi excess samples, as well as for La-doped BSCCO-2201 samples. We have performed XRD model calculations for all samples studied, combined with Fourier analysis of the periodic c-axis modulation. The antisymmetric compressive wave was proven by reconstructing the atomic position profile from the intensity of odd XRD peaks caused by this commensurate modulation. Our results indicate preferential ordered substitution of Bi ions on nominally Sr ion positions. We also discuss implications for oxygen mobility, reversible sample doping, and electronic properties.
Plazas-Nossa, Leonardo; Torres, Andrés
2014-01-01
The objective of this work is to introduce a forecasting method for UV-Vis spectrometry time series that combines principal component analysis (PCA) and discrete Fourier transform (DFT), and to compare the results obtained with those obtained by using DFT. Three time series for three different study sites were used: (i) Salitre wastewater treatment plant (WWTP) in Bogotá; (ii) Gibraltar pumping station in Bogotá; and (iii) San Fernando WWTP in Itagüí (in the south part of Medellín). Each of these time series had an equal number of samples (1051). In general terms, the results obtained are hardly generalizable, as they seem to be highly dependent on specific water system dynamics; however, some trends can be outlined: (i) for UV range, DFT and PCA/DFT forecasting accuracy were almost the same; (ii) for visible range, the PCA/DFT forecasting procedure proposed gives systematically lower forecasting errors and variability than those obtained with the DFT procedure; and (iii) for short forecasting times the PCA/DFT procedure proposed is more suitable than the DFT procedure, according to processing times obtained.
An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.
Eastman, M. P.; And Others
1986-01-01
Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.
Directory of Open Access Journals (Sweden)
Eduardo O. Cerqueira
2000-10-01
Full Text Available Instrumental data always present some noise. The analytical data information and instrumental noise generally has different frequencies. Thus is possible to remove the noise using a digital filter based on Fourier transform and inverse Fourier transform. This procedure enhance the signal/noise ratio and consecutively increase the detection limits on instrumental analysis. The basic principle of Fourier transform filter with modifications implemented to improve its performance is presented. A numerical example, as well as a real voltammetric example are showed to demonstrate the Fourier transform filter implementation. The programs to perform the Fourier transform filter, in Matlab and Visual Basic languages, are included as appendices
Two modified discrete chirp Fourier transform schemes
Institute of Scientific and Technical Information of China (English)
樊平毅; 夏香根
2001-01-01
This paper presents two modified discrete chirp Fourier transform (MDCFT) schemes.Some matched filter properties such as the optimal selection of the transform length, and its relationship to analog chirp-Fourier transform are studied. Compared to the DCFT proposed previously, theoretical and simulation results have shown that the two MDCFTs can further improve the chirp rate resolution of the detected signals.
1-Convergence of Complex Double Fourier Series
Indian Academy of Sciences (India)
Kulwinder Kaur; S S Bhatia; Babu Ram
2003-11-01
It is proved that the complex double Fourier series of an integrable function (, ) with coefficients {} satisfying certain conditions, will converge in 1-norm. The conditions used here are the combinations of Tauberian condition of Hardy–Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.
The multipliers of multiple trigonometric Fourier series
Ydyrys, Aizhan; Sarybekova, Lyazzat; Tleukhanova, Nazerke
2016-11-01
We study the multipliers of multiple Fourier series for a regular system on anisotropic Lorentz spaces. In particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Zn in order to make it a multiplier of multiple trigonometric Fourier series from Lp[0; 1]n to Lq[0; 1]n , p > q. These conditions include conditions Lizorkin theorem on multipliers.
Fourier transform approach in modulation technique of experimental measurements.
Khazimullin, M V; Lebedev, Yu A
2010-04-01
An application of Fourier transform approach in modulation technique of experimental studies is considered. This method has obvious advantages compared with traditional lock-in amplifiers technique--simple experimental setup, a quickly available information on all the required harmonics, high speed of data processing using fast Fourier transform algorithm. A computationally simple, fast and accurate Fourier coefficients interpolation (FCI) method has been implemented to obtain a useful information from harmonics of a multimode signal. Our analysis shows that in this case FCI method has a systematical error (bias) of a signal parameters estimation, which became essential for the short data sets. Hence, a new differential Fourier coefficients interpolation (DFCI) method has been suggested, which is less sensitive to a presence of several modes in a signal. The analysis has been confirmed by simulations and measurements of a quartz wedge birefringence by means of the photoelastic modulator. The obtained bias, noise level, and measuring speed are comparable and even better than in lock-in amplifier technique. Moreover, presented DFCI method is expected to be promised candidate for using in actively developing imaging systems based on the modulation technique requiring fast digital signal processing of large data sets.
Institute of Scientific and Technical Information of China (English)
温芝元; 曹乐平
2013-01-01
Plant pests and diseases image recognition is one of the key technologies of digital agricultural information collection and processing. Usually, based on pest infestation-like plant, it is carried out according to the size, shape, color, texture, etc., or a combination of several parameters. Machine recognition of diseases and insect pests needs to use digitalized characteristics without overlapping. Multi-fractal analysis of Fourier transform spectra was adopted to investigate the possibility of extraction of damage pattern characteristics for Citrus reticulata Blanco var. Ponkan. First, images of the boundary of a damaged pattern are extracted with an improved watershed algorithm and region merging. Secondly, a Discrete Fourier Transform (DFT) was applied to the damaged fruit image. With reference to the boundary of a damaged pattern, a fruit image magnitude spectrum was extracted. Thirdly, a fruit image magnitude spectrum was multi-fractiously analyzed and the multi-fractal spectrum of DFT magnitude spectrum was quadratic fitted. Height, width, and centroid coordinate of a fitting parabolic section were chosen feature values to identify the diseases and insect damage of fruits, with these three feature values as inputs of a BP neural network identifying diseases and insect damage of Ponkan, and the accuracy was up to 92.67%. Finally, the amplitude spectrum of the Fourier transform was adopted for multifractal analysis and multi-fractal spectrum of a quadratic fit;fit parabola segment height, width, and centroid coordinates were regarded as pests’ Eigen values, and then used as input variables to establish a BP citrus pest identification neural network model for pest identification. Among 5 classes of pests, in 30 groups of test samples, such as Pezothrips Kellyanus, Oxycetonia Jucunda, Oraesia Emarginata, Polyphagotarsonemus Latus, Colletotrichum Gloeoporioides Penz, the highest recognition rate was for Oraesia Emarginata, that is 96.67%, Polyphagotarsonemus
Institute of Scientific and Technical Information of China (English)
王本庆; 李兴国
2009-01-01
现有很多LFM信号调频斜率的分析算法,但这些算法存在诸多不足,如计算复杂、搜索时间长,对多LFM信号有交叉项等.该文提出了基于双正交Fourier变换的新LFM信号调频斜率分析算法,其特点是信号在双正交基下展开,通过变换得到信号调频斜率密度谱.该算法不需要搜索,且特别适合对不同调频斜率组成的多LFM信号进行调频斜率分析.文中推导了连续双正交Fourier变换公式和离散变换公式,并讨论了算法的一些主要性质.%There are many analysis algorithms for frequency rate of LFM signal, but those algorithms have some drawbacks, such as highly computational complexity, long time for searching, and cross-term in multi-LFM signal. In this paper, a new analysis algorithm of frequency rate of LFM signal is presented based on Biorthogonal Fourier Transform (BFT), the signal is expanded with biorthogonal base function that could be got frequency rate density spectrum of the signal. This algorithm need no searching, and has better performance for detection different frequency rate of multi-LFM signal. This paper derives continual BFT formula and discrete transform formula and discusses its some main characters.
Indian Academy of Sciences (India)
Renu Singh; K N Uttam; M D Saksena; M N Deo
2009-11-01
The emission spectrum of InBr molecule has been recorded in the region 350–400 nm on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.06 cm-1 using microwave excitation technique. About 61 violet degraded and single headed bands have been recorded and are classified into two band systems, viz. $A^{3} _{0} –X^{1} \\sum^{+}$ and $B^{3} _{1} –X^{1} \\sum^{+}$. A few new bands have been observed and are fitted in the vibrational schemes of the two systems. Revised vibrational constants have been determined. The vibrational assignments have been confirmed by observing isotope effect due to InBr81 in the 30 bands of the $A^{3} _{0} –X^{1} \\sum^{+}$ system and 19 bands of the $B^{3} _{1} –X^{1} \\sum^{+}$ system. The analysis is further supported by calculating the Franck–Condon factor for InBr79 and InBr81 molecules. The following vibrational constants (in cm-1) have been determined from the analysis: $$ \\begin{array}{llll} \\text{A}^{3}_{0}-\\text{X}^{1}^{+} & \\text{system} & v_{00}=26599.1 & '_{\\text{e}} = 226.42, \\ '_{\\text{e}}x'_{\\text{e}}=1.24\\text{~cm}^{-1},\\\\ & & & ''_{\\text{e}} = 221.19, \\ ''_{\\text{e}}x''_{\\text{e}}=0.528\\text{~cm}^{-1}.\\\\ \\text{B}^{3}_{1}-\\text{X}^{1}^{+} & \\text{system} & v_{00}=27380.52 & '_{\\text{e}}=223.086, \\ '_{\\text{e}}x'_{\\text{e}}=1.446\\text{~cm}^{-1},\\\\ & & & ''_{\\text{e}}=221.19, \\ ''_{\\text{e}}x''_{\\text{e}}=0.528\\text{~cm}^{-1}. \\end{array} $$
From "Dirac combs" to Fourier-positivity
Giraud, Bertrand G
2015-01-01
Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms. A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed. As a practical application, we find simple and rapid analytic algorithms for checking Fourier-positivity in 1- and (radial) 2-dimensions among a large variety of real positive functions. This may provide a step towards a classification of positive positive-definite functions.
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.
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Stepwise Iterative Fourier Transform: The SIFT
Benignus, V. A.; Benignus, G.
1975-01-01
A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.
Directory of Open Access Journals (Sweden)
Yasmeen Khan
2016-01-01
Full Text Available Background: Eucalyptus globulus L. (family, Myrtaceae is one of the world′s most widely planted genera. E. globulus L., commonly referred to as Tasmanian blue gum, is a fast growing, evergreen tree, native to Tasmania and South-East Australia. Apart from its extensive use in pulp industry, it is also produces Oleum Eucalypti (eucalyptus oil that is extracted on commercial scale in many countries such as China, India, South Africa, Portugal, Brazil, and Tasmania, as a raw material in perfumery, cosmetics, food beverage, aromatherapy, and phytotherapy. Materials and Methods: Traditional hydrodistillation (HD, solvent extraction (SE, ultrasonication (US, and supercritical fluid extraction (SFE were conducted for the extraction of essential oil from the leaves of E. globulus. Each oil was evaluated in terms of high-performance liquid chromatography (HPTLC and Fourier transform infrared spectroscopy (FTIR fingerprinting with qualitative and semi-quantitative composition of the isolated essential oil by gas chromatography-mass spectroscopy (GCMS, the extract yield of essential oil was 2.60%, 2.2%, 2.0%, and 3.6% v/w, respectively, for HD, SE, US, and SFE. Results: A total of 53 compounds were identified by GCMS. Comparative analysis indicated that SFE was favorable for extraction of monoterpene hydrocarbon, sesquiterpene hydrocarbon, and oxygenated sesquiterpene hydrocarbon. HD, SE, and US had certain advantages in the extraction of aliphatic saturated hydrocarbons organic acid and esters. Overlay, FTIR spectra of oil samples obtained by four extraction methods were superimposed with each other showing similar components. The maximum separation of compound seen at 254 nm and lesser at 366 nm by HPTLC fingerprinting which again showed superimposed chromatograms. Conclusion: It is concluded that different extraction method may lead to different yields of essential oils where the choice of appropriate method is very important to obtained more desired
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.
Lee, Chong-Yong; Bullock, John P; Kennedy, Gareth F; Bond, Alan M
2010-09-23
Large-amplitude ac voltammograms contain a wealth of kinetic information concerning electrode processes and can provide unique mechanistic insights compared to other techniques. This paper describes the effects homogeneous chemical processes have on ac voltammetry in general and provides experimental examples using two well-known chemical systems: one simple and one complex. Oxidation of [Cp*Fe(CO)(2)](2) (Cp* = η(5)-pentamethylcyclopentadienyl) in noncoordinating media is a reversible one-electron process; in the presence of nucleophiles, however, the resulting ligand-induced disproportionation changes the process to a multiple step regeneration. The chemical kinetic parameters of the regeneration mechanism were discerned via analysis of the third and higher harmonics of Fourier-transformed ac voltammetry data. Comparison of experimental data to digital simulations provides clear evidence that the reaction proceeds via a rapid pre-equilibrium between the electrogenerated monocation and the coordinating ligand; simultaneous fitting of the first nine harmonics indicates that k(f) = 7500 M(-1) s(-1) and k(r) = 100 s(-1), and that the unimolecular decomposition of the corresponding intermediate occurs with a rate constant of 2.2 s(-1). The rapid cis(+) → trans(+) isomerization of the electrogenerated cis-[W(CO)(2)(dpe)(2)](+), where dpe = 1,2-diphenylphosphinoethane, was examined to illustrate the effects of a simpler EC mechanism on the higher harmonics; a rate constant of 280 s(-1) was determined. These results not only shed new light on the chemistry of these systems, but provide a clear demonstration that the higher harmonics of ac voltammetry provide mechanistic insights into coupled homogeneous processes far more detailed than those that are readily accessible with dc techniques.
Putri, Vinda Dwi Dini; Nasution, Aulia M. T.
2016-11-01
Frying oil is a cooking medium that is commonly used in Indonesia. Frying process can lead changes in the properties of frying oil. Heating oil with high temperature and many repetition will cause degradation in oil and may cause health problems, such as cholesterol, induces heart disease, and cancer. Degradation of the frying oil can be determined based on changes in the cluster function of fatty acids due to the heating influence. Therefore, it is necessary to test the frying oil under treatments with variety of time heating using a spectrometer Fourier Transform Infrared (FTIR). Spectra from FTIR was processed using derivative spectroscopy method to clearly see the difference in the measured spectra. Range spectra of interest is at wavelength of 13,500 to 14,200 nm i.e. indicating the double bond of carbon in molecule HC = CH. The analysis was performed by calculating the area of the spectral curve from the respected 2nd order derivative. Result show that the absorbance of packaging frying oil is higher than the bulk frying oil. In addition, heating of frying oil can decrease the area of respected 2nd order derivative. Packaging frying oil heating on 30 minutes which has the area of spectral curve of 0.904217 decrease become 0.881394 after 3 times heating. While the bulk frying oil heating 30 minutes, in the first heating which has area of spectral curve of 0.916089 decrease become 0.865379 after 3 times heating. The decline in the area of the curve occurs due to breakdown of the double bond of carbon in the molecule HC = CH that caused by heating at high temperatures and repeated heating.
Fourier time spectral method for subsonic and transonic flows
Institute of Scientific and Technical Information of China (English)
Lei Zhan; Feng Liu; Dimitri Papamoschou
2016-01-01
The time accuracy of the exponentially accu-rate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward differ-ence formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical com-putations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth sub-sonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the predic-tion of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higher-order harmonic contents to the local pressure fluctuations, a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method. The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.
利用傅里叶变换红外光谱法分析燕麦片的品质%Analysis of Oatmeal Quality by Fourier ransform Infrared Spectroscopy
Institute of Scientific and Technical Information of China (English)
周旭章; 彭昕; 张慧恩; 蔡艳
2011-01-01
In order to establish a fast nondestructive method for analysis of oatmeal quality, qualities of eight brands of oatmeal from Ningbo supermarkets were analyzed by Fourier transform infrared spectroscopy ( FTIR). Results showed that the comparison of infrared spectrum and characteristic absorption peaks of different brands of oatmeal could determine the contents and composition of nutritional ingredients in oatmeals; second derivative spectrum which could identify overlapped peaks in conventional IR spectrum and increase resolution had been used to achieve more accurate and finer analysis. FTIR combined with two - dimensional correlation infrared spectrum was applied to study the thermal stability of oatmeal through mini - heating process. In conclusion, FTIR could provide a fast nondestructive method for analysis of oatmeal quality.%为了建立一种快速、无损的鉴定市场所销售的燕麦片的品质鉴定分析方法,对宁波市超市所销售的品牌1～品牌8的燕麦片商品进行了抽样,采取傅里叶变换红外光谱法(FTIR)进行定性分析.结果表明,通过红外光谱图和特征峰之间的比较,可以分析出燕麦中含有的营养成分及其含量高低;结合二阶导数谱能把红外图谱中重叠的峰区分开来,增大谱图的分辨率,使分析更加精细准确;利用热微扰法测定燕麦红外光谱及其二维相关红外光谱可以判断燕麦的热稳定性.因此,傅里叶变换红外光谱法是一种快速、无损的鉴定燕麦片品质的分析方法.
Fourier Series for Kample De Feriet Function
Directory of Open Access Journals (Sweden)
A. D. Wadhwa
1971-07-01
Full Text Available Some integrals involving Kampe de Feriet function have been evaluated. These integrals have further been employed to obtain some Fourier series for Kampe de Feriet functions. Some particular cases have also been discussed.
Electronically-Scanned Fourier-Transform Spectrometer
Breckinridge, J. B.; Ocallaghan, F. G.
1984-01-01
Instrument efficient, lightweight, and stable. Fourier-transform spectrometer configuration uses electronic, instead of mechanical, scanning. Configuration insensitive to vibration-induced sampling errors introduced into mechanically scanned systems.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new me- thod of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
郑建斌; 张红权; 高鸿
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new method of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.
A new twist to fourier transforms
Meikle, Hamish D
2004-01-01
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs
The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.
King, Roy W.; Williams, Kathryn R.
1989-01-01
Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)
Simplification of multiple Fourier series - An example of algorithmic approach
Ng, E. W.
1981-01-01
This paper describes one example of multiple Fourier series which originate from a problem of spectral analysis of time series data. The example is exercised here with an algorithmic approach which can be generalized for other series manipulation on a computer. The generalized approach is presently pursued towards applications to a variety of multiple series and towards a general purpose algorithm for computer algebra implementation.
Non-Euclidean Fourier inversion on super-hyperbolic space
Alldridge, Alexander; Palzer, Wolfgang
2016-01-01
For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason--Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete parts in the spectrum. The proof is based on a detailed study of the spherical superfunctions, using recursion relations and localization techniques to normalize them precisely, careful estimates of their derivatives, and a rigorous analysis of the boundary ...
Kok, S.J.; Wold, C.A.; Hankemeier, Th.; Schoenmakers, P.J.
2003-01-01
Two commercial liquid chromatography-Fourier-transform infrared spectroscopy interfaces (LC-FTIR), viz. a flow cell and a solvent-elimination interface have been assessed for use in size-exclusion chromatography (SEC) with respect to their chromatographic integrity (i.e. peak asymmetry, chromatograp
Institute of Scientific and Technical Information of China (English)
汤南; 陈鸿鹏; 郑军华; 赵仲留; 林坚涛
2012-01-01
OBJECTIVE To establish the X-ray diffraction Fourier fingerprint pattern of Nervilia fordii (Hance) Schltr. and analyze the similarity of different origination. METHODS Powder X-ray diffraction was used. The X-ray diffraction Fourier fingerprint pattern was established by analyzing eight samples of Nervilia fordii (Hance) Schltr. RESULTS The X-ray diffraction Fourier fingerprint pattern, the characteristic diffraction peaks and the similarity of Nervilia fordii (Hance) Schltr were obtained and calculated. CONCLUSION The method is specific, it can be used for identification of Nervilia fordii (Hance) Schltr.%目的:建立青天葵X-射线衍射Fourier(傅立叶)指纹图谱,并对不同产地该药材进行相似度分析.方法:应用粉末X-射线衍射法,通过对8批青天葵药材进行分析,建立青天葵X-射线衍射Fourier指纹图谱,并进行相似度评价 结果:获得了青天葵X-射线衍射Fourier指纹图谱、特征标记峰值和相似度.结论:X-射线衍射Fourier指纹图谱专属性强,可用于中药青天葵的鉴定.
A DISTRIBUTION SPACE FOR FOURIER TRANSFORM
Institute of Scientific and Technical Information of China (English)
Zhou Chaoying; Yang Lihua; Huang Daren
2007-01-01
A space DF is constructed and some characterizations of space DF are given. Itis shown that the classical Fourier transform is extended to the distribution space D'F, whichcan be embedded into the Schwartz distribution space D' continuously. It is also shown thatD'F is the biggest embedded subspace of D' on which the extended Fourier transform, F, is ahomeomorphism of D'F onto itself.
Shift sampling theory of Fourier transform computation
Institute of Scientific and Technical Information of China (English)
柴玉璞
1997-01-01
The DFT transform us extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFTξη A-E equation) is established, and the minimization property of discrete effect and the oscillation property of truncation effect are demonstrated. All these construct the shift sampling theory——a new theory about Fourier transform computation.
Fractional Fourier transform of Lorentz beams
Institute of Scientific and Technical Information of China (English)
Zhou Guo-Quan
2009-01-01
This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.
Bead-Fourier path integral molecular dynamics
Ivanov, Sergei D.; Lyubartsev, Alexander P.; Laaksonen, Aatto
2003-06-01
Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented. Within this scheme, both the bead coordinates and Fourier coefficients, defining the path representing the quantum particle, are treated as generalized coordinates with corresponding generalized momenta and masses. Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations. The method is tested for quantum harmonic oscillator and hydrogen atom (Coulombic potential). The simulation results are compared with the exact analytical solutions available for both these systems. Convergence of the results with respect to the number of beads and Fourier harmonics is analyzed. It was shown that addition of a few Fourier harmonics already improves the simulation results substantially, even for a relatively small number of beads. The proposed Bead-Fourier path integral molecular dynamics is a reliable and efficient alternative to simulations of quantum systems.
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
Energy Technology Data Exchange (ETDEWEB)
Layton, E.G. (Joint Inst. for Lab. Astrophysics, Boulder, CO (United States)); Stade, E. (Colorado Univ., Boulder, CO (United States). Dept. of Mathematics)
1993-08-28
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author).
Locke, Jonathan; White, Paul R
2011-10-01
The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species.
Modeling the reconstructed BAO in Fourier space
Seo, Hee-Jong; Beutler, Florian; Ross, Ashley J.; Saito, Shun
2016-08-01
The density field reconstruction technique, which partially reverses the non-linear degradation of the Baryon acoustic oscillation (BAO) feature in the galaxy redshift surveys, has been successful in substantially improving the cosmology constraints from recent surveys such as Baryon Oscillation Spectroscopic Survey (BOSS). We estimate the efficiency of the method as a function of various reconstruction details. To directly quantify the BAO information in non-linear density fields before and after reconstruction, we calculate the cross-correlations (i.e. propagators) of the pre(post)-reconstructed density field with the initial linear field using a mock sample that mimics the clustering of the BOSS galaxies. The results directly provide the BAO damping as a function of wavenumber that can be implemented into the Fisher matrix analysis. We focus on investigating the dependence of the propagator on a choice of smoothing filters and on two major different conventions of the redshift-space density field reconstruction that have been used in literature. By estimating the BAO signal to noise for each case, we predict constraints on the angular diameter distance and Hubble parameter using the Fisher matrix analysis. We thus determine an optimal Gaussian smoothing filter scale for the signal-to-noise level of the BOSS CMASS. We also present appropriate BAO fitting models for different reconstruction methods based on the first- and second-order Lagrangian perturbation theory in Fourier space. Using the mock data, we show that the modified BAO fitting model can substantially improve the accuracy of the BAO position in the best fits as well as the goodness of the fits.
Institute of Scientific and Technical Information of China (English)
孔新新; 黄旻; 张文喜
2012-01-01
傅里叶望远镜成像技术,综合了激光主动成像技术、光学合成孔径技术和相位闭合技术是一种新的高分辨率成像探测技术.激光频移的效果是影响傅里叶望远镜成像质量的重要因素,特别是使用大功率、宽光束和宽调制带宽激光的系统.构建了不同的误差模型,推导了频移误差在系统中的传递函数,利用仿真实验分析其对系统成像的影响,得到了对应的误差影响分析.结果表明,频移精度和稳定度严重影响到系统的成像效果,部分情况下含有误差的反演图像与理论反演图像的施特雷尔值已降到0.2,因此合理的设计和选择声光频移器是改善系统成像的一个关键因素.%Fourier telescopy (FT) is a sort of high-resolution imaging technology, which integrates laser initiative imaging technology, optical synthetic aperture technology and phase close technology. The effect of frequency shifting of laser is one of the most important factors to influence imaging quality of the FT system, especially in the situation of high power, broad beam and large modulation bandwidth. Various frequency-shifting error models are proposed, the transfer function of error in system is built, the effect of which on imaging of the system is researched by simulation, error analysis results of the various models are obtained. According to the results, the image quality of the system is directly influenced by the frequency shift accuracy and stability, the value of Strehl between the inverted image with error and the theoretically inverted image is below 0. 2 in some of the models. As indicated, the reasonable design of acousto-optical frequency shifter and the driver circuit is an important way to improve the imaging of the system.
Bouvier, A. J.; Veyret, V.; Russier, I.; Inard, D.; Churassy, S.; Bacis, R.; Brion, J.; Malicet, J.; Judge, R. H.
1999-12-01
A high resolution Fourier transform spectrometry comparative analysis of the rotational structure of the 0 00 absorption band of the 3A 2← X˜1A 1 Wulf transition for the isotopomers 16O 3 and 18O 3 of the ozone molecule is presented. With a near pure case (b) coupling model for the upper triplet state, we identified, in these two rovibrational bands, numerous lines of sub-bands associated with the three F1( N= J-1), F2( N= J), F3( N= J+1) spin components. Many superpositions around the origin, plus perturbations and predissociation phenomena limit our unperturbed data set for the 3A 2 state to less than 100 unperturbed rotational lines in the range 9100-9550 cm -1 for each band. Using for each of them the well defined ground state parameters, we obtained a standard deviation of about 0.050 cm -1 in the fits to the lines. The rotational constants A, B, C, the three rotational distortion terms Δ K, Δ K, Δ J, the spin-rotation constants a0, a, and b and the spin-spin constant α are determined for the (0 0 0) vibrational level of the 3A 2 state and of the two isotopomers. The parameter β arbitrarily fixed for 16O 3 was successfully calculated for 18O 3 and this last result justifies the β value adopted for 16O 3. The geometrical parameters of the 3A 2 state for the two isotopomers are close, r=1.343 Å, θ=98.8° for 18O 3 and r=1.345 Å, and θ=98.9° for 16O 3. So are the Δ and κ values. The origin of the 18O 3 0 00 band is blue shifted by 20.6(4) cm -1 with respect to the 16O 3 0 00 band. For the congested parts of the spectra comparisons of both isotopic species has to be done in a special way through sub-band contours. We justify the existence of perturbations in the first vibrational levels of the 3A 2 state by several crossings with high vibrational levels of the ground state.
Institute of Scientific and Technical Information of China (English)
杨铭; 朱小玲; 梁国正
2016-01-01
,thermogravimetric (TG)analysis coupled with Fourier transform infrared spectroscopy(FTIR),are able to an-alyze materials not only qualitatively but also quantitatively.This method has obvious advantages in researching the thermal de-composition of many materials.However,the thermal decomposition processing of Kevlar fibers is rarely reported in the litera-ture,therefore,we firstly studied the pyrolysis behavior of Kevlar fibers with thermogravimetric analysis coupled with Fourier transform infrared spectroscopy at the temperature of 30~800 ℃.We not only obtained the processing of the Kevlar fibers'ther-mal decomposition with great details but also the products of every stage.Experimental results exhibited that the decomposition of Kevlar fibers has experienced three stages:100~240,240~420 and 420~800 ℃.The weight loss of Kevlar fibers was quite slow before 500 ℃.The third stage was the main stage of the decomposition,and the amount of residue finally reached to a mass percent of 56.21%.FTIR analysis illustrated that free water released from Kevlar fibers at the first stage,followed by the dehy-dration and depolymerization which made polymer chains short.Finally the fiber fragments further reacted and produced the ga-ses of small molecular mass,and the main products were water,ammonia,carbon monoxide and carbon dioxide.Generation rate of water was increased;the emission of ammonia was at the same rate;carbon monoxide was only produced at the temperature of 515~630 ℃,then turned into carbon dioxide.The release of carbon dioxide was on rise because of the conversion process of car-bon monoxide,and then dropped to a certain value.
Multiparty Quantum Secret Sharing Using Quantum Fourier Transform
Institute of Scientific and Technical Information of China (English)
HUANG Da-Zu; CHEN Zhi-Gang; GUO Ying
2009-01-01
A (n, n )-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform.In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert.Furthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant.Security analysis shows that our scheme is secure.Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.
Structural disorder correlation examined using the Fourier-Bessel technique
Gauthier, Robert C.
2015-11-01
The presence of structural disorder in a photonic crystal is examined through the rotational symmetry extracted from a Fourier-Bessel approach to solving Maxwell's wave equation in cylindrical space. A dielectric correlation function is proposed that relates the original structure to the disordered structure and when normalized it can be used to quantify the level of any disorder mechanism present. It is shown that the presence of disorder causes a mixing of localized and extended states and that the mixing can be directly attributed to "off diagonal" elements of the eigen-matrix and rotational symmetry breaking within the structure. The properties of disorder in an ordered structure are used to identify locations of local order in disordered structures. The Fourier-Bessel analysis of a disordered structure confirms the presence of localized light states at these sites.
Physics of the Blues: Music, Fourier and Wave - Particle Duality
Energy Technology Data Exchange (ETDEWEB)
Gibson, J. Murray (ANL)
2003-10-15
Art and science are intimately connected. There is probably no art that reveals this more than music. Music can be used as a tool to teach physics and engineering to non-scientists, illustrating such diverse concepts as Fourier analysis and quantum mechanics. This colloquium is aimed in reverse, to explain some interesting aspects of music to physicists. Topics include: What determines the frequency of notes on a musical scale? What is harmony and why would Fourier care? Where did the blues come from? (We' re talking the 'physics of the blues', and not 'the blues of physics' - that's another colloquium). Is there a musical particle? The presentation will be accompanied by live keyboard demonstrations. The presenter will attempt to draw tenuous connections between the subject of his talk and his day job as Director of the Advanced Photon Source at Argonne National Laboratory.
Energy Technology Data Exchange (ETDEWEB)
Weissgerber, Wilfried
2013-05-01
The book under consideration covers the basics and calculation methods of the Laplace-transformation for the regulation technology, Fourier transformation for the signal theory, the quadrupole theory for the communications engineering and balancing processes for linear networks. The book is dedicated to the students of engineering and natural sciences, electrical engineering, technical informatics and physics at higher institutes of applied sciences, technical colleges, universities and universities of cooperative education.
Institute of Scientific and Technical Information of China (English)
楚杰; 马莉; 张军华
2016-01-01
Thermochemical pretreatment of lignocellulosic biomass is a critical step in obtaining high yields of cellulose and hemi-cellulose-derived sugars to realize effective utilization of cellulose in renewable biofuels.The pretreatment process can quickly re-move hard dissolving lignin and the physical separation of hemicelluloses in the cell wall while changing the chemical composition in plant cell wall,so as to increase the production of lignocellulose.Research with medium of sulfuric acid (H2 SO4 ),dilute alka-li (NaOH)and glycerin,and at different pretreatment temperature (117 and 135 ℃ in sulfuric acid (H2 SO4 )and dilute alkali (NaOH),117 ℃ in glycerin)analyzed and compared the main changes of chemical composition before and after the bamboo pro-cessing,and further confirmed that the mechanism of the chemical conversion after chemical pretreatment of bamboo through the Fourier infrared spectrum.The results showed that the output cellulose increased significantly after the thermochemical pretreat-ment.The change rules for yield of cellulose and the removal rate of lignin under the different pretreatment condition had been indicated dilute alkali (NaOH)treatment effect is better than that of dilute acid (H2 SO4 )and glycerin.In addition,the effect is more remarkable under the condition of 1 3 5 ℃ than 1 1 7 ℃ in the same medium.The changes of degradation degree of hemicellu-lose with different processing conditions were the same.The infrared spectrum analysis provided that C—O—C asymmetric stretching vibration peak appeared in cellulose decomposition after heat treatment,and it is the obvious steep fall in hemicellulo-ses infrared absorption characteristic peaks,benzene ring characteristic absorption peak of lignin has been abated.It is prove that yield of cellulose increased significantly,degradation trend of hemicelluloses is obviously,removal effect of lignin has also been better.The analysis results of Fourier infrared spectrum are consistent with
Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation.
Li, Xin; Zhong, Yongmin; Smith, Julian; Gu, Chengfan
2017-01-02
Prediction of tissue damage under thermal loads plays important role for thermal ablation planning. A new methodology is presented in this paper by combing non-Fourier bio-heat transfer, constitutive elastic mechanics as well as non-rigid motion of dynamics to predict and analyze thermal distribution, thermal-induced mechanical deformation and thermal-mechanical damage of soft tissues under thermal loads. Simulations and comparison analysis demonstrate that the proposed methodology based on the non-Fourier bio-heat transfer can account for the thermal-induced mechanical behaviors of soft tissues and predict tissue thermal damage more accurately than classical Fourier bio-heat transfer based model.
Energy Technology Data Exchange (ETDEWEB)
Zheng, Y. [Pennsylvania State Univ., University Park, PA (United States)]|[Lawrence Berkeley Lab., CA (United States); Shirley, D.A. [Pennsylvania State Univ., University Park, PA (United States)
1995-02-01
The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.
Glasser, L.
1987-01-01
This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…
Replica Fourier Transform: Properties and applications
Directory of Open Access Journals (Sweden)
A. Crisanti
2015-02-01
Full Text Available The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically.
A resource-efficient adaptive Fourier analyzer
Hajdu, C. F.; Zamantzas, C.; Dabóczi, T.
2016-10-01
We present a resource-efficient frequency adaptation method to complement the Fourier analyzer proposed by Péceli. The novel frequency adaptation scheme is based on the adaptive Fourier analyzer suggested by Nagy. The frequency adaptation method was elaborated with a view to realizing a detector connectivity check on an FPGA in a new beam loss monitoring (BLM) system, currently being developed for beam setup and machine protection of the particle accelerators at the European Organisation for Nuclear Research (CERN). The paper summarizes the Fourier analyzer to the extent relevant to this work and the basic principle of the related frequency adaptation methods. It then outlines the suggested new scheme, presents practical considerations for implementing it and underpins it with an example and the corresponding operational experience.
COMPARISON OF FOURIER AND WAVELET TRANSFORMS IN GEOPHYSICAL APPLICATIONS
Directory of Open Access Journals (Sweden)
Hakan ALP
2008-01-01
Full Text Available In this study, it was compared Fourier Transformation using widely in analysing of geophysics data and image processing and Wavelet Transformation using in image processing, boundary analysis and recently years in use geophysical data analysis. It was applicated and compared two transformations in the both geophysical data and fundamental functions. Then the results obtained were evaluated. In this study it was compared two transformation using earthquake records and Bouger gravity anomalies map of Hatay region geophysical data. At the end of the our study it was clearly seen that wavelet transform can be used by geophysical data analysing.
Fast Fourier Transform algorithm design and tradeoffs
Kamin, Ray A., III; Adams, George B., III
1988-01-01
The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.
Quantum transport efficiency and Fourier's law.
Manzano, Daniel; Tiersch, Markus; Asadian, Ali; Briegel, Hans J
2012-12-01
We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. We relate these results to recent discussions of energy transport in biological light-harvesting systems, and discuss the role of quantum coherence and entanglement.
Quantum transport efficiency and Fourier's law
Manzano, Daniel; Asadian, Ali; Briegel, Hans J
2011-01-01
We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. Implications of these results on energy transfer in biological light harvesting systems, and the role of quantum coherences and entanglement are discussed.
Illustrative EDOF topics in Fourier optics
George, Nicholas; Chen, Xi; Chi, Wanli
2011-10-01
In this talk we present a series of illustrative topics in Fourier Optics that are proving valuable in the design of EDOF camera systems. They are at the level of final examination problems that have been made solvable by a student or professoi having studied from one of Joseph W. Goodman's books---our tribute for his 75fr year. As time permits, four illustrative topics are l) Electromagnetic waves and Fourier optics;2) The perfect lens; 3) Connection between phase delay and radially varying focal length in an asphere and 4) tailored EDOF designs.
Fourier transforms and convolutions for the experimentalist
Jennison, RC
1961-01-01
Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t
Adaptive optics implementation with a Fourier reconstructor.
Glazer, Oded; Ribak, Erez N; Mirkin, Leonid
2007-02-01
Adaptive optics takes its servo feedback error cue from a wavefront sensor. The common Hartmann-Shack spot grid that represents the wavefront slopes is usually analyzed by finding the spot centroids. In a novel application, we used the Fourier decomposition of a spot pattern to find deviations from grid regularity. This decomposition was performed either in the Fourier domain or in the image domain, as a demodulation of the grid of spots. We analyzed the system, built a control loop for it, and tested it thoroughly. This allowed us to close the loop on wavefront errors caused by turbulence in the optical system.
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.
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.