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...
Digital Fourier analysis advanced techniques
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to advanced digital Fourier analysis for advanced undergraduate and graduate students. Assuming knowledge of the Fast Fourier Transform, this book covers advanced topics including the Hilbert transform, cepstrum analysis, and the two-dimensional Fourier transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Advanced Techniques" includes practice problems and thorough Appendices. As a central feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. The applet source code in Visual Basic is provided online, enabling advanced students to tweak and change the programs for more sophisticated results. A complete, intuitive guide, "Digital Fourier Analysis - Advanced Techniques" is an essential reference for students in science and engineering.
Fourier Analysis of Musical Intervals
LoPresto, Michael C.
2008-11-01
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 MacScope2 in just such a manner as a way to teach Fourier analysis.3 A logical continuation of this project is to use MacScope not just to analyze the Fourier composition of musical tones but also musical intervals.
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...
On higher order Fourier analysis
Szegedy, Balazs
2012-01-01
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the notion "higher order Fourier analysis" in terms of continuous morphisms between structures called compact $k$-step nilspaces. As a byproduct of our results we obtain a new type of limit theory for functions on abelian groups in the spirit of the so-called graph limit theory. Our proofs are based on an exact (non-approximative) version of higher order Fourier analysis which appears on ultra product groups.
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.
Fourier analysis of blazar variability
Finke, Justin D. [U.S. Naval Research Laboratory, Code 7653, 4555 Overlook Avenue SW, Washington, DC 20375-5352 (United States); Becker, Peter A., E-mail: justin.finke@nrl.navy.mil [School of Physics, Astronomy, and Computational Sciences, MS 5C3, George Mason University, 4400 University Drive, Fairfax, VA 22030 (United States)
2014-08-10
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, and external Compton emission components, from submillimeter to γ-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 also find that FSRQs should have steeper γ-ray PSD power-law indices than BL Lac objects at Fourier frequencies ≲ 10{sup –4} Hz, in qualitative agreement with previously reported observations by the Fermi Large Area Telescope.
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Fourier methods for biosequence analysis.
Benson, D C
1990-01-01
Novel methods are discussed for using fast Fourier transforms for DNA or protein sequence comparison. These methods are also intended as a contribution to the more general computer science problem of text search. These methods extend the capabilities of previous FFT methods and show that these methods are capable of considerable refinement. In particular, novel methods are given which (1) enable the detection of clusters of matching letters, (2) facilitate the insertion of gaps to enhance seq...
Fourier analysis and synthesis tomography.
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.
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.
Adaptive Fourier Analysis For Unequally-Spaced Time Series Data
Liang, Hong
2002-01-01
Adaptive Fourier Analysis For Unequally-Spaced Time Series Data by Hong Liang Robert V. Foutz, Chairman Statistics (ABSTRACT) Fourier analysis, Walsh-Fourier analysis, and wavelet analysis have often been used in time series analysis. Fourier analysis can be used to detect periodic components that have sinusoidal shape; however, it might be misleading when the periodic components are not sinusoidal. Walsh-Fourier analysis is suitable for revealing the rectangular ...
Functional Equations and Fourier Analysis
Yang, Dilian
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.
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...
A Fourier analysis of extremal events
Zhao, Yuwei
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...
Harmonic oscillator: an analysis via Fourier series
de Castro, A. S.
2013-01-01
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.
Adaptive Fourier Decomposition Based Time-Frequency Analysis
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
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.
Modified Tangential Frequency Filtering Decomposition and its Fourier Analysis
Niu, Qiang; Grigori, Laura; Kumar, Pawan; Nataf, Frédéric
2008-01-01
In this paper, a modified tangential frequency filtering decomposition (MTFFD) preconditioner is proposed. The optimal order of the modification and the optimal relaxation parameter are determined by Fourier analysis. With this choice of the optimal order of modification, the Fourier results show that the condition number of the preconditioned matrix is ${\\cal O}(h^{-\\frac{2}{3}})$, and the spectrum distribution of the preconditioned matrix can be predicted by the Fourier results. The perform...
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...
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
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
Fourier mode analysis of source iteration in spatially periodic media
The standard Fourier mode analysis is an indispensable tool when designing acceleration techniques for transport iterations; however, it requires the assumption of a homogeneous infinite medium. For problems of practical interest, material heterogeneities may significantly impact iterative performance. Recent work has applied a Fourier analysis to the discretized two-dimensional transport operator with heterogeneous material properties. The results of these analyses may be difficult to interpret because the heterogeneity effects are inherently coupled to the discretization effects. Here, the authors describe a Fourier analysis of source iteration (SI) that allows the calculation of the eigenvalue spectrum for the one-dimensional continuous transport operator with spatially periodic heterogeneous media
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...
International conference Fourier Analysis and Pseudo-Differential Operators
Turunen, Ville; Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations
2014-01-01
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. This collection of 20 refereed articles is based on selected talks given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
Fourier analysis of 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
Fourier analysis of the aerodynamic behavior of cup anemometers
The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force. (paper)
Discrete Fourier analysis with lattices on planar domains
Li, Huiyuan; Xu, Yuan
2009-01-01
A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible choices of lattices are discussed in the case of lattices that tile $\\RR^2$ and several new results on cubature and interpolation by trigonometric, as well as algebraic, polynomials are obtained.
Fourier analysis of the parametric resonance in neutrino oscillations
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.
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.
Fourier analysis for discontinuous Galerkin and related methods
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.
Higher order Fourier analysis as an algebraic theory II
Szegedy, Balazs
2009-01-01
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of approximative statements. The present paper is the second part of a paper in which higher order characters and decompositions were introduced. We generalize the concept of the Pontrjagin dual group and introduce higher order versions of it. We study the algebraic structure of the higher order dual groups. We prove a simple formula for the Gowers uniformity norms in terms of higher order decompositions. We present a simple spectral algorithm to produce higher order decompositions. We briefly study a multi linear version of Fourier analysis. Along these lines we obtain new inverse theorems for Gowers's norms.
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.
Higher order Fourier analysis as an algebraic theory I
Szegedy, Balazs
2009-01-01
Ergodic theory, Higher order Fourier analysis and the hyper graph regularity method are three possible approaches to Szemer\\'edi type theorems in abelian groups. In this paper we develop an algebraic theory that creates a connection between these approaches. Our main method is to take the ultra product of abelian groups and to develop a precise algebraic theory of higher order characters on it. These results then can be turned back into approximative statements about finite Abelian groups.
Evaluation of gastric motility by Fourier analysis of condensed images
Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K. [Dept. of Nuclear Medicine, Univ. of Munich, Munich (Germany)
2000-10-01
In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)
Fourier Transform Infrared Spectroscopic Analysis of Protein Secondary Structures
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.
Fourier analysis of conductive heat transfer for glazed roofing materials
Roslan, Nurhana Lyana; Bahaman, Nurfaradila; Almanan, Raja Noorliyana Raja; Ismail, Razidah; Zakaria, Nor Zaini
2014-07-01
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.
Fourier analysis of conductive heat transfer for glazed roofing materials
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
Fourier analysis of conductive heat transfer for glazed roofing materials
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.
Spatial Fourier analysis of video photobleaching measurements. Principles and optimization.
Tsay, T T; Jacobson, K A
1991-08-01
The major use of the fluorescence recovery after photobleaching (FRAP) technique is to measure the translational motion of the molecular components in various condensed media. In a conventional laser spot photobleaching experiment, a photomultiplier is used to measure the total brightness levels of the bleached region in the sample, so no spatial information can be directly obtained. In video-FRAP, a series of images after photobleaching is acquired, allowing the spatial character of the recovery to be determined; this permits direct detection of both anisotropic diffusion and flow. To utilize all of the available image data to determine the transport coefficients, a two-dimensional spatial Fourier transform analysis of the images after photobleaching was employed. The change in the transform between two time points reflects the action of diffusion during the interim. An important advantage of this method, which involves taking the ratio of image transforms at different time points, is that it does not require a specific initial condition to be created by laser photobleaching. The ability of the analysis to extract transport coefficients from computer-simulated diffusional recovery is assessed in the presence of increasing amounts of noise. Experimental data analysis from the diffusion of proteins in viscous solutions and from the diffusion of protein receptors on cell surfaces demonstrate the feasibility of the Fourier analysis to obtain transport coefficients from the video FRAP measurement. PMID:1912279
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...
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Ovidiu Hâruţa
2011-06-01
Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage development of the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, centroid position, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
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.
Non-Harmonic Fourier Analysis for bladed wheels damage detection
Neri, P.; Peeters, B.
2015-11-01
The interaction between bladed wheels and the fluid distributed by the stator vanes results in cyclic loading of the rotating components. Compressors and turbines wheels are subject to vibration and fatigue issues, especially when resonance conditions are excited. Even if resonance conditions can be often predicted and avoided, high cycle fatigue failures can occur, causing safety issues and economic loss. Rigorous maintenance programs are then needed, forcing the system to expensive shut-down. Blade crack detection methods are beneficial for condition-based maintenance. While contact measurement systems are not always usable in exercise conditions (e.g. high temperature), non-contact methods can be more suitable. One (or more) stator-fixed sensor can measure all the blades as they pass by, in order to detect the damaged ones. The main drawback in this situation is the short acquisition time available for each blade, which is shortened by the high rotational speed of the components. A traditional Discrete Fourier Transform (DFT) analysis would result in a poor frequency resolution. A Non-Harmonic Fourier Analysis (NHFA) can be executed with an arbitrary frequency resolution instead, allowing to obtain frequency information even with short-time data samples. This paper shows an analytical investigation of the NHFA method. A data processing algorithm is then proposed to obtain frequency shift information from short time samples. The performances of this algorithm are then studied by experimental and numerical tests.
Analysis of morphology of pulmonary nodules using a fourier descriptor
The usefulness of computer aided diagnosis (CAD) systems in the differential diagnosis of pulmonary nodules detected by lung cancer screening CT has been widely acknowledged. In this study, we quantified the morphological features of such nodules and assessed whether they could be used for objective evaluation to improve diagnostic accuracy, based on hypotheses regarding differences in growth appearance between benign and malignant nodules. Quantification was achieved for both high-resolution CT images and simulation images using Fourier description. Benign pulmonary nodules (inflammatory scars) showed high amplitude in the lower harmonics, while malignant nodules (lung cancers) showed high amplitude in the higher harmonics. These values were compared by Mahalanobis generalized distance multivariate analysis. The mean predictive values of this analysis for the inflammatory scar and lung cancer groups were 85% and 90%, respectively. The mean predictive value for the two groups was 87.5%. (author)
Construction and Fourier analysis of invariant surfaces from tracking data
We study invariant surfaces in phase space by application of a symplectic tracking code. For motion in two degrees of freedom we use the code to compute I(s), /Phi/(s) for s = 0,C,2C...nC, where I = (I1,I2), /Phi/ = (/phi/1,/phi/2) are action-angle coordinates of points on a single orbit, and C is the circumference of the reference orbit. As a test to see whether the orbit lies on an invariant surface (i.e., to test for regular and nonresonant motion) we fit the points to a smooth, piece-wise polynomial surface I = /cflx I/(/phi/1,/phi/2). We then compute additional points on the same orbit, and test for their closeness to /cflx I/. We find that data from a few thousand turns are sufficient to construct accurate approximations to an invariant surface, even in cases with strong nonlinearities. Two-dimensional Fourier analysis of the surface leads to information on the strength of nonlinear resonances, and provides the generator of a canonical transformation as a Fourier series in angle variables. The generator can be used in a program to derive rigorous bounds on the motion for a finite time T. 6 refs., 2 figs., 1 tab
Determination of total body water by Fourier transform infrared analysis
A new technique for determinig body water using deuterium isotope dilution for Fourier transform infrared (FTIR) analysis is described. The advantages of the FTIR over conventional dispersion and filter infrared instruments include greater flexibility through computer controlled operations and availability of 'on-line' analytical software. The technique was further improved by the development of a simple procedure for determining D2O concentration in untreated serum samples. A validation study of six normal adults showed that the fat-free-mass determined from the deuterium-space (total body water) correlated well with the results obtained by total body nitrogen (r = 0.997), total body potassium (r = 0.99f6) and anthropometric (r = 0.995) measurements. 17 refs., 4 tabs., 4 figs
Higher-order Fourier analysis over finite fields and applications
Hatami, Pooya
Higher-order Fourier analysis is a powerful tool in the study of problems in additive and extremal combinatorics, for instance the study of arithmetic progressions in primes, where the traditional Fourier analysis comes short. In recent years, higher-order Fourier analysis has found multiple applications in computer science in fields such as property testing and coding theory. In this thesis, we develop new tools within this theory with several new applications such as a characterization theorem in algebraic property testing. One of our main contributions is a strong near-equidistribution result for regular collections of polynomials. The densities of small linear structures in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by approximating the indicator function of a subset by a function of bounded number of polynomials. Then, to approximate the average, it suffices to know the joint distribution of the polynomials applied to the linear forms. We prove a near-equidistribution theorem that describes these distributions for the group F(n/p) when p is a fixed prime. This fundamental fact was previously known only under various extra assumptions about the linear forms or the field size. We use this near-equidistribution theorem to settle a conjecture of Gowers and Wolf on the true complexity of systems of linear forms. Our next application is towards a characterization of testable algebraic properties. We prove that every locally characterized affine-invariant property of functions f : F(n/p) → R with n∈ N, is testable. In fact, we prove that any such property P is proximity-obliviously testable. More generally, we show that any affine-invariant property that is closed under subspace restrictions and has "bounded complexity" is testable. We also prove that any property that can be described as the property of decomposing into a known structure of low
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...
Optical polarimeter based on Fourier analysis and electronic control
In this paper, we show the design and implementation of an optical polarimeter using electronic control and the Fourier analysis. The polarimeter prototype will be used as a main tool for the students of the Universidad Popular del Cesar that belong to the following university programs: Electronics engineering (optoelectronics area), Math and Physics degree and the Master in Physics Sciences, in order to learning the theory and experimental aspects of the state of optical polarization via the Stokes vector measurement. Using the electronic polarimeter proposed in this paper, the students will be able to observe (in an optical bench) and understand the different interactions of the states of optical polarization when the optical waves pass through to the polarizers and retarder waves plates. The electronic polarimeter has a software that captures the optical intensity measurement and evaluates the Stokes vector. (Author)
Factor analysis was applied to multigated cardiac pool scintigraphy to evaluate its ability to detect left ventricular wall motion abnormalities in 35 patients with old myocardial infarction (MI), and in 12 control cases with normal left ventriculography. All cases were also evaluated by conventional Fourier analysis. In most cases with normal left ventriculography, the ventricular and atrial factors were extracted by factor analysis. In cases with MI, the third factor was obtained in the left ventricle corresponding to wall motion abnormality. Each case was scored according to the coincidence of findings of ventriculography and those of factor analysis or Fourier analysis. Scores were recorded for three items; the existence, location, and degree of asynergy. In cases of MI, the detection rate of asynergy was 94 % by factor analysis, 83 % by Fourier analysis, and the agreement in respect to location was 71 % and 66 %, respectively. Factor analysis had higher scores than Fourier analysis, but this was not significant. The interobserver error of factor analysis was less than that of Fourier analysis. Factor analysis can display locations and dynamic motion curves of asynergy, and it is regarded as a useful method for detecting and evaluating left ventricular wall motion abnormalities. (author)
Gas Analysis by Fourier Transform Mm-Wave Spectroscopy
Harris, Brent J.; Steber, Amanda L.; Lehmann, Kevin K.; Pate, Brooks H.
2013-06-01
Molecular rotational spectroscopy of low pressure, room temperature gases offers high chemical selectivity and sensitivity with the potential for a wide range of applications in gas analysis. A strength of the technique is the potential to identify molecules that have not been previously studied by rotational spectroscopy by comparing experimental results to predictions of the spectroscopic parameters from quantum chemistry -6 so called library-free detection. The development of Fourier transform mm-wave spectrometers using high peak power (30 mW) active multiplier chain mm-wave sources brings new measurement capabilities to the analysis of complex gas mixtures. Strategies for gas analysis based on high-throughput mm-wave spectroscopy and arbitrary waveform generator driven mm-wave sources are described. Several new measurement capabilities come from the intrinsic time-domain measurement technique. High-sensitivity double-resonance measurements can be performed to speed the analysis of a complex gas sample containing several species. This technique uses a "pi-pulse" to selectively invert the population of two selected rotational energy levels and the effect of this excitation pulse on all other transitions in the spectrometer operating range is monitored using segmented chirped-pulse Fourier transform spectroscopy. This method can lead to automated determination of the molecular rotational constants. Rapid pulse duration scan experiments can be used to estimate the magnitude and direction of the dipole moment of the molecule from an unknown spectrum. Coherent pulse echo experiments, using the traditional Hahn sequence or two-color population recovery methods, can be used to determine the collisional relaxation rate of the unknown molecule. This rate determination improves the ability to estimate the mass of the unknown molecule from the determination of the Doppler dephasing rate. By performing a suite of automated, high-throughput measurements, there is the
Fast Fourier transformation in vibration analysis of physically active systems
Vibration of all physical systems may be expressed as the summation of an infinite number of sine and cosine terms known as Fourier series. The basic vibration analysis tool used is the frequency 'spectrum' (a graph of vibration where the amplitude of vibration is plotted against frequency). When a particular rotating component begins to fail, its vibration tends to increase. Spectra graphs are powerful diagnostic tool for detecting components' degradation. Spectra obtained with accelerometers located at the various locations on the components and their analysis in practice from rotating machines enable early detecting of incipient failure. Consequence of unexpected failure can be catastrophic and costly. This study provides basis to relate defective component by its constituent frequencies and then to the known discrete frequency of its 'signature' or 'thumbprint' to predict and verify the sustained dynamic behavior of machine designs harmful effects of forced vibration. The spectra for gearbox of a vane with teeth damaged fault are presented here which signified the importance of FFT analysis as diagnostic tool. This may be helpful to predictive maintenance of the machinery. (author)
Experimental display of Fourier analysis through the optical physics and its didatical utilization
The properties of Fourier analysis through physical optics are displayed experimentally. Within physical optics topics that illustrate didactically Fourier analysis, a subject usually considered purely mathematical are selected. The most important properties of Fourier transform and their utilization in cleaning up images through spatial filtering are presented, in this way the properties of convolution to analyse image formation and characterize some diffraction patterns are also used. (Author)
Fourier Analysis of the Parametric Resonance in Neutrino Oscillations
Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe
2009-01-01
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to th...
Quantitative analysis of iron oxides using Fourier transform infrared spectrophotometry
In this study, a systematic approach based on the application of Fourier transform infrared spectrophotometry (FTIR) was taken, in order to quantitatively analyze the corrosion products formed in the secondary cycle of pressurized water reactors (PWR). Binary mixtures of iron oxides were prepared with known compositions containing pure commercial magnetite (Fe3O4), maghemite (γ-Fe2O3), and hematite (α-Fe2O3) for calibration purposes. Calcium oxide (lime) was added to all samples as a standard reference in obtaining the calibration curves. Using regression analysis, relationships were developed for intensity versus concentration for absorption bands corresponding to each of the phases in their corresponding FTIR spectrum. Correlation coefficients, R2, of 0.82, 0.87, and 0.86 were obtained for maghemite-magnetite, hematite-magnetite, and hematite-maghemite systems, respectively. The calibration curves generated were used to quantify phases in multi-component unknown field samples that were obtained from different components (moisture separators, condensers, and high- and low- pressure heaters) of the two units (units 1 and 2) of the secondary cycle of the Comanche Peak PWR
Fourier analysis of polar cap electric field and current distributions
Barbosa, D. D.
1984-01-01
A theoretical study of high-latitude electric fields and currents, using analytic Fourier analysis methods, is conducted. A two-dimensional planar model of the ionosphere with an enhanced conductivity auroral belt and field-aligned currents at the edges is employed. Two separate topics are treated. A field-aligned current element near the cusp region of the polar cap is included to investigate the modifications to the convection pattern by the east-west component of the interplanetary magnetic field. It is shown that a sizable one-cell structure is induced near the cusp which diverts equipotential contours to the dawnside or duskside, depending on the sign of the cusp current. This produces characteristic dawn-dusk asymmetries to the electric field that have been previously observed over the polar cap. The second topic is concerned with the electric field configuration obtained in the limit of perfect shielding, where the field is totally excluded equatorward of the auroral oval. When realistic field-aligned current distributions are used, the result is to produce severely distorted, crescent-shaped equipotential contours over the cap. Exact, analytic formulae applicable to this case are also provided.
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 ...
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.
Using musical intervals to demonstrate superposition of waves and Fourier analysis
LoPresto, Michael C.
2013-09-01
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.
Neutron Fourier Diffractometer FSD for Internal Stress Analysis First Results
Aksenov, V L; Bokuchava, G D; Zhuravlev, V V; Kuzmin, E S; Bulkin, A P; Kudryashov, V A; Trounov, V A
2001-01-01
At the IBR-2 pulsed reactor (FLNP, JINR) a specialised instrument - neutron Fourier diffractometer FSD - intended for internal stress measurements in bulk materials is under construction. Internal stress studies by neutron diffraction has been successfully developed last years in leading neutron centres, including Dubna and Gatchina, due to several important advantages of this method in comparison with other techniques. In current work the operation principles and construction of the diffractometer, basic parameters and outcomes of test experiments are presented.
Fourier analysis of a gated blood-pool study during atrial flutter
First-harmonic Fourier analysis of a gated blood-pool study is based on the assumption that the cardiac chambers contract once per cardiac cycle. In atrial arrhythmias this condition may not exist for the atria. We recently studied a patient with atrial flutter and 2:1 artioventricular conduction. There were predictable alterations in the first-harmonic Fourier phase and amplitude images. The observed changes from first-harmonic Fourier analysis were: (a) very low atrial amplitude values, and (b) absence of identifiable atrial regions on the phase image
Fast fourier algorithms in spectral computation and analysis of vibrating machines
In this work we have discussed Fourier and its history series, relationships among various Fourier mappings, Fourier coefficients, transforms, inverse transforms, integrals, analyses, discrete and fast algorithms for data processing and analysis of vibrating systems. The evaluation of magnitude of the source signal at transmission time, related coefficient matrix, intensity, and magnitude at the receiving end (stations). Matrix computation of Fourier transform has been explained, and applications are presented. The fast Fourier transforms, new computational scheme. have been tested with an example. The work also includes digital programs for obtaining the frequency contents of time function. It has been explained that how the fast Fourier algorithms (FFT) has decreased computational work by several order of magnitudes and split the spectrum of a signal into two (even and odd modes) at every successive step. That fast quantitative processing for discrete Fourier transforms' computations as well as signal splitting and combination provides an efficient. and reliable tool for spectral analyses. Fourier series decompose the given variable into a sum of oscillatory functions each having a specific frequency. These frequencies, with their corresponding amplitude and phase angles, constitute the frequency contents of the original time functions. These fast processing achievements, signals decomposition and combination may be carried out by the principle of superposition and convolution for, even, signals of different frequencies. Considerable information about a machine or a structure can be derived from variable speed and frequency tests. (author)
Fourier and spectral envelope analysis of medically important bacterial and fungal sequences
Chang, C.; Chan, KKH; Chan, FHY
2004-01-01
In this paper, we introduce the Fourier and spectral envelope analysis methods to analyze some biomolecular sequences, particularly medically important bacteria and fungi DNA sequences, to get their interesting frequency properties. Fourier analysis includes mapping character strings into numerical sequences, calculating spectra of DNA sequences and setting and solving optimization problem in order to construct a powerful predictor of exons along the long DNA sequences. The spectral envelope ...
A Fourier analysis for a fast simulation algorithm. [for switching converters
King, Roger J.
1988-01-01
This paper presents a derivation of compact expressions for the Fourier series analysis of the steady-state solution of a typical switching converter. The modeling procedure for the simulation and the steady-state solution is described, and some desirable traits for its matrix exponential subroutine are discussed. The Fourier analysis algorithm was tested on a phase-controlled parallel-loaded resonant converter, providing an experimental confirmation.
Fourier analysis of metallic near-field superlens
Sheng, Yunlong; Tremblay, Guillaume; Gravel, Yann
2011-11-01
In the application to nanometre resolution lithography of the metallic near-field superlens, the image quality becomes a critical issue. Fundamental Fourier optics is applied to analyze the image system. The transfer function is computed with the transfer matrix method, the Surface Plasmon Polariton (SPP) resonance and the SPP waveguide theory. However, as the scattering of the object nano-structure involving the solution of the Maxwell's equations, so that the object function is in general unknown, and the impulse response is less likely useful for computing the image. Especially, metal object may induce the electrical dipoles, which launch the SPP and act as sources of radiation. The superlens may be optimized based on the transfer function using the long-range SPP mode cut-off technique, the genetic algorithm and other techniques in order to improve significantly the image quality. Design examples are presented, and confirmed by the real image computed with numerical simulation using the FDTD method.
Tow-dimensional Strain Analysis by Fourier Transform Moire Interferometry
Moire interferometry using a diffraction grating and a laser is a powerful technique for analyzing small deformation of a specimen. In the method, the x and y-directional fringe patterns are obtained by using the x and y-directional sets of two beams. If the both sets of two beams are simultaneously incident to the specimen, the x and y-directional fringe patterns are super imposed. In this case, it is difficult to separate each directional fringe pattern. Therefore each fringe pattern has been separately recorded by selecting each set of two beams. In order to analyze a two-dimensional strain changing with time, Moire interferometry using the two-dimensional fourier transform method is proposed and the x and y-directional fringes are separated. By this method, the thermal deformation of a glass plate is analyzed
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: 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 ...
Analysis of ovarian tumor pathology by Fourier Transform Infrared Spectroscopy
Mehrotra Ranjana
2010-12-01
Full Text Available Abstract Background Ovarian cancer is the second most common cancer among women and the leading cause of death among gynecologic malignancies. In recent years, infrared (IR spectroscopy has gained attention as a simple and inexpensive method for the biomedical study of several diseases. In the present study infrared spectra of normal and malignant ovarian tissues were recorded in the 650 cm-1 to 4000 cm-1 region. Methods Post surgical tissue samples were taken from the normal and tumor sections of the tissue. Fourier Transform Infrared (FTIR data on twelve cases of ovarian cancer with different grades of malignancy from patients of different age groups were analyzed. Results Significant spectral differences between the normal and the ovarian cancerous tissues were observed. In particular changes in frequency and intensity in the spectral region of protein, nucleic acid and lipid vibrational modes were observed. It was evident that the sample-to-sample or patient-to-patient variations were small and the spectral differences between normal and diseased tissues were reproducible. Conclusion The measured spectroscopic features, which are the spectroscopic fingerprints of the tissues, provided the important differentiating information about the malignant and normal tissues. The findings of this study demonstrate the possible use of infrared spectroscopy in differentiating normal and malignant ovarian tissues.
Fourier Analysis for Demand Forecasting in a Fashion Company
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.
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Ovidiu Hâruţa
2011-01-01
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 ...
The combined use of order tracking techniques for enhanced Fourier analysis of order components
Wang, K. S.; Heyns, P. S.
2011-04-01
Order tracking is one of the most important vibration analysis techniques for diagnosing faults in rotating machinery. It can be performed in many different ways, each of these with distinct advantages and disadvantages. However, in the end the analyst will often use Fourier analysis to transform the data from a time series to frequency or order spectra. It is therefore surprising that the study of the Fourier analysis of order-tracked systems seems to have been largely ignored in the literature. This paper considers the frequently used Vold-Kalman filter-based order tracking and computed order tracking techniques. The main pros and cons of each technique for Fourier analysis are discussed and the sequential use of Vold-Kalman filtering and computed order tracking is proposed as a novel idea to enhance the results of Fourier analysis for determining the order components. The advantages of the combined use of these order tracking techniques are demonstrated numerically on an SDOF rotor simulation model. Finally, the approach is also demonstrated on experimental data from a real rotating machine.
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 (…) ...
Wahbi, A M; Abdine, H; Korany, M A
1978-05-01
The basic principle for the use of Fourier functions in spectrophotometric analysis is discussed. Fourier function coefficients are linearly related to concentration and are associated with relative standard deviations of less than 1%. The proper choice of function and range, number of points and the transformation of an absorption curve are discussed. New trigonometric functions are derived to correct for linear irrelevant absorption. The method is illustrated by the determination of progesterone and testosterone propionate in oily solutions without prior chromatography. The results obtained are compared with those obtained using orthogonal polynomials. PMID:674337
The methods and computer structures for adaptive Fourier descriptive image analysis
V.Perzhu; A. Gurau
1997-01-01
New architectures of image processing computer systems, based on the algorithms of Fourier - descriptive (FD) analysis have been developed. A new computing processes organisation method on the basis of FD image features has been proposed. The structures of two problem-oriented optical-electronic computer systems have been developed. The estimation of time expenditures in the systems have been carried out.
Analysis of Index Gases of Coal Spontaneous Combustion Using Fourier Transform Infrared Spectrometer
Xiaojun Tang; Yuntao Liang; Haozhe Dong; Yong Sun; Haizhu Luo
2014-01-01
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 analysi...
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.
Performance analysis of SHE-PWM using Fourier Series and Newton-Raphson analysis
Lada, M. Y.; Khiar, M. S. A.; Ghani, S. A.; Nawawi, M. R. M.; Nor, A. S. M.; Yuen, J. G. M.
2015-05-01
The performance of inverter has become a vital role in contributing effective power system nowadays. However the major issue that will reduce the inverter performance is the harmonic distortions that contribute to power losses. Thus, there are a variety of controls techniques have been implemented for inverters switching such as square wave, SHE-PWM, unipolar and bipolar. The square wave type inverter produces output voltage in square shape which has simple logic control and power switches. Next, unipolar and bipolar techniques are using comparator to compare the reference voltage waveform with the triangular waveform. The difference between unipolar and bipolar is there are two reference signals which are compared with the triangular waveform for unipolar switching. On the other hand, bipolar switching compares triangular waveform with a reference signal. Selective Harmonic Elimination Pulse-Width Modulation (SHE-PWM) is another control technique for inverters. This research propose SHE-PWM as a low switching frequency strategy that uses Fourier Series and Newton-Raphson analysis to calculate the switching angles for elimination of harmonic distortion. Fourier Series is used to determine the amplitude of any odd harmonic in the output signal whereas Newton-Raphson is used to solve the equation for finding switching angles. As a result, SHE-PWM can select the low frequency harmonic components need to be eliminated and reduce the harmonic distortion. It also prevents the harmonic distortion that sensitive to the inverter performance
Fourier analysis in magnetic induction tomography: mapping of anisotropic, inhomogeneous resistivity
Magnetic induction tomography is an electromagnetic technique for mapping the passive electromagnetic properties of conductors and has the potential for applications in biomedical imaging. In a previous analysis, we approached the inverse problem of determining isotropic resistivity with a Fourier-based analysis. Here, we extend that analysis to anisotropic media. The proposed Fourier-based solution method, when properly filtered, robustly handles noise to accurately map the inhomogeneous terms of the resistivity tensor. We observe a random variation in the measure of accuracy (mean deviation) that is resolved with independent spatial frequencies in the x- and y-directions in the applied field. Further, the formation of improper images we noted in our previous analysis is addressed through the use of independent spatial frequencies and through the use of additional applied fields. We conclude with a discussion of computation time for the large system of linear equations that this method requires and propose methods for limiting memory usage
Time sequence analysis of flickering auroras. I - Application of Fourier analysis. [in atmosphere
Berkey, F. T.; Silevitch, M. B.; Parsons, N. R.
1980-01-01
Using a technique that enables one to digitize the brightness of auroral displays from individual fields of a video signal, we have analyzed the frequency content of flickering aurora. Through the application of Fourier analysis to our data, we have found that flickering aurora contains a wide range of enhanced frequencies, although the dominant frequency enhancement generally occurs in the range 6-12 Hz. Each incidence of flickering that we observed was associated with increased radio wave absorption. Furthermore, we have found that flickering occurs in bright auroral surges, the occurrence of which is not limited to the 'breakup' phase of auroral substorms. Our results are interpreted in terms of a recently proposed theory of fluctuating double layers that accounts for a number of the observational features.
Almeida Assis, A.C.; Barbosa, M F; Valente Nabais, J.M.; Custódio, A.F.; Tropecelo, P.
2012-01-01
This paper describes the use of a diamond cell Fourier transform infrared (FTIR) spectroscopy methodology for the analysis of black toners commercialised in Portugal. A total of one hundred and thirty-eight samples from eighteen manufacturers were analysed in transmittance mode through a diamond cell. This methodology was considered to be non-destructive as it allows the forensic analysis of the questioned documents while preserving their integrity. The questioned documents’ subst...
Interpreting the Phase Spectrum in Fourier Analysis of Partial Ranking Data
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.
Advantages Of A Time Series Analysis Using Wavelet Transform As Compared With A Fourier Analysis
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.
Application of Fourier analysis to the study of roughness profiles of eroded samples
Fourier transforms are applied to analyse surface roughness profiles recorded on samples coming from erosion-corrosion essays. The information retrieved using this method clearly complements that revealed by the more classical roughness amplitude parameters. The analysis procedure here proposed can be applied not only to characterise the surface of corroded samples but, in general, to evaluate the quality of any surface after application of finishing treatments. (Author) 7 refs
A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations
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.
Fourier amplitude and phase analysis in the clinical evaluation of patients with cardiomyopathy
Fifty-four patients with a cardiomyopathy were studied by Radionuclide Cardangiography (RNCA) and Fourier amplitude and phase image analysis. The study group included patients with ischemic cardiomyopathy (27) and an equal number of patients with a primary cardiomyopathy: drug-induced (22), idiopathic (three), radiation-induced (one), and amyloidosis (one). Twenty-eight patients had rest studies alone and 26 had both rest and stress studies (80 total). The mean rest LVEF in the ischemic group was 27.9%, in the drug-induced group 36.5%, and in the idiopathic group 30%. The stress LVEF decreased in 92% of patients with ischemic cardiomyopathy and 45% of patients with primary (drug-induced) cardiomyopathy. Fourier amplitude and phase images were generated for each study. Amplitude and phase images were abnormal in all patients with an ischemic cardiomyopathy. LV amplitude abnormalities were regional and phase was directional. A zone of dysynergy on phase analysis was present in 44% of patients with ischemic cardiomyopathy. In the drug-induced primary cardiomyopathy group, all patients had abnormal amplitude and 86% had abnormal phase. Amplitude abnormalities were global rather than regional and phase patterns were nondirectional. Only one patient had a zone of dysynergy on the phase image. We conclude that the stress LVEF alone cannot consistently differentiate between ischemic and primary cardiomyopathies and that Fourier amplitude and phase analysis may be useful in determining the etiology of a cardiomyopathy (ischemic vs primary)
Menenti, M.; Azzali, S.; Verhoef, W.; Van Swol, R.
1993-01-01
Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.
A new approach to the Fourier analysis on semi-direct products of groups
Farashahi, Arash Ghaani
2012-01-01
Let $H$ and $K$ be locally compact groups and also $\\tau:H\\to Aut(K)$ be a continuous homomorphism and $G_\\tau=H\\ltimes_\\tau K$ be the semi-direct product of $H$ and $K$ with respect to the continuous homomorphism $\\tau$. This paper presents a novel approach to the Fourier analysis of $G_\\tau$, when $K$ is abelian. We define the $\\tau$-dual group $G_{\\hat{\\tau}}$ of $G_\\tau$ as the semi-direct product $H\\ltimes_{\\hat{\\tau}}\\hat{K}$, where $\\hat{\\tau}:H\\to Aut(\\hat{K})$ defined via (\\ref{A}). We prove a Ponterjagin duality Theorem and also we study $\\tau$-Fourier transforms on $G_\\tau$. As a concrete application we show that how these techniques apply for the affine group and also we compute the $\\tau$-dual group of Euclidean groups and the Weyl-Heisenberg groups.
Assessment of valve actuator motor rotor degradation by Fourier analysis of current waveform
This paper presents a test report of a motor diagnostic system that uses Fourier Analysis of the motor current waveform to detect broken rotor bars in the motor or defects in the driven equipment. The test was conducted on a valve actuator motor driving a valve actuator that was in turn driving a dynamometer to measure the actuator torque output. The motor was gradually degraded by open circuiting rotor bars. The test confirmed the efficacy of the waveform analysis method for assessing motor rotor degradation and also provided data regarding the change in waveform characteristic as motor rotors are gradually degraded to failure
Processing of gamma-ray spectra employing a Fourier deconvolver for the analysis of complex spectra
Processing of a nuclear spectrum e.g. gamma ray spectrum is concerned with the estimation of energies and intensities of radiation. The processing involves filtering, peak detection and its significance, baseline delineation, the qualitative and the quantitative analysis of singlets and multiplets present in the spectrum. The methodology for the analysis of singlets is well established. However, the analysis of multiplets provides a challenge and is a extremely difficult problem. This report incorporates a Fourier deconvolver for the quantitative analysis of doublets separated by more than a full width at half maximum. The method is easy to implement. The report discusses the methodology, mathematical analysis, and the results obtained by analyzing both synthetic and observed spectra. A computer program, developed for the analysis of a nuclear spectrum, was verified by analyzing a 152Eu gamma ray spectrum. The proposed technique compared favourably with SAMPO and MDFT method. (author). 16 refs., 3 tabs
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. PMID:1768719
Fourier transform method for sensitivity analysis in coal fired power plant
This work proposes a Fourier transform method to determine the sensitivities associated with a real coal power plant using a Rankine cycle. Power demand determines the plant revenue and is supposed to be the most important parameter to be accurately measured, and this hypothesis is at the center of this study. The results confirm that under full design load, variables such as steam pressure, temperature and mass flow rate are closely dependent on power demand, though overall thermal efficiency is more sensitive to boiler efficiency. Partial load simulation shows that the overall thermal efficiency remains strongly dependent on the boiler parameters, but other operational variables such as steam temperature at the turbine outlet changes its sensitivity according to the load. The results from the Fourier transform method are in good agreement with those determined by classical differential and Monte Carlo methods. However, the Fourier transform method requires only a single run, providing major savings in computational time as compared to the Monte Carlo method, a major advantage for analysis of power systems whether operating under full or partial load
Fourier and factorial analysis: An objective and comparative evaluation on a cardiac phantom
Orthogonal and oblique factor analysis represent an alternative to Fourier analysis in the evaluation of cardiac dynamic behaviour in gated blood pool studies. In order to estimate their respective places, orthogonal factor analysis (OFA), factor analysis of dynamic structures (FADS) and Fourier analysis (FA) are tested on a dynamic and periodical phantom with well known and reproducible kinetics. The phantom data are acquired under standard conditions by varying the counting rates and the temporal frequency sampling. To compare the results of the three methods with maximal objectivity, the relative contribution of each component is calculated. With standard acquisition conditions, FA and OFA give very close results. Only a minor advantage in evaluation of small phase differences is observed with OFA. FADS solutions are effectively related to the dynamic behaviour of the phantom, but their interpretation is more complicated and the quality of the oblique factors is reduced as the number of calculated factors increases. The influence of the counting statistics on FA, OFA and FADS is very similar. However, in cases of undersampling, robustness is demonstrated with the factorial technics. (orig.)
Pressure Vessel Code, Section VIII, Division 2 and ASME STS-1. -- Highlights: • Fourier series is used to predict the load carrying capacity of cylindrical vessel. • Reliability approach used for analysis as against the deterministic approach. • Cylindrical pressure vessel is subjected to axial end load and external pressure. • Axisymmetric and asymmetric analysis carried out for imperfect pressure vessels. • Results are compared to the recommendations laid out in ASME B and PV Code
Analysis of thermal plasma radiation by Fourier transform, wavelet analysis and phase portraits
Gruber, Jan; Šonský, Jiří; Hlína, Jan
Prague: Institute of Thermomechanics ASCR, v. v. i., 2014, s. 19-20. ISBN 978-80-87012-52-9. [Symposium on Electric Machines, Drives and Power Electronics. Prague (CZ), 09.09.2014-11.09.2014] Institutional support: RVO:61388998 Keywords : atmospheric-pressure plasmas * Fourier transform * plasma cutting Subject RIV: BL - Plasma and Gas Discharge Physics
Motion analysis of optically trapped particles and cells using 2D Fourier analysis
Kristensen, Martin Verner; Ahrendt, Peter; Lindballe, Thue Bjerring;
2012-01-01
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...... of diffusion coefficients and the trapping forces....
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.
Fourier analysis of blurred images for the measurement of the in-plane dynamics of MEMS
The goal of this paper is to use FFT imaging techniques to measure in-plane resonances of MEMS devices from blurred microphotographs where the presence of resonance is not visually discernable. A method is presented for measuring the high-frequency (in the 10s–100s of kHz range) response characteristics of MEMS devices using only standard optical microscope cameras (15–30 Hz frame rate) and applying Fourier analysis of camera images of periodic patterns on the oscillating devices. In the frequency domain, in-plane blurring acts as a low pass filter, attenuating all frequency components, but preferentially attenuating the higher order harmonics. A theoretical formula for the blur-induced attenuation of the harmonics of Fourier series components is derived and it is shown that it follows a Bessel curve. The theoretical predictions were verified experimentally using a series of camera microphotographs of three different variations of an electro-thermally driven pad suspended on springs. The predicted attenuations of harmonics were observed and verified. The analysis of the measured attenuation was able to (1) determine in-plane resonant frequencies, (2) measure submicron motions and (3) characterize the nonlinear dynamics (modeled by the Duffing equation). The amplitude uncertainty of the FFT method for detecting in-plane resonant peaks at 75 kHz and 3.5 V was found to be ±0.027 µm using a single image and ±0.011 µm using an average of 10 images. (paper)
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.
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.
Zhang, Yong; Cao, Chun-yu; Feng, Wen-ying; Xu, Ming; Su, Zhen-hua; Liu, Xiao-meng; Lü, Wei-jun
2011-03-01
As one of the most powerful tools to investigate the compositions of raw materials and the property of pulp and paper, infrared spectroscopy has played an important role in pulp and paper industry. However, the traditional transmission infrared spectroscopy has not met the requirements of the producing processes because of its disadvantages of time consuming and sample destruction. New technique would be needed to be found. Fourier transform attenuated total reflection infrared spectroscopy (ATR-FTIR) is an advanced spectroscopic tool for nondestructive evaluation and could rapidly, accurately estimate the production properties of each process in pulp and paper industry. The present review describes the application of ATR-FTIR in analysis of pulp and paper industry. The analysis processes will include: pulping, papermaking, environmental protecting, special processing and paper identifying. PMID:21595211
Fourier mode analysis of slab-geometry transport iterations in spatially periodic media
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
Requirements Formulation and Dynamic Jitter Analysis for Fourier-Kelvin Stellar Interferometer
Liu, Kuo-Chia; Hyde, Tristram; Blaurock, Carl; Bolognese, Jeff; Howard, Joseph; Danchi, William
2004-01-01
The Fourier-Kelvin Stellar Interferometer (FKSI) has been proposed to detect and characterize extra solar giant planets. The baseline configuration for FKSI is a two- aperture, structurally connected nulling interferometer, capable of providing null depth less than lo4 in the infrared. The objective of this paper is to summarize the process for setting the top level requirements and the jitter analysis performed on FKSI to date. The first part of the paper discusses the derivation of dynamic stability requirements, necessary for meeting the FKSI nulling demands. An integrated model including structures, optics, and control systems has been developed to support dynamic jitter analysis and requirements verification. The second part of the paper describes how the integrated model is used to investigate the effects of reaction wheel disturbances on pointing and optical path difference stabilities.
Manokaran Kalaiselvi
2012-02-01
Full Text Available Ananas comosus (L. Merrill is belonging to the family Bromeliaceae which act as an anti-inflammatory, antitumor effect. The present study is aimed to appraise the antioxidant potential and Fourier transform infrared spectroscopy (FTIR analysis in Ananus comosus peel. The enzymatic and non enzymatic antioxidants profiles were analyzed in fresh peel of pineapple with the standard protocols and the FTIR was applied and Infrared spectrum in mid infrared region 4000–400 cm–1 was used for discriminating and to identify various functional groups present in the ethanolic extract of Ananus comosus. The fresh peel shows the significant amount of antioxidants and the FTIR analysis also found the presence of amino acids, alkenes, nitrates, nitrites, ethers, esters, aldehydes, alkynes, aromatic compounds, organic halogen compounds, carbohydrates, sulphur derivatives and polysaccharides. In conclusion, the results presented in the peel of Ananus comosus have strong antioxidant content which may be act as good pharmacotherapeutic agents in future.
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...
Characterization of right or left ventricular contraction heterogeneity using Fourier phase analysis
The standard deviation of the first harmonic Fourier phase histogram is an indicator of the contraction heterogeneity of the heart ventricles. This approach has been applied to analyse tomographic blood pool (99mTc) examinations in a group of 32 patients with angiographically verified mainly right (RV) but also left (LV) kinetic disorders in relation to severe ventricular arrhythmias and suspicion of arrhythmogenic right ventricular dysplasia (ARVD). The reference group consisted of ten patients with low probability of cardiac kinetic abnormalities. Thick tomographic slices including both ventricles have been reconstructed in the horizontal long axis orientation from a series of 32 gated projections recorded over a 3600 rotation. Separately for each ventricle the Fourier phase histograms have been computed and characterized by their standard deviations (PSD). Normal values were significantly lower than those measured in abnormal cases. Detailed analysis of the data supports the hypothesis of a primary RV disease in ARVD, with secondary LV extension. PSD seems to be a good predictor of an organic cardiac disease underlying ventricular arrhythmias and may be used for screening the patients. (orig.)
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
The use of artificial hearts, developed for total heart replacement programs, allows assessment of the accuracy of measuring the first Fourier component phase and amplitude when applied to gated cardiac technetium 99 scans. In the extreme example of asynchrony of ventricular contraction in coronary artery disease that of ventricular aneurysms, the first Fourier component measurements of amplitude were highly correlated to volume increases suggesting that the calculated amplitude accurately reflects volume changes. The calculated asynchrony using Fourier analysis of the gated technetium 99 studies of two artificial hearts was highly accurate when compared to the predetermined calculation of phase angle difference and hence degree of asynchrony. The studies suggest that measurement of phase and amplitude using the first Fourier component of time-activity waves of gated cardiac technetium 99 studies accurately measure degree of asynchrony and volume changes respectively
Chen, Cheng; Liang, Jingqiu; Liang, Zhongzhu; Lü, Jinguang; Qin, Yuxin; Tian, Chao; Wang, Weibiao
2015-12-01
A method of "slope splicing" is proposed to build a tall-stepped mirror with high precision in a stepped-mirror-based static Fourier transform infrared spectrometer. The structural parameters were designed, and their errors were analyzed. We present the test results and an analysis of the combined effect of the errors on the recovered spectrum. The spectrum-constructing error of the constructed spectrum, 5.81%, meets the requirements for the system and suitable for realization of a miniaturized spectrometer. We performed experiments with the tall-stepped mirror to obtain the interferogram and spectrum of a silicon carbide light source. Further work is needed to optimize the capability of the system.
Single frame method for resolution enhancement of the Fourier fringe analysis method
Tavares, Paulo J.; Vaz, Mário A. P.
2013-11-01
Fourier Transform Profilometry (FTP) is one of the most popular fringe analysis methods in Optical Metrology for a wealth of applications in Mechanical Engineering, such as shape profilometry or defect detection with shearography or holographic interferometry methods. Gradient range and spatial resolution in the FTP method depend on the size of the filter window in reciprocal space. The authors have previously reported on a method that uses a single crossed fringe pattern for the elimination of the fundamental frequency and enlargement of the carrier window, which is therefore inherently able to cope with dynamic situations. This article describes an improved version of the technique that no longer resources to bit-shifting operations, greatly improving the flexibility of the previously reported technique, whilst retaining its main advantages.
Bing DENG; Jun-bao LUAN; Shi-qi CUI
2014-01-01
Parameter estimation is analyzed using two kinds of common sampling-type DFRFT (discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation accuracy are analyzed. And the simulation is made to verify the conclusions. From the theoretic analysis and simulation verification, it can be drawn that, for the estimation of chirp-rate and initial fre-quency, Pei's method [10] is more suitable if the absolute value of chirp-rate is small relatively; Ozaktas' method [9] is more suitable if the absolute value of chirp-rate is large relatively;and the two methods are both workable if the absolute value of chirp-rate is moderate. The scope of moderate chirp-rate can be approximately determined as [40 Hz/s, 110 Hz/s].
Zhang, Xiaoxing; Liu, Heng; Ren, Jiangbo; Li, Jian; Li, Xin
2015-02-01
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.
Fast Fourier transform analysis of sounds made while swallowing various foods.
Taniwaki, Mitsuru; Kohyama, Kaoru
2012-10-01
The cervical auscultation method was applied to investigate sounds generated while swallowing various foods with unique physical properties, including liquid (water), semiliquid (yogurt), and solid (konjac jelly). To study the differences among swallowing sounds for various foods, fast Fourier transform (FFT) analysis was applied to signals that were attributed to the flow of a food bolus, which is a swallowable soft mass of chewed food. An FFT program was developed that enabled the calculation of a spectrum for a specified region of time domain swallowing sound signals. The intensity of spectra in the frequency range between 400 and 1000 Hz significantly differed: liquid > semiliquid > solid. The FFT spectrum in this range was suggested to represent the frequency characteristics of the swallowing sounds of various foods. PMID:23039442
Local Fourier Analysis of the Complex Shifted Laplacian preconditioner for Helmholtz problems
Cools, Siegfried
2011-01-01
In this paper we solve the Helmholtz equation with multigrid preconditioned Krylov subspace methods. The class of Shifted Laplacian preconditioners are known to significantly speed-up Krylov convergence. However, these preconditioners have a parameter \\beta, a measure of the complex shift. Due to contradictory requirements for the multigrid and Krylov convergence, the choice of this shift parameter can be a bottleneck in applying the method. In this paper, we propose a wavenumber-dependent minimal complex shift parameter which is predicted by a rigorous k-grid Local Fourier Analysis (LFA) of the multigrid scheme. We claim that, given any (regionally constant) wavenumber, this minimal complex shift parameter provides the reader with a parameter choice that leads to efficient Krylov convergence. Numerical experiments in one and two spatial dimensions validate the theoretical results. It appears that the proposed complex shift is both the minimal requirement for a multigrid V-cycle to converge, as well as being ...
Analysis of Index Gases of Coal Spontaneous Combustion Using Fourier Transform Infrared Spectrometer
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.
Fourier transform infrared and fluorescence spectroscopy for analysis of vegetable oils
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.
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.
Mao, Zhi-Hua; Yin, Jian-Hua; Zhang, Xue-Xi; Wang, Xiao; Xia, Yang
2016-02-01
Fourier transform infrared spectroscopic imaging (FTIRI) technique can be used to obtain the quantitative information of content and spatial distribution of principal components in cartilage by combining with chemometrics methods. In this study, FTIRI combining with principal component analysis (PCA) and Fisher's discriminant analysis (FDA) was applied to identify the healthy and osteoarthritic (OA) articular cartilage samples. Ten 10-μm thick sections of canine cartilages were imaged at 6.25μm/pixel in FTIRI. The infrared spectra extracted from the FTIR images were imported into SPSS software for PCA and FDA. Based on the PCA result of 2 principal components, the healthy and OA cartilage samples were effectively discriminated by the FDA with high accuracy of 94% for the initial samples (training set) and cross validation, as well as 86.67% for the prediction group. The study showed that cartilage degeneration became gradually weak with the increase of the depth. FTIRI combined with chemometrics may become an effective method for distinguishing healthy and OA cartilages in future. PMID:26977354
von Aulock, F. W.; Kennedy, B. M.; Schipper, C. I.; Castro, J. M.; Martin, D. E.; Oze, C.; Watkins, J. M.; Wallace, P. J.; Puskar, L.; Bégué, F.; Nichols, A. R. L.; Tuffen, H.
2014-10-01
Fourier transform infrared spectroscopy (FTIR) is an analytical technique utilized to measure the concentrations of H and C species in volcanic glasses. Water and CO2 are the most abundant volatile species in volcanic systems. Water is present in magmas in higher concentrations than CO2 and is also more soluble at lower pressures, and, therefore it is the dominant volatile forming bubbles during volcanic eruptions. Dissolved water affects both phase equilibria and melt physical properties such as density and viscosity, therefore, water is important for understanding magmatic processes. Additionally, quantitative measurements of different volatile species using FTIR can be achieved at high spatial resolution. Recent developments in analytical equipment such as synchrotron light sources and the development of focal plane array (FPA) detectors allow higher resolution measurements and the acquisition of concentration maps. These new capabilities are being used to characterize spatial gradients (or lack thereof) around bubbles and other textural features, which in turn lead to new insights into the behavior of volcanic feeder systems. Here, practical insights about sample preparation and analysis of the distribution and speciation of volatiles in volcanic glasses using FTIR spectroscopy are discussed. New advances in the field of FTIR analysis produce reliable data at high spatial resolution that can be used to produce datasets on the distribution, dissolution and diffusion of volatiles in volcanic materials.
Fourier Analysis of the OMC1 Image at 1.1 mm Wavelength
Youn, Soyoung
2012-01-01
We present a 1.1 mm emission map of the OMC1 region observed with AzTEC, a new large-format array composed of 144 silicon-nitride micromesh bolometers that was in use at the James Clerk Maxwell Telescope (JCMT). The AzTEC observations of the OMC1 region at 1.1 mm reveal dozens of cloud cores and a tail of filaments in a manner that is almost identical to the submillimeter continuum emission of the entire OMC1 region at 450 and 850 micronm. We perform Fourier analysis of the image with a modified periodogram and the density power spectrum which provides the distribution of length scale of the structures is measured. The expected value of the periodogram converges to the resulting power spectrum in the mean squared sense. From the present analysis of the OMC1 filaments at the 1.1 mm emission, the power spectrum steepens at relatively smaller scales. At largest scales, the power spectrum flattens and the large scale power law becomes shallower. The power spectra of the 1.1 mm emission show clear deviations from ...
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.
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.
Moffat, Jonathan G; Mayes, Andrew G; Belton, Peter S; Craig, Duncan Q M; Reading, Mike
2010-01-01
Photothermal-Fourier transform-infrared (PT-FT-IR) microspectroscopy employs a thermal probe mounted in a scanning probe microscope (SPM). By placement of the tip of the probe on the surface of a solid sample, it can obtain localized IR spectra of a wide range of samples. A second mode of analysis is also available; a sample can be taken from the selected location using a technique called thermally assisted nanosampling (TAN), then a spectrum can be obtained of the nanosample while the probe is remote from the surface. We report a novel method of local compositional analysis that combines both of these types of measurement; a reagent is attached to the tip using TAN, then the reagent is placed in contact with analyte. IR spectroscopy can then be used to analyze any interaction between the reagent and surface it is placed in contact with. All of these modes of analysis were illustrated using a metal chelating agent. In the surface mode, changes to a solid bead of a chelating resin were measured using standard PT-FT-IR. In the nanosampling mode of analysis, a particle of a chelating polymer was attached to the tip of the probe using TAN and this was placed in contact with a concentrated calcium solution. Strong spectral changes were observed that mirrored those found when exposing the surface bound chelating resin bead to a solution of the same ion. A semiquantitative simulation of the PT spectrum for a chelating resin bead was achieved using a thermal diffusion model derived from photoacoustic spectroscopy indicating that semiquantitative or quantitative measurements will be possible in such a system. PMID:19957959
Neutron Noise Analysis with Flash-Fourier Algorithm at the IBR-2M Reactor
Mihai O. Dima
2013-01-01
Full Text Available Neutron noise spectra in nuclear reactors are a convolution of multiple effects. For the IBR-2M pulsed reactor (JINR, Dubna, one part of these is represented by the reactivities induced by the two moving auxiliary reflectors and another part of these by other sources that are moderately stable. The study of neutron noise involves, foremostly, knowing its frequency spectral distribution, hence Fourier transforms of the noise. Traditional methods compute the Fourier transform of the autocorrelation function. We show in the present study that this is neither natural nor real-time adapted, for both the autocorrelation function and the Fourier transform are highly CPU intensive. We present flash algorithms for processing the Fourier-like transforms of the noise spectra.
Theoretical Analysis and Experimental Evidence of NonFourier Heat Conduction Behavior
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-bessel based image analysis for multi-parameter particle characterization
Vandewiele, Stijn; Drobchak, Oksana; Beunis, Filip; Neyts, Kristiaan; Strubbe, Filip
2014-01-01
We demonstrate a novel particle characterization method based on decomposition of conventional microscopy images in Fourier-Bessel (FB) components. This allows the simultaneous measurement of size, refractive index, 3D position and orientation of single colloidal particles.
Neutron Noise Analysis with Flash-Fourier Algorithm at the IBR-2M Reactor
Dima, Mihai O.; Pepelyshev, Yuri N.(Joint Institute for Nuclear Research, FLNP, Dubna, Moscow 141980, Russia); Lachin Tayibov
2014-01-01
Neutron noise spectra in nuclear reactors are a convolution of multiple effects. For the IBR-2M pulsed reactor (JINR, Dubna), one part of these is represented by the reactivities induced by the two moving auxiliary reflectors and another part of these by other sources that are moderately stable. The study of neutron noise involves, foremostly, knowing its frequency spectral distribution, hence Fourier transforms of the noise. Traditional methods compute the Fourier transform of the autocorrel...
One of the paradigmatic classes of problems that frequently arise in piping stress analysis discipline is the effect of local stresses created by supports and restraints attachments. Over the past 20 years, concerns have been identified by both regulatory agencies in the nuclear power industry and others in the process and chemicals industries concerning the effect of various stiff clamping arrangements on the expected life of the pipe and its various piping components. In many of the commonly utilized geometries and arrangements of pipe clamps, the elasticity problem becomes the axisymmetric stress and deformation determination in a hollow cylinder (pipe) subjected to the appropriate boundary conditions and respective loads per se. One of the geometries that serve as a pipe anchor is comprised of two pipe clamps that are bolted tightly to the pipe and affixed to a modified shoe-type arrangement. The shoe is employed for the purpose of providing an immovable base that can be easily attached either by bolting or welding to a structural steel pipe rack. Over the past 50 years, the computational tools available to the piping analyst have changed dramatically and thereby have caused the implementation of solutions to the basic problems of elasticity to change likewise. The need to obtain closed form elasticity solutions, however, has always been a driving force in engineering. The employment of symbolic calculus that is currently available through numerous software packages makes closed form solutions very economical. This paper briefly traces the solutions over the past 50 years to a variety of axisymmetric stress problems involving hollow circular cylinders employing a Fourier series representation. In the present example, a properly chosen Fourier series represent the mathematical simulation of the imposed axial displacements on the outside diametrical surface. A general solution technique is introduced for the axisymmetric discontinuity stresses resulting from an
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.
ZUOSong-lin; GAOShang-yu; YUANXi-gen; XUBo-sen
2003-01-01
Bamboo was carbonized at different temperatures ranging from 200℃ to 600℃.The dependence of the change of hemicellulose,cellulose,and lignin on the temperature was investigated by means of elemental analysis and Fourier Transform Infrared (FTIR) spectra of the residual solid products.The results showed:(1)Below 200℃,hemicellulose in bamboo wasdecomposed and a large amount of hydroxyl groups are dislocated from hemicellulose and cellulose,accompanied by the evolution of water to escape.(2)200℃-250℃,cellulose in bamboo was brastically decomposed whereas the net structure of lignin keep stable,with the except of the dislocation of methoxyl groups from lignin.(3)250℃-400℃,the net structure of lignin collapse,up to 400℃,followed by that the more position in aryl groups are substituted.(4)For bamboo carbonization,the aromatization of residual carbon has approximately completed at the temperature as high as 600℃.But the fusion of aromatic rings possibly does not occur.
Temporal behavior of lung motion assested by xenon-127 scintigraphy using temporal Fourier analysis
Temporal Fourier Analysis (TFA) was applied to standard 127Xe ventilation studies to determine the time-activity curves up to the third harmonic for a single composite respiratory cycle. A global respiratory index, RI3, defined as the ratio of the amplitude for the first three harmonics. Three nonobstructed subjects, two subjects with only small airway disease, five subjects with chronic ostructive pulmonary disease (COPD) and onne subject with restrictive lung disease were studied. Geometric mean values of posterior and anterior images gave a closer relationship between RI3 and flow or volume parameters than either image alone. RI3 of the first three harmonics correlated linearly with the values of 1-s forced expiratory volume (FEV1)(r 0.783, p 3 values for the five COPD subjects were significantly lower (t = 2.582, p 127Xe ventilation data therefore appears to be a potentially useful, noninvasive, in vivo technique for evaluation of lung ventilation at the localized level. (author). 20 refs.; 6 figs.; 3 tabs
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 ...
Spectroscopic analysis of bladder cancer tissues using Fourier transform infrared spectroscopy
Al-Muslet, Nafie A.; Ali, Essam E.
2012-03-01
Bladder cancer is one of the most common cancers in Africa. It takes several days to reach a diagnosis using histological examinations of specimens obtained by endoscope, which increases the medical expense. Recently, spectroscopic analysis of bladder cancer tissues has received considerable attention as a diagnosis technique due to its sensitivity to biochemical variations in the samples. This study investigated the use of Fourier transform infrared (FTIR) spectroscopy to analyze a number of bladder cancer tissues. Twenty-two samples were collected from 11 patients diagnosed with bladder cancer from different hospitals without any pretreatment. From each patient two samples were collected, one normal and another cancerous. FTIR spectrometer was used to differentiate between normal and cancerous bladder tissues via changes in spectra of these samples. The investigations detected obvious changes in the bands of proteins (1650, 1550 cm-1), lipids (2925, 2850 cm-1), and nucleic acid (1080, 1236 cm-1). The results show that FTIR spectroscopy is promising as a rapid, accurate, nondestructive, and easy to use alternative method for identification and diagnosis of bladder cancer tissues.
Smoke gas analysis by Fourier transform infrared spectroscopy. The SAFIR project
Hakkarainen, T. [ed.] [VTT Building Technology, Espoo (Finland). Building Physics, Building Services and Fire Technology
1999-07-01
The determination of toxic components from fire gases is difficult because the environment is hot, reactions are often temperature dependent, and a lot of soot may be produced. Due to the different properties of the gas components, a different timeconsuming procedure for each species has traditionally been used. The use of FTIR (Fourier Transform InfraRed) spectrometers as a continuous monitoring technique overcomes many of the problems in smoke gas analyses. FTIR offers an opportunity to set up a calibration and prediction method for each gas showing a characteristic spectral band in the infra-red region of the spectrum. The objective of this project was to further develop the FTIR gas analysis of smoke gases to be an applicable and reliable method for the determination of toxic components in combustion gases related to fire test conditions. The project included the following tasks: small scale and large scale sampling; analysis, calibration and software techniques; the verification of the method; and an interlaboratory trial. The optimum probe design, filter parameters and the most suitable sampling lines in terms of flow rate, diameter, construction material and operating temperature have been specified. The gas adsorption onto the filter and the soot have been measured. In the large scale, special concern was given to the probe design and the effects of the probe location in relation to the fire source as well as practical considerations of the sampling line length. Quantitative calibration and prediction methods have been constructed for different components present in smoke gases. Recommendations on how to deal with interferents, non-linearities and outliers have been provided and a verification method for the spectrometer for unexpected variations and for the different models have been described. FTIR measurement procedures in different fire test scenarios have been studied using the recommendations of this project for measurement techniques and analysis
Fourier transform infrared spectroscopic analysis of sperm chromatin structure and DNA stability.
Oldenhof, H; Schütze, S; Wolkers, W F; Sieme, H
2016-05-01
Sperm chromatin structure and condensation determine accessibility for damage, and hence success of fertilization and development. The aim of this study was to reveal characteristic spectral features coinciding with abnormal sperm chromatin packing (i.e., DNA-protein interactions) and decreased fertility, using Fourier transform infrared spectroscopy. Chromatin structure in spermatozoa obtained from different stallions was investigated. Furthermore, spermatozoa were exposed to oxidative stress, or treated with thiol-oxidizing and disulfide-reducing agents, to alter chromatin structure and packing. Spectroscopic studies were corroborated with flow cytometric analyses using the DNA-intercalating fluorescent dye acridine orange. Decreased fertility of individuals correlated with increased abnormal sperm morphology and decreased stability toward induced DNA damage. Treatment with the disulfide reducing agent dithiothreitol resulted in increased sperm chromatin decondensation and DNA accessibility, similar as found for less mature epididymal spermatozoa. In situ infrared spectroscopic analysis revealed that characteristic bands arising from the DNA backbone (ν1230, ν1086, ν1051 cm(-1) ) changed in response to induced oxidative damage, water removal, and decondensation. This coincided with changes in the amide-I region (intensity at ν1620 vs. ν1640 cm(-1) ) denoting concomitant changes in protein secondary structure. Reduction in protein disulfide bonds resulted in a decreased value of the asymmetric to symmetric phosphate band intensity (ν1230/ν1086 cm(-1) ), suggesting that this band ratio is sensitive for the degree of chromatin condensation. Moreover, when analyzing spermatozoa from different individuals, it was found that the asymmetric/symmetric phosphate band ratio negatively correlated with the percentage of morphologically abnormal spermatozoa. PMID:26916383
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. PMID:25208386
This is a survey of new results related to the study of the full Navier-Stokes-Fourier system for a general compressible, viscous, and heat conducting fluid, and its asymptotic behaviour as the Mach number approaches zero. The classical Navier-Stokes system for an incompressible fluid with lift, combined with the corresponding heat equation, is a limiting case.
A new chemometric method based on absorbance ratios from Fourier transform infrared spectra was devised to analyze multicomponent biodegradable plastics. The method uses the BeerLambert law to directly compute individual component concentrations and weight losses before and after biodegradation of c...
Analysis of hybrid dielectric-plasmonic slot waveguide structures with 3D Fourier modal methods
Čtyroký, Jiří; Kwiecien, P.; Richter, I.
2013-01-01
Roč. 8, 23 March (2013), s. 130241-130246. ISSN 1990-2573 R&D Projects: GA ČR(CZ) GAP205/10/0046; GA MŠk OC09061 Institutional support: RVO:67985882 Keywords : Fourier modal method * Hybrid dielectric-plasmonic waveguide * Plasmonic waveguides Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.152, year: 2013
Schirmer, Sophie; Langbein, Frank
2014-01-01
We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and maximum likelihood estimation is superior to common techniques based on Fourier analysis. Even for simple two-parameter estimation problems, the Bayesian approach yields higher accuracy and precision for the parameter estimates obtained. It requires less dat...
Suriyawichitseranee, A.; Grigoriev, Yu. N.; Meleshko, S. V.
2014-01-01
The paper is devoted to group analysis of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. Using a particular class of solutions, the determining equation for the admitted Lie group is reduced to a partial differential equation for the source function. The latter equation is analyzed by an algebraic method. A complete group classification of the...
Ovalles, Fernando; Gallignani, Máximo; Rondón, Rebeca; Brunetto, Maria R.; Luna, Rafael
2009-01-01
The viability of employing flow analysis coupled to Fourier transform infrared spectroscopy (FA-FTIR) as a useful tool for quantitative measuring of magnesium sulphate in pharmaceuticals was explored, developed and validated. The method was based on mid-IR transmittance measurements of the peak-area belonging to the sulphate band around 1110 cm–1 and the use of an external calibration curve. Dynamic range was established over a concentration range from 1 to 50 mg.ml–1 , with a lim...
M. E. Ali; Nina Naquiah, A. N.; Mustafa, S; S. B. A. Hamid
2015-01-01
The agro-based production and consumption of frogs coupled with world-wide trading have been increased in the recent years giving rise to the risk of frog fat adulteration in expensive vegetable and marine oils. For the first time, we profiled here frog fats using Fourier Transform Infrared (FTIR) Spectroscopy coupled with multivariate principal component analysis (PCA). The comparison of the FTIR spectral absorbance intensities demonstrated linkage of frog fats to other edible fats and oils....
Glaucia Braz Alcantara; Andersson Barison; Maiara da Silva Santos; Luis P. S. Santos; José F. F. de Toledo; Antonio Gilberto Ferreira
2010-01-01
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 convent...
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...
This study presents an analysis of trabecular bone structure in standard radiographs using Fourier transforms and principal components analysis (PCA) to identify contributions to hip fracture risk. Radiographs were obtained from 26 hip fracture patients and 24 controls. They were digitised and five regions of interest (ROI) were identified from the femoral head and neck for analysis. The power spectrum was obtained from the Fourier transform of each region and three profiles were produced; a circular profile and profiles parallel and perpendicular to the preferred orientation of the trabeculae. PCA was used to generate a score from each profile, which we hypothesised could be used to discriminate between the fracture and control groups. The fractal dimension was also calculated for comparison. The area under the receiver operating characteristic curve (Az) discriminating the hip fracture cases from controls was calculated for each analysis. Texture analysis of standard radiographs using the fast Fourier transform yielded variables that were significantly associated with fracture and not significantly correlated with age, body mass index or femoral neck bone mineral density. The anisotropy of the trabecular structure was important; both the perpendicular and circular profiles were significantly better than the parallel-profile (P < 0.05). No significant differences resulted from using the various ROI within the proximal femur. For the best three groupings of profile (circular, parallel or perpendicular), method (PCA or fractal) and ROI (Az = 0.84 – 0.93), there were no significant correlations with femoral neck bone mineral density, age, or body mass index. PCA analysis was found to perform better than fractal analysis (P = 0.019). Both PCA and fractal analysis of the FFT data could discriminate successfully between the fracture and control groups, although PCA was significantly stronger than fractal dimension. This method appears to provide a powerful tool for
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.
Stahn, Thorsten
2008-01-01
Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on the total length (T), quality, and completeness of the observations. Except in a few simple cases, the effect of gaps in the data on measurement precision is poorly understood, in particular in Fourier space where the convolution of the observable with the observation window introduces correlations between different frequencies. Here we describe and implement a rather general method to retrieve maximum likelihood estimates of the oscillation parameters, taking into account the proper statistics of the observations. Our fitting method applies in complex Fourier space and exploits the phase information. We consider both solar-like stochastic oscillations and long-lived harmonic oscillations, plus random noise. Using numerical simulations, we demonstrate the existence of cases...
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).
The Navier-Stokes-Fourier system: From weak solutions to numerical analysis
Feireisl, Eduard
2015-01-01
Roč. 35, č. 3 (2015), s. 185-193. ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300.xml
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.
Fourier Transform Analysis of STM Images of Multilayer Graphene Moir\\'e Patterns
Joucken, Frédéric; Frising, Fernande; Sporken, Robert
2014-01-01
With the help of a simple model, we analyze Scanning Tunneling Microscopy images of simple and double moir\\'e patterns resulting from misoriented bi- and tri-layers graphene stacks. It is found that the model reproduces surprisingly well non-trivial features observed in the Fast Fourier Transform of the images. We point out difficulties due to those features in interpreting the patterns seen on the FFT.
Fourier Series, the DFT and Shape Modelling
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...
Chae, Byung Gyu
2014-05-20
We carry out a comparative analysis on a viewing angle change in Fresnel and Fourier holographic images reconstructed by a tilted plane wave. A tilted plane wave illuminating an on-axis hologram generates a diffractive wave carrying the holographic image in a paraxial region of a new diffraction axis. The reconstructed image in the Fresnel hologram is deformed along the new viewing direction, which is well described as Affine transformation. In the Fourier holographic image, the replica of the image is formed without its deformation when the hologram is placed in the front focal plane of the lens, whereas in the case of a hologram that is located at a distance different from a focal length, image deformation arises. This property is investigated through numerical simulation based on a wide-angle diffraction phenomenon. We also perform a similar interpretation for high-order diffraction images appearing in the sampled Fourier hologram and discuss a method for enlarging the viewing angle of the holographic image. PMID:24922205
Tavares, Paulo J.; Vaz, Mário A. P.
2013-03-01
Gradient range and spatial resolution in Fourier Transform Profilometry depend on the size of the filter window in reciprocal space. The proposed methods to date for the elimination of the fundamental frequency and enlargement of the filter window are either too computationally complex or depend on the possibility of using two frames, thus disabling the method's ability to cope with dynamic situations and subjecting the results to possible intensity changes between the two frame acquisitions. This article describes a simple method for using a single crossed fringe pattern to accomplish that objective, greatly improving the previously reported technique, whilst retaining its main advantages.
Fluorescence spectrum analysis using Fourier series modeling for Fluorescein solution in Ethanol
Hadi, Mahasin F
2011-01-01
We have measured the fluorescence spectrum for fluorescein solution in ethanol with concentration 1 {\\times} 10-3 mol/liter at different temperatures from room temperature to freezing point of solvent, (T = 153, 183, 223, 253, and 303 K) using liquid nitrogen. Table curve 2D version 5.01 program has been used to determine the fitting curve and fitting equation for each fluorescence spectrum. Fourier series (3 {\\times} 2) was the most suitable fitting equation for all spectra. Theoretical fluorescence spectrum of fluorescein in ethanol at T = 183K was calculated and compared with experimental fluorescence spectrum at the same temperature. There is a good similarity between them.
An application of linear programming duality to discrete Fourier analysis and additive problems
Croot, Ernie
2007-01-01
Suppose that f is a function from Z_p -> [0,1] (Z_p is my notation for the integers mod p, not the p-adics), and suppose that a_1,...,a_k are some places in Z_p. In some additive number theory applications it would be nice to perturb f slightly so that Fourier transform f^ vanishes at a_1,...,a_k, while additive properties are left intact. In the present paper, we show that even if we are unsuccessful in this, we can at least say something interesting by using the principle of the separating ...
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 Chaperone Complexes by Fourier Transform Ion Cyclotron Resonance Mass Spectrometry
Geels, R.B.J.
2008-01-01
Investigation of methodologies for analyses of noncovalently bound protein assemblies using Fourier transformation ion cyclotron resonance mass spectrometry (FT-ICR-MS) and quadrupole Time-of-Flight (qToF) mass spectrometry. Specifically, the co-chaperonins GroEL and gp31 are used to perform activation measurements on in the gas-phase and in the solution-phase. Both protein complexes are noncovalently bound homoheptamers of 72kDa and 84kDa respectively. They have a slight functional differenc...
Characterizing the Nanoscale Layers of Tomorrow___s Electronics An Application of Fourier Analysis
Payne, Christopher Bishop; /Princeton U. /SLAC
2012-08-24
Thin film applications are of great interest to the semiconductor industry due to the important role they play in cutting edge technology such as thin film solar cells. X-Ray Reflectivity (XRR) characterizes thin films in a non-destructive and efficient manner yet complications exist in extracting these characteristics from raw XRR data. This study developed and tested two different algorithms to extract quantity of layers and thickness information on the nanometer scale from XRR data. It was concluded that an algorithm involving a local averaging technique revealed this information clearly in Fourier space.
Drifting Sub-Pulse Analysis Using the Two-Dimensional Fourier Transform
Edwards, R,A; Stappers, B. W.
2002-01-01
The basic form of drifting sub-pulses is that of a periodicity whose phase depends (approximately linearly) on both pulse longitude and pulse number. As such, we argue that the two-dimensional Fourier transform of the longitude-time data (called the Two-Dimensional Fluctuation Spectrum; 2DFS) presents an ideal basis for studies of this phenomenon. We examine the 2DFS of a pulsar signal synthesized using the parameters of an empirical model for sub-pulse behaviour. We show that the transform c...
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.
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.
Piotr CZECH
2007-01-01
Full Text Available This paper presents the results of an experimental application of artificial neural network as a classifier of the degree of cracking of a tooth root in a gear wheel. The neural classifier was based on the artificial neural network of Probabilistic Neural Network type (PNN. The input data for the classifier was in a form of matrix composedof statistical measures, obtained from fast Fourier transform (FFT and principal component analysis (PCA. The identified model of toothed gear transmission, operating in a circulating power system, served for generation of the teaching and testing set applied for the experiment.
Air samples from F-Canyon effluents were collected at the F-Canyon stack and transported to a laboratory at the Savannah River Technology Center (SRTC) for analysis using a Fourier transform infrared spectrometer in conjunction with a multipath cell. Air samples were collected during the decladding and acid cuts of the dissolution of the irradiated aluminum-cladded slugs. The FTIR analyses of the air samples show the presence of NO2, NO, HNO2, N2O, SF6, and 85Kr during the dissolution cycle. The concentration time profiles of these effluents corresponded with expected release rates from the F-Canyon operations
Iwamoto, T. [Graduate School of Engineering, Hiroshima Univ., Kagamiyama, Hiroschima (Japan); Tsuta, T. [Faculty of Health Science, Hiroshima International Univ., Hiroshima (Japan)
2003-07-01
Due to strain-induced martensitic transformation, TRIP steel possesses favorable mechanical properties such as high strength, ductility and toughness. From SEM observations, it was clarified that the martensitic particles orient geometrically against the loading axis in the micro region. It is necessary to evaluate their orientations in TRIP steel to describe in detail deformation behavior of TRIP steel. Here, in order to discuss the geometrical orientation distribution of the micrograph, the Fourier and Wavelet transformation image analysis (FTIA and WTIA) are used. Then, the dependence of their orientation on plastic strain, temperature and stress state will be investigated by the FTIA and WTIA. (orig.)
ANALYSIS OF NON-FOURIER THERMAL BEHAVIOUR FOR MULTI-LAYER SKIN MODEL
Kuo-Chi Liu
2011-01-01
Full Text Available This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes' model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.
El-Agez, T M; Taya, S A, E-mail: staya@iugaza.edu.p [Physics Department, Islamic University of Gaza, PO Box 108, Gaza (Palestinian Territory, Occupied)
2011-02-15
A full description of a scanning ellipsometer that incorporates the rotation of two polarizing elements simultaneously is presented in detail in this paper. Both the polarizer and the analyzer are rotating synchronously such that the angular speed of the analyzer is two times that of the polarizer. The intensity of the detected light is modulated by the rotation of these elements and by the reflection from the surface of the sample. The ideal Fourier spectrum of this signal includes nine coefficients, of which five are even and the rest are odd. All of these coefficients contain valuable information about the physical properties of the studied sample. Therefore, it is feasible to extract the ellipsometric parameters {psi} and {Delta} as well as the optical parameters of the sample by using any set containing three different coefficients. A comparison between these sets regarding the effect of noise on these parameters and on the results is presented.
Zimmerman, G. A.; Gulkis, S.
1991-01-01
The sensitivity of a matched filter-detection system to a finite-duration continuous wave (CW) tone is compared with the sensitivities of a windowed discrete Fourier transform (DFT) system and an ideal bandpass filter-bank system. These comparisons are made in the context of the NASA Search for Extraterrestrial Intelligence (SETI) microwave observing project (MOP) sky survey. A review of the theory of polyphase-DFT filter banks and its relationship to the well-known windowed-DFT process is presented. The polyphase-DFT system approximates the ideal bandpass filter bank by using as few as eight filter taps per polyphase branch. An improvement in sensitivity of approx. 3 dB over a windowed-DFT system can be obtained by using the polyphase-DFT approach. Sidelobe rejection of the polyphase-DFT system is vastly superior to the windowed-DFT system, thereby improving its performance in the presence of radio frequency interference (RFI).
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.
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
The right ventricular (RV) emptying performance in patients with congenital heart diseases was investigated by temporal Fourier analysis of multigated cardiac blood-pool studies on a pixel-by-pixel basis. In 15 normal subjects, no significant differences were detected between the mean values of phase of left ventricle (LV) and RV. In patients with ventricular septal defect (VSD), cases with minimal interventricular left-to-right (L-to-R) shunt without pulmonary hypertension (PH) showed normal phase and amplitude images, and cases with moderate or large L-to-R shunt with hyperkinetic PH showed delay of RV phase compared to LV, however, in a case of Eisenmenger type VSD, as well as in patients with primary PH, RV phase lag was not detected. In patients with mild pulmonary stenosis with intact ventricular septum, phase and amplitude images were normal. A case with moderate pulmonary artery stenosis showed mild delay of RV phase. Distinct phase lag of RV was shown in patients with tetralogy of Fallot. Evaluation of RV emptying performance by temporal Fourier analysis is highly valuable for pathophysiologic investigation of congenital heart disease
Surrogates with random Fourier Phases
Raeth, Christoph
2008-01-01
The method of surrogates is widely used in the field of nonlinear data analysis for testing for weak nonlinearities. The two most commonly used algorithms for generating surrogates are the amplitude adjusted Fourier transform (AAFT) and the iterated amplitude adjusted Fourier transfom (IAAFT) algorithm. Both the AAFT and IAAFT algorithm conserve the amplitude distribution in real space and reproduce the power spectrum (PS) of the original data set very accurately. The basic assumption in both algorithms is that higher-order correlations can be wiped out using a Fourier phase randomization procedure. In both cases, however, the randomness of the Fourier phases is only imposed before the (first) Fourier back tranformation. Until now, it has not been studied how the subsequent remapping and iteration steps may affect the randomness of the phases. Using the Lorenz system as an example, we show that both algorithms may create surrogate realizations containing Fourier phase correlations. We present two new iterativ...
The Spectrum and Term Analysis of Co III Measured Using Fourier Transform and Grating Spectroscopy
Smillie, D. G.; Pickering, J. C.; Nave, G.; Smith, P. L.
2016-03-01
The spectrum of Co iii has been recorded in the region 1562-2564 Å (64,000 cm-1-39,000 cm-1) by Fourier transform (FT) spectroscopy, and in the region 1317-2500 Å (164,000 cm-1-40,000 cm-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-1 (approximately 0.2 mÅ at 2000 Å, or 1 part in 107), and 240 lines measured with grating spectroscopy with uncertainties between 5 and 10 mÅ. The wavelength calibration of 790 lines of Raassen & 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 3d64s and almost half of the 3d64p 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.
Fourier spatial frequency analysis for image classification: training the training set
Johnson, Timothy H.; Lhamo, Yigah; Shi, Lingyan; Alfano, Robert R.; Russell, Stewart
2016-04-01
The Directional Fourier Spatial Frequencies (DFSF) of a 2D image can identify similarity in spatial patterns within groups of related images. A Support Vector Machine (SVM) can then be used to classify images if the inter-image variance of the FSF in the training set is bounded. However, if variation in FSF increases with training set size, accuracy may decrease as the size of the training set increases. This calls for a method to identify a set of training images from among the originals that can form a vector basis for the entire class. Applying the Cauchy product method we extract the DFSF spectrum from radiographs of osteoporotic bone, and use it as a matched filter set to eliminate noise and image specific frequencies, and demonstrate that selection of a subset of superclassifiers from within a set of training images improves SVM accuracy. Central to this challenge is that the size of the search space can become computationally prohibitive for all but the smallest training sets. We are investigating methods to reduce the search space to identify an optimal subset of basis training images.
Voigt-function modeling in Fourier analysis of size- and strain-broadened X-ray diffraction peaks
Balzar, D.; Ledbetter, H. (Materials Science and Engineering Lab., National Inst. of Standards and Technology, Boulder, CO (United States))
1993-02-01
With the assumption that both size- and strain-broadened profiles of the pure-specimen function are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren-Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the 'hook' effect occurs when the Cauchy content of the size-broadened profile is underestimated. The ratio of volume-weighted and surface-weighted domain sizes can change from [proportional to]1.31, for the minimum allowed Cauchy content, to 2, when the size-broadened profile is given solely by a Cauchy function. If the distortion coefficient is approximated by a harmonic term, mean-square strains decrease linearly with increasing the averaging distance. The local strain is finite only in the case of purely Gaussian strain broadening, because strains are then independent of averaging distance. (orig.).
Wavelet-fractional Fourier transforms
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.
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. PMID:23769600
Caprioli, A.; Cigada, A.; Raveglia, D.
2007-02-01
Nowadays the power of data analysis tools like the wavelet decomposition of signals is well known and spread. On the other hand the theoretical advantages of such methods often fight with reality, when real field signals are collected and analysed: it sometimes comes out that this time-frequency approach somehow fails, demanding for a deeper insight into the kind of physical problem to be considered, and requiring a sort of "benchmark" between the traditional Fourier approach and the more recent time-frequency one. In this paper, sharply application-oriented, the possibilities offered by the wavelet techniques have been analysed: both the DSP specialist and the field engineer points of view have been joined to exploit the new approach of its best. A real problem has been considered, in which acceleration signals from a train bogie are collected and real-time analysed, to get a diagnostic tool to know the track condition of a subway line. This paper would like to look for a compromise point between complex mathematics based techniques, such as wavelet packet, sometimes hard to comprehend to the application engineer, and the physical meaning of these tools helping in fixing the real method limits. Therefore the aim is not just trying this analysis on an almost random process, like the accelerations measured on a running bogie, to locate defects, but rather a discussion on the development of the continuous and discrete wavelet transform, in comparison with the classical Fourier analysis or filter banks. Only the minimum mathematical background is provided in the text, with the needed references, to give tools fit for comprehending the physical meaning of the new tools, capable of sparing computing effort, while preserving or even improving the system effectiveness.
Fujii, Satoshi; Sato, Shinobu; Fukuda, Keisuke; Okinaga, Toshinori; Ariyoshi, Wataru; Usui, Michihiko; Nakashima, Keisuke; Nishihara, Tatsuji; Takenaka, Shigeori
2016-01-01
Diagnosis of periodontal disease by Fourier transform infrared (FT-IR) microscopic technique was achieved for saliva samples. Twenty-two saliva samples, collected from 10 patients with periodontal disease and 12 normal volunteers, were pre-processed and analyzed by FT-IR microscopy. We found that the periodontal samples showed a larger raw IR spectrum than the control samples. In addition, the shape of the second derivative spectrum was clearly different between the periodontal and control samples. Furthermore, the amount of saliva content and the mixture ratio were different between the two samples. Partial least squares discriminant analysis was used for the discrimination of periodontal samples based on the second derivative spectrum. The leave-one-out cross-validation discrimination accuracy was 94.3%. Thus, these results show that periodontal disease may be diagnosed by analyzing saliva samples with FT-IR microscopy. PMID:26860570
Schirmer, Sophie G.; Langbein, Frank C.
2015-02-01
We compare the accuracy, precision, and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modeling and maximum likelihood estimation is superior to common techniques based on Fourier analysis. Even for simple two-parameter estimation problems, the Bayesian approach yields higher accuracy and precision for the parameter estimates obtained. It requires less data, is more flexible in dealing with different model systems, can deal better with uncertainty in initial conditions and measurements, and enables adaptive refinement of the estimates. The comparison results show that this holds for measurements of large ensembles of spins and atoms limited by Gaussian noise as well as projection noise limited data from repeated single-shot measurements of a single quantum device.
Sample of Lincomycin were irradiated by means of gamma radiation (60Co) at dose rate ca. (408 kGy/h) in the range (3, 5, 15, 20)kGy in presence of air. Samples were investigated using two techniques: Thermal analysis (Differential Scanning Calorimetry (DSC) and Thermogravimetry (TG)) and Fourier Transform Infrared (FTIR). DSC purity study, which depends on Vant Hof equation, showed that the purity of Lincomycin reduced by means of gamma radiation. The purity of theses samples decreased by increasing the dose, and the purity of lincomycin was still above (99%) at dose (10 kGy). To follow up this effects, (FTIR) spectrums of these sample were recorded before and after irradiation. The two peaks at (1500 - 1750 Cm-1) which belong to amide group, and the peak at (1050 - 1100 Cm-1) which belongs to the S-C groups have reduced. (author)
Batina, N.; Reyna-Cordova, A.; Trinidad-Reyes, Y.;
2005-01-01
Thin films of crude oil samples were prepared for atomic force microscopy (AFM) analysis on the gold substrate. Sample preparation involved evaporation during a long (24 h) but mild thermal exposure (80 °C). Fourier transform infrared (FTIR) microscopy (reflectance spectroscopy) was employed...... to determinate the quality of the thin film surface, before the morphology characterization. The surface reflectance spectra were compared to direct transmittance FTIR of liquid oil samples. The two FTIR techniques showed different spectral characteristics related to oxygenated functionalities. This clearly...... 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...
We report experimental results on the correlations between welding penetration depth and the frequencies of the radiation from the welding pool. Various welding samples such as SUS304, brass, SUS316, etc. have been investigated with 2 kW CW Nd:YAG laser welding machine. The radiation signals from the plume generated by the interactions between the welding sample and laser with respect to the defocusing length was measured with fiber system collecting the plume signal. Analysis of the frequencies by using fast Fourier transform (FFT) shows that the penetration depth is deep as plume signal frequencies are low, shallow penetration depth for high frequencies. Frequencies up to 250 Hz for obtained signals can be analyzed with the discrete FFT. This is the useful method fur closed loop control of the laser power with respect to the welding penetration depth and is used for real time inspection of the welding quality
In the context of the fact that Einstein's general relativity has become an inevitable part of deep space missions, we will extend previous works on relativistic transformation between the proper time τ of a clock onboard a spacecraft orbiting Mars and the Barycentric Coordinate Time (TCB) by taking the clock offset into account and investigate its accessibility by Fourier analysis on the residuals after fitting the τ-TCB curve in terms of n-th order polynomials. We find that if the accuracy of a clock can achieve better than ∼ 10−5 s or ∼ 10−6 s (depending on the type of clock offset) in one year after calibration, the relativistic effects on the difference between τ and TCB will need to be carefully considered
Brüning, Rainer; Scholz, Peter; Ondruschka, Bernd
2005-07-01
The construction of a stage-II-screening device for heterogeneous catalysts in gas phase reactions under ambient pressure is described. The concentrations of the reaction products are determined by Fourier transform infrared analysis in combination with a chemometric interpretation of the obtained spectra. Thus, fast high-precision product analyses with complete mass balances are feasible, within the limits of accuracy of the measurements. The device is designed to screen up to 17 catalysts in one testing cycle. It is possible to determine temperature-conversion-selectivity dependencies as well as long-term measurements under constant conditions. With the help of the device described, the catalytic properties of new materials were parallel tested for the oxidative dehydrogenation of isopropanol.
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.
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.)
Civco, Daniel L.; Witharana, Chandi
2012-10-01
Pan-sharpening of moderate resolution multispectral remote sensing data with those of a higher spatial resolution is a standard practice in remote sensing image processing. This paper suggests a method by which the spatial properties of resolution merge products can be assessed. Whereas there are several accepted metrics, such as correlation and root mean square error, for quantifying the spectral integrity of fused images, relative to the original multispectral data, there is less agreement on a means by which to assess the spatial properties, relative to the original higher-resolution, pansharpening data. In addition to qualitative, visual, and somewhat subjective evaluation, quantitative measures used have included correlations between high-pass filtered panchromatic and fused images, gradient analysis, wavelet analysis, among others. None of these methods, however, fully exploits the spatial and structural information contained in the original high resolution and fused images. This paper proposes the use of the Fourier transform as a means to quantify the degree to which a fused image preserves the spatial properties of the pan-sharpening high resolution data. A highresolution 8-bit panchromatic image was altered to produce a set of nine different test images, as well as a random image. The Fourier Magnitude (FM) image was calculated for each of the datasets and compared via FM to FM image correlation. Furthermore, the following edge detection algorithms were applied to the original and altered images: (a) Canny; (b) Sobel; and (c) Laplacian. These edge-filtered images were compared, again by way of correlation, with the original edge-filtered panchromatic image. Results indicate that the proposed method of using FTMI as a means of assessing the spatial fidelity of high-resolution imagery used in the data fusion process outperforms the correlations produced by way of comparing edge-enhanced images.
Debnath, Lokenath
2012-07-01
The profound study of nature is the most fertile source of mathematical discoveries. Not only does this study, by offering a definite goal to research, have the advantage of excluding vague questions and futile calculations, but it is also a sure means of moulding analysis itself, and discerning those elements in it which it is still essential to know and which science ought to conserve. These fundamental elements are those which recur in all natural phenomena. Joseph Fourier pure mathematics enables us to discover the concepts and laws connecting them, which gives us the key to the understanding of the phenomena of nature. Albert Einstein 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 to his splendid research contributions to mathematical physics, pure and applied mathematics and his unprecedented public service accomplishments in the history of France. This is followed by historical comments about the significant and major impact of Fourier analysis on mathematical physics, probability and mathematical statistics, mathematical economics and many areas of pure and applied mathematics including geometry, harmonic analysis, signal analysis, wave propagation and wavelet analysis. Special attention is also given to the Fourier integral formula, Brownian motion and stochastic processes and many examples of applications including isoparametric inequality, everywhere continuous but nowhere differentiable functions, Heisenberg uncertainty principle, Dirichlets' theorem on primes in arithmetic progression, the Poisson summation formula and solutions of wave and diffusion equations. It is also shown that Fourier coefficients c n (t) in the Fourier expansion of a scalar field
A Novel Method for Comparative Analysis of DNA Sequences by Ramanujan-Fourier Transform
Yin, Changchuan; Yin, Xuemeng E.; Wang, Jiasong
2014-01-01
Alignment-free sequence analysis approaches provide important alternatives over multiple sequence alignment (MSA) in biological sequence analysis because alignment-free approaches have low computation complexity and are not dependent on high level of sequence identity, however, most of the existing alignment-free methods do not employ true full information content of sequences and thus can not accurately reveal similarities and differences among DNA sequences. We present a novel alignment-fre...
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.
Takeda, Kan; Maeda, Hisato; Nakagawa, Tsuyoshi; Ito, Tsunao; Yamaguchi, Nobuo; Matsuda, Akira (Mie Univ., Tsu (Japan). School of Medicine)
1989-12-01
Comparison of emptying patterns between left and right ventricles (LV, RV) was performed with Fourier analysis of gated blood-pool data in patients with tetralogy of Fallot (TF). Using global time-activity curves, the phase and amplitude at the first-harmonic component of Fourier series were calculated and emptying patterns of both ventricles were evaluated by phase difference {l brace}D(phase)=RV phase minus LV phase{r brace} and RV/LV amplitude ratio {l brace}R(amp){r brace}. In 20 patients with normal cardiac function, D(phase) was minimal (mean 2.0{plus minus}6.6 degrees) and R(amp) was less than 1.0 (mean 0.60{plus minus}0.19). In 11 patients with TF, D(phase) was significantly larger than normal, with a mean value of 24.3{plus minus}10.0 degrees (p<0.01) and became greater in a reversed proportion to the ratio of the pulmonary-to-systemic blood flow (p<0.01). In all but one cases with TF, R(amp) was greater than 1.0 with a mean value of 1.4{plus minus}0.4, significantly larger than normal (p<0.001). Furthermore, using time-activity curves approximated by terms up to the 3rd-harmonic component, the temporal difference in emptying patterns between both ventricles was investigated. In TF cases, the time from end-diastole to minimum count (T2) was significantly larger in RV than in LV (p<0.001). The elongated T2 interval of RV seemed to play an important role in producing RV phase lag. Thus, this non-invasive method is valuable for pathophysiologic investigation of patients with TF and can be of help in estimating the severity of their disease. (author).
We have developed a rapid method to screen large numbers of mutant plants for a broad range of cell wall phenotypes using Fourier transform infrared (FTIR) microspectroscopy of leaves. We established and validated a model that can discriminate between the leaves of wild-type and a previously defined set of cell-wall mutants of Arabidopsis. Exploratory principal component analysis indicated that mutants deficient in different cell-wall sugars can be distinguished from each other. Discrimination of cell-wall mutants from wild-type was independent of variability in starch content or additional unrelated mutations that might be present in a heavily mutagenised population. We then developed an analysis of FTIR spectra of leaves obtained from over 1000 mutagenised flax plants, and selected 59 plants whose spectral variation from wild-type was significantly out of the range of a wild-type population, determined by Mahalanobis distance. Cell wall sugars from the leaves of selected putative mutants were assayed by gas chromatography-mass spectrometry and 42 showed significant differences in neutral sugar composition. The FTIR spectra indicated that six of the remaining 17 plants have altered ester or protein content. We conclude that linear discriminant analysis of FTIR spectra is a robust method to identify a broad range of structural and architectural alterations in cell walls, appearing as a consequence of developmental regulation, environmental adaptation or genetic modification. (author)
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 63000K. 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 47000K. 31 references
Ashraf Adamu Ahmad
2015-11-01
Full Text Available The electronic intelligence (ELINT system is used by the military to detect, extract information and classify incoming radar signals. This work utilizes short time Fourier transform (STFT - time frequency distribution (TFD for inter-pulse analysis of the radar signal in order to estimate basic radar signal time parameters (pulse width and pulse repetition period. Four well-known windows functions of different and unique characteristics were used for the localization of STFT to determine their various effects on the analysis. The window functions are Hamming, Hanning, Bartlett and Blackman window functions. Monte Carlo simulation is carried out to determine the performance of the signal analysis in presence of additive white Gaussian noise (AWGN. Results show that the lower the transition of main lobe width and higher the peak side lobe, the better the performance of the window function irrespective of time parameter being estimated. This is because 100 percent probability of correct estimation is achieved at signal to noise ratio of about -2dB for Bartlett, 4dB for both Hamming and Hanning, and 9dB for Blackman.
Mass Spectrometry and Fourier Transform Infrared Spectroscopy for Analysis of Biological Materials
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.
Fourier-Domain Analysis of Hydriding Kinetics Using Pneumato-Chemical Impedance Spectroscopy
Millet, P.; C. Decaux; R. Ngameni; Guymont, M.
2007-01-01
Analysis of phase transformation processes observed in hydrogen absorbing materials (pure metals, alloys, or compounds) is still a matter of active research. Using pneumato-chemical impedance spectroscopy (PIS), it is now possible to analyze the mechanism of hydriding reactions induced by the gas phase. Experimental impedance diagrams, measured on activated LaNi5 in single- and two-phase domains, are reported in this paper. It is shown that their shape is mostly affected by the slope of the i...
Complex wavenumber Fourier analysis of the B-spline based finite element method
Kolman, Radek; Plešek, Jiří; Okrouhlík, Miloslav
2014-01-01
Roč. 51, č. 2 (2014), s. 348-359. ISSN 0165-2125 R&D Projects: GA ČR(CZ) GAP101/11/0288; GA ČR(CZ) GAP101/12/2315; GA ČR GPP101/10/P376; GA ČR GA101/09/1630 Institutional support: RVO:61388998 Keywords : elastic wave propagation * dispersion errors * B-spline * finite element method * isogeometric analysis Subject RIV: JR - Other Machinery Impact factor: 1.513, year: 2014 http://www.sciencedirect.com/science/article/pii/S0165212513001479
Zhou, Xibin; Shi, Quan; Zhang, Yahe; Zhao, Suoqi; Zhang, Rui; Chung, Keng H; Xu, Chunming
2012-04-01
A novel technique was developed for characterization of saturated hydrocarbons. Linear alkanes were selectively oxidized to ketones by ruthenium ion catalyzed oxidation (RICO). Branched and cyclic alkanes were oxidized to alcohols and ketones. The ketones were then reduced to alcohols by lithium aluminum hydride (LiAlH(4)). The monohydric alcohols (O(1)) in the products obtained from the RICO and RICO-LiAlH(4) reduction reactions were characterized using negative-ion electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) for identification of iso-paraffins, acyclic paraffins and cyclic paraffins. Various model saturated compounds were used to determine the RICO reaction and ionization selectivity. The results from the FTICR MS analysis on the petroleum distillates derived saturated fraction were in agreement with those from field ionization gas chromatography time-of-flight mass spectrometry (FI GC-TOF MS) analysis. The technique was also used to characterize a petroleum vacuum residue (VR) derived saturates. The results showed that the saturated molecules in the VR contained up to 11 cyclic rings, and the maximum carbon number was up to 92. PMID:22424498
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.
The use of Fourier transform (FT) surface-enhanced Raman scattering for biochemical analysis
Jeffers, Robert Butler
Surface-enhanced Raman scattering (SERS) is a powerful spectroscopic technique that has created exciting opportunities in the field of bioanalytical chemistry, where it combines ultrasensitive detection of biologically relevant molecules with vibrational spectroscopy. Due to the difficulties in preparing reproducible SERS active substrates, SERS has been mainly used as a qualitative tool. In order for SERS to be utilized as a viable tool for quantitative analysis, simple, facile SERS substrates which generate clean, highly reproducible signals must be developed. This dissertation deals with the evaluation of three different methods of SERS that led to the development of a novel substrate for the analysis of biological molecules. In this dissertation, I demonstrated the generation of a SERS signal from pyridine adsorbed to the surface of a roughened silver electrode. The Raman signal was detected utilizing a remote fiber optic probe dispersive Raman instrument. The necessary parameters for generating the optimal SERS signal were established. The SERS spectrum of pyridine was successfully characterized. The synthesis of silver colloid solutions for use as a SERS active substrate was demonstrated. Two different synthetic methods were utilized and the conditions for optimal SERS signal strength were established. SERS signals from solutions of tryptophan were successfully generated and detected using an FT-Raman spectrometer. In this dissertation. I report the successful chemical deposition of a thin silver film on the surface of a quartz/glass fiber filter for use as a SERS active substrate. The successful detection of the SERS signal of solutions of phenylalanine and tryptophan utilizing the silver-coated filters and a FT-Raman instrument was demonstrated. Significant progress was made to develop a quantifiable SERS method utilizing the silver-coated filters. The silver-coated filter SERS method presented here is a novel and promising method for biochemical analysis
An X-ray Fourier line shape analysis in cold-worked hexagonal titanium base alloys
X-ray diffraction is an established technique for the analysis of microstructural parameters such as domain sizes, microstrains within the domains, and deformation fault densities in the deformed state of metals and alloys. These microstructural parameters influence the flow of dislocation in the lattice under deformation and thus regulate the strength and hardenability of the materials. The evaluation of such microdefects is this necessary for understanding the mechanical behavior of materials. In the present study, considering the wide applicability of titanium-base alloys in aviation industry, two alloy systems, i.e., titanium-base aluminum and titanium-base zirconium, have been selected. A number of X-ray diffraction profiles belonging to both fault-affected (H - K = 3N ± 1) and fault-unaffected (H - K = 3N) reflections have been recorded by a SIEMENS Kristolloflex-4 diffractometer using Cu Kα radiation, and the profiles have been analyzed to evaluate the microstructural parameters
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.
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.…
Hyatt, C J; Maughan, D W
1994-01-01
A method for determining and analyzing the wing beat frequency in Diptera is presented. This method uses an optical tachometer to measure Diptera wing movement during flight. The resulting signal from the optical measurement is analyzed using a Fast Fourier Transform (FFT) technique, and the dominant frequency peak in the Fourier spectrum is selected as the wing beat frequency. Also described is a method for determining quantitatively the degree of variability of the wing beat frequency about...
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...
Ross, Charles W.; Simonsick, William J.; Bogusky, Michael J.; Celikay, Recep W.; Guare, James P.; Newton, Randall C.
2016-01-01
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. PMID:27367671
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.
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.
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.
Ruíz, A; Ayora Cañada, M J; Lendl, B
2001-02-01
The development of an automated, rapid and highly precise method for determination of the peroxide value in edible oils based on a continuous flow system and Fourier transform infrared (FTIR) spectroscopic detection is described. The sample stream was mixed with a solvent mixture consisting of 25% (v/v) toluene in hexanol which contained triphenylphosphine (TPP). The hydroperoxides present in the sample reacted stoichiometrically with TPP to give triphenylphosphine oxide (TPPO) which has a characteristic and intense absorption band at 542 cm-1. A 10% (m/v) TPP solution in the solvent mixture and a 100 cm reaction coil were necessary for complete reaction. FTIR transmission spectra were recorded using a flow cell equipped with CsI windows having an optical pathlength of 100 microns. By using tert-butyl hydroperoxide spiked oil standards and evaluation of the band formed at 542 cm-1 a linear calibration graph covering the range 1-100 PV (peroxide value; mequiv O2 kg-1 oil) was obtained. The relative standard deviation was 0.23% (n = 11) and the throughput 24 samples h-1. The developed system was also applied to the determination of PV in olive, sunflower and corn oils, showing good agreement with the official reference method of the European Community which is based on titration using organic solvents. The results obtained clearly show that the developed method is superior to the standard wet chemical method, hence suggesting its application in routine analysis and quality control. PMID:11235111
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.
For many years, the IAEA has fostered the more widespread use of stable isotope techniques to assess body composition in different population groups to address priority areas in public health nutrition in Member States. The objective is to support national and regional nutrition projects through both the IAEA's technical cooperation programme and its coordinated research projects. In particular, during the last few years, the increased access to analyses of deuterium enrichment by Fourier transform infrared (FTIR) spectrometry has increased the application of this technique in Africa, Asia and Latin America. This publication was developed by an international group of experts to provide practical, hands-on guidance in the use of this technique in settings where the analysis of deuterium enrichment in saliva samples will be made by FTIR. It is targeted at new users of this technique, for example nutritionists, analytical chemists and other professionals. More detailed information on the theoretical background and the practical application of state of the art methodologies to monitor changes in body composition can be found in an IAEA publication entitled Assessment of Body Composition and Total Energy Expenditure in Humans by Stable Isotope Techniques (IAEA Human Health Series No. 3)
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.
The clinical usefulness of Fourier analysis of multi-gated cardiac blood-pool data was evaluated in 18 subjects with normal cardiac functions and 14 patients with complex cardiac anomalies (ten with tetralogy of Fallot, two with tricuspid atresia (TA), one with double-outlet right ventricle (DORV), and one with Ebstein's anomaly (EA)). Using global ventricular time-activity curves, the phase and amplitude at fundamental frequency were calculated, and emptying patterns of the left and right ventricles (LV, RV) were evaluated by phase difference [D(phase)=RV phase minus LV phase] and amplitude ratio of RV to LV [R(amp)]. In patients with TOF, mean values of D (phase) and R(amp) were 25.3+-10.5 degrees and 13.5+-0.49 respectively and significantly larger than those of normal subjects (p<0.001). D (phase) became larger in inverse proportion to the ratio of pulmonary-to-systemic blood flow and there was an inverse linear correlation between these two variables (r=-0.830, p<0.01). On visual interpretation of functional images, the dynamic property of hypoplastic ventricles could be easily estimated in patients with TA or DORV. In a case with EA, the atrialized RV was shown clearly as a hypokinetic, atrial phase area. This method is valuable for pathophysiologic investigation of diseases with complex cardiac anomalies. (author)
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.
Samsir, Sri A’jilah; Bunawan, Hamidun; Yen, Choong Chee; Noor, Normah Mohd
2016-01-01
In this dataset, we distinguish 15 accessions of Garcinia mangostana from Peninsular Malaysia using Fourier transform-infrared spectroscopy coupled with chemometric analysis. We found that the position and intensity of characteristic peaks at 3600–3100 cm− 1 in IR spectra allowed discrimination of G. mangostana from different locations. Further principal component analysis (PCA) of all the accessions suggests the two main clusters were formed: samples from Johor, Melaka, and Negeri Sembilan (...
Ogawa, T; Shibata, A; Maeda, Y; Uno, Y; Okano, M; Nishizaki, K; Ohsaki, K
2003-06-01
A quite rare case of nasopharyngeal calculus in a woman in her twenties associated with the nasal discharge of pseudomonas infection was reported. As the substance was irregularly large in size, we extracted it partially by piecemeal resection using forceps and also by cracking technique using the holmium yttrium-aluminum-garnet (YAG) laser, under saline irrigation and stereotactic microscopic navigator (SMN) system under endoscopic observation. The substance was firmly fixed to the pharyngeal tonsil bed. The final extract was a small piece of singly folded bandage, which is probably the focal background for calculus formation. In a cross section of calculus specimen removed during surgery, Fourier transform infrared (FT-IR) analysis revealed that a) signal ratio of methylene group (organic substance) to amide I (protein) was 21.6% at the nasal cavity side, gradually decreased toward nasal mucous membrane showing approximate 50%, b) signal ratio of amide I to P04(3-) (inorganic substance) ranged between 17.7% and 26.7% at the different sites and inside the calculus, the protein content was approximate 1/5 of the inorganic substance, and c) signal ratio of the methylene group to amide I at the nasal cavity site showed that their contents were almost equal. The quantity of the organic substance was estimated at approximate 1/2 quantity of the protein at both the central part and the part contacted with the mucous membrane. From these results, it seems that throughout the course of calculus growth, both inorganic substance and protein remain almost constant inside the calculus, while organic substance is released from the internal part of the calculus being probably formed at an early stage. PMID:12899453
Gas chromatography/mass spectrometry(GC/MS) is commonly used for oil fingerprinting and provides investigators with good forensic data. However, new challenges face oil spill forensic chemistry with the growing use of biodiesel as well as the recycling and reprocessing of used oil, particularly lubricating oils. This paper demonstrated that Fourier transform infrared (FTIR) spectroscopy may be a fast, cost effective and complementary method for forensic analysis of biodiesels (fatty acid methyl esters) and lubricating oils. Attenuated total reflectance (ATR)-FTIR spectroscopy was shown to be an interesting analytic method because of its use in monitoring and quantifying minor chemical compounds in sample matrices and its ability to identify a broad range or organic compounds. Unlike chromatography, FTIR spectroscopy with ATR can provide results without compound separation or lengthy sample preparation steps. This study described the combined use of GC and ATR-FTIR in environmental oil spill identification through the matching of source lube oil samples with artificially weathered samples. Samples recovered from a biodiesel spill incident were also investigated. ATR-FTIR provided detailed spectral information for rapid lube oil differentiation. This study was part of a continuing effort to develop a methodology to deal with chemical spills of unknown origin, which is an important aspect in environmental protection and emergency preparedness. This method was only successfully applied to the short term artificially weathered and fresh lube oil characterization, and to limited cases of biodiesel spills. It was concluded that further validation tests are needed to determine if this method can be applied to real-world weather lube oil samples. 10 refs., 11 figs.
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 ...
Fourier analysis of blood plasma laser images phase maps in the diagnosis of cancer in human organs
Ushenko, A. G.; Boychuk, T. M.; Mincer, O. P.; Kushnerick, L. Y.; Angelsky, P. O.; Bodnar, N. B.; Oleinichenko, B. P.
2013-09-01
The optical model of polycrystalline networks of histological sections of rectum wall is suggested. The results of investigating the interrelation between the values of statistical (statistical moments of the 1st-4th order) parameters are presented. They characterize the coordinate polarization distributions of Fourier transforms of laser images of blood plasma and oncological changes. The diagnostic criteria of rectum cancer are determined.
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...
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
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.
Stunned myocardium of right ventricle was studied by radionuclide angiography (RNA) and thallium myocardial scintigraphy (TL) in 39 patients with inferior myocardial infarction (MI) with and without right ventricular myocardial infarction (RVMI). RNA was performed within 1 week of the onset (acute phase) and after 1 month, when exercise cardiac scintigraphy (EX-TL) was also performed. The ejection fraction (EF) of each ventricle calculated from RNA and the phase and amplitude evaluated visually and quantitatively by Fourier analysis were compared between the acute phase and 1 month after the onset of MI. The degree of visualization of right ventricle (RV) was examined in EX-TL 1 month after the onset. In RNA obtained in the acute MI, abnormalities in RV (delayed phase or low amplitude image) were observed in 18 (46%) but not in 21 (54%) of the 39 patients (N group). Of those 18 patients, the abnormalities in RV alleviated in 11 (RVMI-A group) but persisted in 7 (RVMI-B group) in RNA obtained 1 month after the onset. In the acute phase, RVEF was 39.4±10.4% in N group, 30.8±5.3% in RVMI-A group, and 29.6±8.9% in RVMI-B group, with significant differences between N group and the other two groups, but no significant difference between RVMI-A and RVMI-B groups. After 1 month, RVEF was 40.1±10.1% in N group, 42.2±8.4% in RVMI-A group and 32.2±9.8% in RVMI-B group, being improved in RVMI-A group and showing a significant difference as compared with RVMI-B group. In EX-TL of RVMI-A group, RV was visible although the uptake of TL was reduced in the entire right ventricle. In RVMI-B group, only part of the right ventricular free wall was visible with defects in the other areas of RV. The sign of RVMI showed improvements in many of the patients after the acute phase, and their condition was considered to have been so-called stunned myocardium, which is a complex of symptoms of reversible myocardial ischemia, rather than RVMI. (author)
Full text: Determinants of bone fracture risk include indices of bone 'quantity' such as bone mineral content (BMC, mineral mass per unit scanned bone length), plus 'environmental' (eg impact force) and 'quality' factors (Melton L.J. III et al, Bone and Min 2: 321, 1987). Bone 'quality' refers largely to the micro-geometry of bone (∼ 10-200μ), but has been less well studied because of the need for bone slices from (invasive) bone biopsies. Such studies often compare the geometry of trabecular networks (eg trabecular bone volume, trabecular number) with clinical outcomes such as fracture rates. Another (invasive) approach is to examine the two-dimensional (2-D) Fourier transform (FT) of a high-resolution radiographic image of the bone slice, since structural information is in theory encoded in the 2-D spatial-frequency (ν) spectrum. Additionally, the FT method can be applied to bone images obtained in-vivo, though superposition of information from the third dimension is a major confounding factor in their interpretation. Quantitative radiography of the ultradistal (UD) forearm permits determination of BMC (Price R et al; ACPSEM 6: 128- 137, 1983 and ACPSEM 11: 36-43, 1988), and (as a bonus) reveals a pattern (suitable for FT analysis) of the radiographic shadows of the 3-D trabecular network projected onto the image plane. Hemiplegia is associated with excessive bone loss in the paralysed (hemi) forearm, and is a model for the study of immobilisation osteoporosis. Thus, by comparing hemiplegia-induced changes in BMC and trabecular structure, derived from the same in vivo radiographic image, it is possible to compare directly the effects of disease on both bone quantity and quality, using the image of the non-paralysed (non-hemi) arm as a control. Seventy-four patients with hemiplegia of duration 3.6±3.6 (Mean±SD) years were studied cross-sectionally for radiographic BMC of their normal and paralysed UD forearms in AP view, each arm in duplicate. Methods
Dehaeck, S.; Colinet, P.
2016-02-01
When analysing fringe images, wavelet and windowed Fourier ridge algorithms allow to extract phase and local frequency even in the presence of considerable noise levels. However, the precision of the local frequency information is often limited by the relatively small number of analysing frequencies used in practice. This on account of the direct trade-off between frequency precision and processing time, which can become prohibitive in some cases. In the present paper, a method is shown capable of reducing the processing time by a factor 3 for the wavelet ridge technique and by up to 15 times for the windowed Fourier ridge algorithm. This is accomplished by a 3-point Gaussian ridge interpolation. This approach is also shown to lead to an improved frequency precision for moderate noise levels.
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...
Tátrai, Erika; Ranganathan, Sudarshan; Ferencz, Mária; Debuc, Delia Cabrera; Somfai, Gábor Márk
2011-05-01
Purpose: To compare thickness measurements between Fourier-domain optical coherence tomography (FD-OCT) and time-domain OCT images analyzed with a custom-built OCT retinal image analysis software (OCTRIMA). Methods: Macular mapping (MM) by StratusOCT and MM5 and MM6 scanning protocols by an RTVue-100 FD-OCT device are performed on 11 subjects with no retinal pathology. Retinal thickness (RT) and the thickness of the ganglion cell complex (GCC) obtained with the MM6 protocol are compared for each early treatment diabetic retinopathy study (ETDRS)-like region with corresponding results obtained with OCTRIMA. RT results are compared by analysis of variance with Dunnett post hoc test, while GCC results are compared by paired t-test. Results: A high correlation is obtained for the RT between OCTRIMA and MM5 and MM6 protocols. In all regions, the StratusOCT provide the lowest RT values (mean difference 43 +/- 8 μm compared to OCTRIMA, and 42 +/- 14 μm compared to RTVue MM6). All RTVue GCC measurements were significantly thicker (mean difference between 6 and 12 μm) than the GCC measurements of OCTRIMA. Conclusion: High correspondence of RT measurements is obtained not only for RT but also for the segmentation of intraretinal layers between FD-OCT and StratusOCT-derived OCTRIMA analysis. However, a correction factor is required to compensate for OCT-specific differences to make measurements more comparable to any available OCT device.
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. PMID:27257614
Weighted Fourier and Fourier-Stieltjes Algebras
Amin Mahmoodi
2010-10-01
Full Text Available Let $G$ be a locally compact group and $omega$ be a symmetric weight function on $G$. We define a co-product $Gamma_omega$ on the weighted algebra $L^infty(G, omega^{-1}$ of essentially $omega$-bounded Borel measurable functions on $G$ and show that $L^infty(G, omega^{-1}$ becomes a Kac algebra with natural co-inverse $kappa_omega$ and Haar weight $phi_omega$. We use the machinery of Kac algebras to introduce the weighted Fourier and Fourier-Stieltjes algebra $ A(G,omega^{-1}$ and $ B(G,omega^{-1}$ of $G$.
Weighted Fourier and Fourier-Stieltjes Algebras
Amin Mahmoodi
2010-01-01
Let $G$ be a locally compact group and $omega$ be a symmetric weight function on $G$. We define a co-product $Gamma_omega$ on the weighted algebra $L^infty(G, omega^{-1})$ of essentially $omega$-bounded Borel measurable functions on $G$ and show that $L^infty(G, omega^{-1})$ becomes a Kac algebra with natural co-inverse $kappa_omega$ and Haar weight $phi_omega$. We use the machinery of Kac algebras to introduce the weighted Fourier and Fourier-Stieltjes algebra $ A(G,omega^{-1})$ and $ B(G,o...
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 phthalat...... 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....
Bakewell, D J, E-mail: d.bakewell@liv.ac.uk [Department of Electrical Engineering and Electronics, University of Liverpool, Brownlow Hill, Liverpool, L69 3GJ (United Kingdom)
2011-03-02
A Fourier-Bessel (FB) series solution is derived that describes the dielectrophoretic-driven transport of nanoparticles in a microdevice. The solution assumes that the nanoparticles do not interact and is based on a linear Fokker-Planck equation that includes the effects of thermal diffusion. The solution is applicable for a dielectrophoretic force that varies exponentially in the microdevice, such as in the far field of planar interdigitated arrays. Important applications of the FB solution are demonstrated that include simulation and system classification of nanoparticle movement under the action of weak and strong dielectrophoretic forces. Methods are demonstrated for the inverse process of estimating model parameters, such as the dielectrophoretic force, based on nanoparticle concentration data obtained experimentally. Data decomposition into separate spatial and temporal modes is demonstrated and Fourier transformation of the series solution yields a representation in the frequency domain. The frequency response predicted by transforming the time-dependent FB solution indicates the presence of a dielectrophoresis modulation bandwidth that concurs with observations of preliminary experiments.
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.
Abdulla, Hussain A N; Sleighter, Rachel L; Hatcher, Patrick G
2013-04-16
Two-dimensional (2D) correlation analysis was applied to 20 Fourier transform ion cyclotron resonance mass spectra (FTICR-MS) of ultrafiltered dissolved organic matter samples from a salinity transect of the lower Chesapeake Bay. We were able to investigate the chemical changes in the dissolved organic matter pool at the molecular level and classify the individual peaks based on their biogeochemical reactivity. The power of this technique is its ability to be used on either the presence/absence of the individual peaks or their normalized magnitudes. The presence or absence of the peaks are utilized to identify the reactivity and correlation between peaks that plot in different regions of the van Krevelen diagram, whereas the normalized magnitudes are used to correlate the changes among individual peaks. One of the promising advantages of 2D correlation of FTICR-MS data is the ability to associate the variations of the individual peaks with the changes in the functional groups that are measured by other spectroscopic techniques. This approach takes us one step further from identifying molecular formulas to proposing chemical structures. PMID:23472832
Klein, Thomas; Wieser, Wolfgang; Biedermann, Benjamin R; Eigenwillig, Christoph M; Palte, Gesa; Huber, Robert
2008-12-01
We demonstrate a Raman-pumped Fourier-domain mode-locked (FDML) fiber laser and optical coherence tomography imaging with this source. The wavelength sweep range of only 30 nm centered around 1550 nm results in limited axial resolution, hence a nonbiological sample is imaged. An output power of 1.9 mW was achieved at a sweep rate of 66 kHz and a maximum ranging depth of ~2.5 cm. Roll-off characteristics are found to be similar to FDML lasers with semiconductor optical amplifiers as gain media. The application of Raman gain also enables unperturbed cavity ring-down experiments in FDML lasers for the first time, providing direct access to the photon lifetime in the laser cavity. Good agreement with nonswept cw operation is proof of the stationary operation of FDML lasers. PMID:19037436
Generalized Fourier transforms classes
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....
Hu, J.; Pavel, I.; Moigno, D.; Wumaier, M.; Kiefer, W.; Chen, Z.; Ye, Y.; Wu, Q.; Huang, Q.; Chen, S.; Niu, F.; Gu, Y.
2003-07-01
The Fourier-transform Raman (FT-Raman) and infrared (FT-IR) spectra of 2-nitro-tetraphenylporphyrin (2-NO 2-TPP), nickel-2-nitro-tetraphenylporphyrin (Ni-2-NO 2-TPP), zinc-2-nitro-tetraphenylporphyrin (Zn-2-NO 2-TPP) and copper-2-nitro-tetraphenylporphyrin (Cu-2-NO 2-TPP) were acquired for the first time and carefully assigned and discussed. The effects of a β-NO 2 group and the influence of the central metal on the molecular symmetry and vibrational spectra of the porphyrin macrocycle were also examined. The bands at 1323-1339, 1516-1526 and 961-971 cm -1 were attributed to the symmetric and asymmetric stretching vibration of the NO 2 group and to the stretching vibration of the C βN bond, respectively, which connects the NO 2 group with the β-carbon of the porphyrin macrocycle. These bands can act as a marker to distinguish β-NO 2 TPPs from other β-substituent TPPs. Cu-2-NO 2-TPP has a C4 ν molecular symmetry, which is different from those of Ni-2-NO 2-TPP and Zn-2-NO 2-TPP, i.e. D4 h.
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...
Winding numbers and Fourier series
Kahane, Jean-Pierre
2010-01-01
This is an expository talk on a topic of classical analysis, arising from the VMO theory of the topological degree due to Br\\'ezis and Nirenberg (1995). We sketch the history of the subject and some of its recent developments. The paper is organized as a sequence of questions. Most of them, in particular the last one, deal with Fourier series of continuous functions of constant absolute value. One of them contains new results on the comparison of summation processes.
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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.
Akyuz, Sevim; Akyuz, Tanil; Mukhamedshina, Nuranya M.; Mirsagatova, A. Adiba; Basaran, Sait; Cakan, Banu
2012-05-01
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.