2012 • 312 Pages • 12.38 MB • English

Posted April 14, 2020 • Uploaded
by winfield52

PREVIEW PDF

Page 1

FOURIER TRANSFORM APPLICATIONS Edited by Salih Mohammed Salih

Page 2

Fourier Transform Applications Edited by Salih Mohammed Salih Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2012 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. As for readers, this license allows users to download, copy and build upon published chapters even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Vana Persen Technical Editor Teodora Smiljanic Cover Designer InTech Design Team First published April, 2012 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from [email protected] Fourier Transform Applications, Edited by Salih Mohammed Salih p. cm. ISBN 978-953-51-0518-3

Page 3

Page 4

Page 5

Contents Preface IX Part 1 Electromagnetic Field and Microwave Applications 1 Chapter 1 Computation of Transient Near-Field Radiated by Electronic Devices from Frequency Data 3 Blaise Ravelo and Yang Liu Chapter 2 Impulse-Regime Analysis of Novel Optically-Inspired Phenomena at Microwaves 27 J. Sebastian Gomez-Diaz, Alejandro Alvarez-Melcon, Shulabh Gupta and Christophe Caloz Chapter 3 Fourier Transform Application in the Computation of Lightning Electromagnetic Field 57 Vesna Javor Chapter 4 Robust Beamforming and DOA Estimation 87 Liu Congfeng Chapter 5 Analysis of Long-Periodic Fluctuations of Solar Microwave Radiation, as a Way for Diagnostics of Coronal Magnetic Loops Dynamics 143 Maxim L. Khodachenko, Albert G. Kislyakov and Eugeny I. Shkelev Part 2 Medical Applications 167 Chapter 6 Spectral Analysis of Heart Rate Variability in Women 169 Ester da Silva, Ana Cristina S. Rebelo, Nayara Y. Tamburús, Mariana R. Salviati, Marcio Clementino S. Santos and Roberta S. Zuttin Chapter 7 Cortical Specification of a Fast Fourier Transform Supports a Convolution Model of Visual Perception 181 Phillip Sheridan

Page 6

VI Contents Chapter 8 Spectral Analysis of Global Behaviour of C. Elegans Chromosomes 205 Afef Elloumi Oueslati, Imen Messaoudi, Zied Lachiri and Noureddine Ellouze Part 3 Fourier and Helbert Transform Applications 229 Chapter 9 The Fourier Convolution Theorem over Finite Fields: Extensions of Its Application to Error Control Coding 231 Eric Sakk and Schinnel Small Chapter 10 Application of the Weighted Energy Method in the Partial Fourier Space to Linearized Viscous Conservation Laws with Non-Convex Condition 249 Yoshihiro Ueda Chapter 11 Fourier Transform Methods for Option Pricing 265 Deng Ding Chapter 12 Hilbert Transform and Applications 291 Yi-Wen Liu

Page 7

Page 8

Page 9

Preface During the preparation of this book, we found that almost all the textbooks on signal analysis have a section devoted to the Fourier transform theory. The Fourier transform is a mathematical operation with many applications in physics, and engineering that express a mathematical function of time as a function of frequency, known as its frequency spectrum; Fourier's theorem guarantees that this can always be done. The basic idea behind all those horrible looking formulas is rather simple, even fascinating: it is possible to form any function as a summation of a series of sine and cosine terms of increasing frequency. In other words, any space or time varying data can be transformed into a different domain called the frequency space. A fellow called Joseph Fourier first came up with the idea in the 19th century, and it was proven to be useful in various applications, mainly in signal processing. As far as we can tell, Gauss was the first to propose the techniques that we now call the Fast Fourier Transform (FFT) for calculating the coefficients in a trigonometric expansion of an asteroid's orbit in 1805. However, it was the seminal paper by Cooley and Tukey in 1965 that caught the attention of the science and engineering community and, in a way, founded the discipline of digital signal processing. While the Discrete Fourier Transform (DFT) can be applied to any complex valued series, in practice for large series it can take considerable time to compute, the time taken being proportional to the square of the number on points in the series. It is hard to overemphasis the importance of the DFT, convolution, and fast algorithms. The FFT may be the most important numerical algorithm in science, engineering, and applied mathematics. New theoretical results are still appearing, advances in computers and hardware continually restate the basic questions, and new applications open new areas for research. It is hoped that this book will provide the background, references and incentive to encourage further research and results in this area as well as provide tools for practical applications. One of the attractive features of this book is the inclusion of extensive simple, but practical, examples that expose the reader to real- life signal analysis problems, which has been made possible by the use of computers in solving practical design problems. The aim of this book is to expand the applications of Fourier transform into main three sections: The first section deals with Electromagnetic Field and Microwave Applications. It consists of five chapters. The chapters are related to: the computation of transient near-field radiated by electronic devices, analysis of novel optically-inspired phenomena at

Page 10

X Preface microwaves, the computation of lightning electromagnetic field, beamforming and DOA estimation, and the solar microwave radiation. The chapters of the second section discuss some advanced methods used in Fourier transform analysis which are related to the Medical Applications. This section consists of three chapters. The chapters are related to: spectral analysis of global behaviour of C. Elegans chromosomes, spectral analysis of heart rate variability in women, and the cortical specification of a fast Fourier transform supports a convolution model of visual perception. The third section includes the Fourier and Helbert Transform Applications. This section consists of four chapters. The chapters are concerns to: the Fourier convolution theorem over finite fields (error control coding), application of the weighted energy method in the partial Fourier space to linearized viscous conservation laws with non- convex condition, Fourier transform methods for option pricing, and the Hilbert transform applications. Finally, we would like to thank all the authors who have participated in this book for their valuable contribution. Also we would like to thank all the reviewers for their valuable notes. While there is no doubt that this book may have omitted some significant findings in the Fourier transform field, we hope the information included will be useful for electrical engineers, control engineers, communication engineers, signal processing engineers, medical researchers, and the mathematicians, in addition to the academic researchers working in the above fields. Salih Mohammed Salih College of Engineering University of Anbar Iraq

Fourier Transform Applications

2012 • 310 Pages • 16.34 MB

Fourier Series • Fourier Transform • Laplace Transform • Applications of Laplace Transform • Z ...

2011 • 77 Pages • 1.11 MB

Applications of the Fourier Transform

2013 • 87 Pages • 4.66 MB

Fast Fourier Transform and Its Applications

1988 • 463 Pages • 8.55 MB

Fast Fourier Transform - Algorithms and Applications

2010 • 437 Pages • 11.21 MB

Fast Fourier Transform - Algorithms and Applications

2010 • 443 Pages • 5.13 MB

Fast Fourier Transform - Algorithms and Applications

2012 • 443 Pages • 5.79 MB

The Fourier Transform and its Applications

2009 • 100 Pages • 1.07 MB

The Fourier Transform and its Applications

2007 • 428 Pages • 30.06 MB

TRANSFORM´EE DE FOURIER ET APPLICATIONS

2017 • 133 Pages • 6.58 MB

Fast Fourier Transform Algorithms with Applications

2016 • 341 Pages • 1.42 MB

The fast Fourier transform and its applications

1988 • 463 Pages • 8.51 MB

The Fast Fourier Transform and Its Applications

1988 • 463 Pages • 7.19 MB

The Fourier Transform And Its Applications

2000 • 636 Pages • 128.47 MB

TRANSFORM´EE DE FOURIER ET SES APPLICATIONS

2017 • 134 Pages • 6.25 MB

Fourier Series, Fourier Transform and their Applications to Mathematical Physics

2017 • 516 Pages • 4.46 MB