Download or read book Fast Fourier Transforms written by James S. Walker and published by CRC Press. This book was released on 2017-11-22 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :
Download or read book The Fast Fourier Transform and Its Applications written by E. Oran Brigham and published by Pearson. This book was released on 1988 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.
Download or read book Fast Fourier Transform and Convolution Algorithms written by H.J. Nussbaumer and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a unified way the various fast algorithms that are used for the implementation of digital filters and the evaluation of discrete Fourier transforms. The book consists of eight chapters. The first two chapters are devoted to background information and to introductory material on number theory and polynomial algebra. This section is limited to the basic concepts as they apply to other parts of the book. Thus, we have restricted our discussion of number theory to congruences, primitive roots, quadratic residues, and to the properties of Mersenne and Fermat numbers. The section on polynomial algebra deals primarily with the divisibility and congruence properties of polynomials and with algebraic computational complexity. The rest of the book is focused directly on fast digital filtering and discrete Fourier transform algorithms. We have attempted to present these techniques in a unified way by using polynomial algebra as extensively as possible. This objective has led us to reformulate many of the algorithms which are discussed in the book. It has been our experience that such a presentation serves to clarify the relationship between the algorithms and often provides clues to improved computation techniques. Chapter 3 reviews the fast digital filtering algorithms, with emphasis on algebraic methods and on the evaluation of one-dimensional circular convolutions. Chapters 4 and 5 present the fast Fourier transform and the Winograd Fourier transform algorithm.
Download or read book Computational Frameworks for the Fast Fourier Transform written by Charles Van Loan and published by SIAM. This book was released on 1992-01-01 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author captures the interplay between mathematics and the design of effective numerical algorithms.
Download or read book A First Course in Wavelets with Fourier Analysis written by Albert Boggess and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
Download or read book Fourier Transforms in Radar and Signal Processing Second Edition written by David Brandwood and published by Artech House. This book was released on 2012 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a critical new chapter on periodic waveforms a topic not covered in any other book and detailed coverage of asymmetric triangular pulse. By building upon Woodward's well known "Rules and Pairs" method and related concepts and procedures, this book establishes a unified system that makes implicit the integration required for performing Fourier transforms on a wide variety of functions. It details how complex functions can be broken down to their constituent parts for analysis. You can now concentrate on functional relationships instead of getting bogged down in the details of integration. This approach to implementing Fourier transforms is illustrated with many specific examples from digital signal processing as well as radar and antenna operation. DVD-ROM Included! Contains MATLAB programs that implement many of the results presented in the book.
Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics of the Discrete Fourier Transform DFT written by Julius O. Smith and published by Julius Smith. This book was released on 2008 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The DFT can be understood as a numerical approximation to the Fourier transform. However, the DFT has its own exact Fourier theory, and that is the focus of this book. The DFT is normally encountered as the Fast Fourier Transform (FFT)--a high-speed algorithm for computing the DFT. The FFT is used extensively in a wide range of digital signal processing applications, including spectrum analysis, high-speed convolution (linear filtering), filter banks, signal detection and estimation, system identification, audio compression (such as MPEG-II AAC), spectral modeling sound synthesis, and many others. In this book, certain topics in digital audio signal processing are introduced as example applications of the DFT"--Back cover
Download or read book Wave Propagation in Structures written by James F. Doyle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of wave propagation seems very remote to many engineers, even to those who are involved in structural dynamics. I think one of the reasons for this is that the examples usually taught in school were either so simple as to be inapplicable to real world problems, or so mathematically abstruse as to be intractable. This book contains an approach, spectral analysis, that I have found to be very effective in analyzing waves. What has struck me most about this approach is how I can use the same analytic framework to do predictions as well as to manipulate experimental data. As an experimentalist, I had found it very frustrating having my analytical tools incompatible with my experiments. For example, it is experimentally impos sible to generate a step-function wave and yet that is the type of analytical solution available. Spectral analysis is very encompassing - it touches on analysis, numerical meth ods, and experimental methods. I wanted this book to do justice to its versatility, so many subjects are introduced. As a result some areas may seem a little thin and I regret this. But I do hope, nonetheless, that the bigger picture, the unity, comes across. To encourage you to try the spectral analysis approach I have included complete source code listings to some of the computer programs mentioned in the text.
Download or read book Inside the FFT Black Box written by Eleanor Chu and published by CRC Press. This book was released on 1999-11-11 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.
Download or read book Fast Fourier Transforms written by C. Sidney Burrus and published by Lulu.com. This book was released on 2012-11-30 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.
Download or read book Fourier Transform Infrared Spectrometry written by Peter R. Griffiths and published by John Wiley & Sons. This book was released on 2007-03-16 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bestselling classic reference, now expanded and updated to cover the latest instrumentation, methods, and applications The Second Edition of Fourier Transform Infrared Spectrometry brings this core reference up to date on the uses of FT-IR spectrometers today. The book starts with an in-depth description of the theory and current instrumentation of FT-IR spectrometry, with full chapters devoted to signal-to-noise ratio and photometric accuracy. Many diverse types of sampling techniques and data processing routines, most of which can be performed on even the less expensive instruments, are then described. Extensively updated, the Second Edition: * Discusses improvements in optical components * Features a full chapter on FT Raman Spectrometry * Contains new chapters that focus on different ways of measuring spectra by FT-IR spectrometry, including fourteen chapters on such techniques as microspectroscopy, internal and external reflection, and emission and photoacoustic spectrometry * Includes a new chapter introducing the theory of vibrational spectrometry * Organizes material according to sampling techniques Designed to help practitioners using FT-IR capitalize on the plethora of techniques for modern FT-IR spectrometry and plan their experimental procedures correctly, this is a practical, hands-on reference for chemists and analysts. It's also a great resource for students who need to understand the theory, instrumentation, and applications of FT-IR.
Download or read book Fast Fourier Transform Algorithms and Applications written by K.R. Rao and published by Springer Science & Business Media. This book was released on 2011-02-21 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
Download or read book Applications of Fourier Transforms to Generalized Functions written by M. Rahman and published by WIT Press. This book was released on 2011 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized function is one of the important branches of mathematics which has enormous applications in practical fields. In particular its applications to the theory of distribution and signal processing are very much essential. In this computer age, information science plays a very important role and the Fourier transform is extremely significant in deciphering obscured information to be made understandable. The book contains six chapters and three appendices. Chapter 1 deals with the preliminary remarks of Fourier series from general point of view. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. Chapter 4 deals with the asymptotic estimation of Fourier transforms. Chapter 5 is devoted to the study of Fourier series as a series of generalized functions. Chapter 6 deals with the fast Fourier transforms.Appendix A contains the extended list of Fourier transform pairs.Appendix B illustrates the properties of impulse function.Appendix C contains an extended list of biographical references
Download or read book Fourier Transforms written by Ian Naismith Sneddon and published by Courier Corporation. This book was released on 1995-01-01 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on applications of Fourier transforms and related topics rather than theory, this accessible treatment is suitable for students and researchers interested in boundary value problems of physics and engineering. 1951 edition.
Download or read book A Student s Guide to Fourier Transforms written by John Francis James and published by Cambridge University Press. This book was released on 2002-09-19 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.
Download or read book A Student s Guide to Fourier Transforms written by J. F. James and published by Cambridge University Press. This book was released on 2011-03-31 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier transform theory is of central importance in a vast range of applications in physical science, engineering and applied mathematics. Providing a concise introduction to the theory and practice of Fourier transforms, this book is invaluable to students of physics, electrical and electronic engineering, and computer science. After a brief description of the basic ideas and theorems, the power of the technique is illustrated through applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of Computer Axial Tomography (CAT scanning). The book concludes by discussing digital methods, with particular attention to the Fast Fourier Transform and its implementation. This new edition has been revised to include new and interesting material, such as convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert–Zernike theorem, Babinet's principle and dipole arrays.
