Mathematics Of The Discrete Fourier Transform Dft

Author : Julius O. Smith
Publisher : Julius Smith
Page : 323 pages
File Size : 50,8 Mb
Release : 2008
Category : Fourier transformations
ISBN : 9780974560748

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Mathematics of the Discrete Fourier Transform (DFT) by Julius O. Smith Pdf

"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

Author : Julius Smith
Publisher : Unknown
Page : 322 pages
File Size : 54,8 Mb
Release : 2008-08-26
Category : Electronic
ISBN : 1439208875

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Mathematics of the Discrete Fourier Transform (DFT) by Julius Smith Pdf

Author : D. Sundararajan
Publisher : World Scientific
Page : 400 pages
File Size : 44,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9812810293

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The Discrete Fourier Transform by D. Sundararajan Pdf

This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and WalshOCoHadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book will be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. Errata(s). Preface, Page viii. OC www.wspc.com/others/software/4610/OCO. The above links should be replaced with. OC www.worldscientific.com/doi/suppl/10.1142/4610/suppl_file/4610_software_free.zipOCO. Contents: The Discrete Sinusoid; The Discrete Fourier Transform; Properties of the DFT; Fundamentals of the PM DFT Algorithms; The u X 1 PM DFT Algorithms; The 2 X 2 PM DFT Algorithms; DFT Algorithms for Real Data OCo I; DFT Algorithms for Real Data OCo II; Two-Dimensional Discrete Fourier Transform; Aliasing and Other Effects; The Continuous-Time Fourier Series; The Continuous-Time Fourier Transform; Convolution and Correlation; Discrete Cosine Transform; Discrete WalshOCoHadamard Transform. Readership: Upper level undergraduate students, graduates, researchers and lecturers in engineering and applied mathematics."

Author : William L. Briggs,Van Emden Henson
Publisher : SIAM
Page : 446 pages
File Size : 53,9 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 9780898713428

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The DFT by William L. Briggs,Van Emden Henson Pdf

This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.

Author : Isaac Amidror
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 48,8 Mb
Release : 2013-07-19
Category : Mathematics
ISBN : 9781447151678

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Mastering the Discrete Fourier Transform in One, Two or Several Dimensions by Isaac Amidror Pdf

The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and two dimensional cases due to their particular importance, but the discussion covers the general multidimensional case, too. The book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. Mastering the Discrete Fourier Transform in One, Two or Several Dimensions is intended for scientists, engineers, students and any readers who wish to widen their knowledge of the DFT and its practical use. This book will also be very useful for ‘naive’ users from various scientific or technical disciplines who have to use the DFT for their respective applications. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the continuous and discrete Fourier theory.

Author : Duraisamy Sundararajan
Publisher : World Scientific
Page : 392 pages
File Size : 45,9 Mb
Release : 2001-04-30
Category : Technology & Engineering
ISBN : 9789814491723

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Discrete Fourier Transform, The: Theory, Algorithms And Applications by Duraisamy Sundararajan Pdf

This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice.This book will be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis.Errata(s)Preface, Page viii“www.wspc.com/others/software/4610/”The above links should be replaced with“www.worldscientific.com/doi/suppl/10.1142/4610/suppl_file/4610_software_free.zip”

Author : Julius O. Smith III
Publisher : Unknown
Page : 264 pages
File Size : 55,9 Mb
Release : 2003-01-01
Category : Fourier transformations
ISBN : 0974560707

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Mathematics of the Discrete Fourier Transform (DFT) with Music and Audio Applications by Julius O. Smith III Pdf

Author : Eleanor Chu
Publisher : CRC Press
Page : 423 pages
File Size : 43,6 Mb
Release : 2008-03-19
Category : Mathematics
ISBN : 9781420063646

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Discrete and Continuous Fourier Transforms by Eleanor Chu Pdf

Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transform

Author : C. Sidney Burrus
Publisher : Lulu.com
Page : 256 pages
File Size : 50,9 Mb
Release : 2024-06-10
Category : Computer science
ISBN : 9781300461647

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Fast Fourier Transforms by C. Sidney Burrus Pdf

Author : Vaclav Cizek,Václav Cízek,Václav Čížek
Publisher : CRC Press
Page : 141 pages
File Size : 47,9 Mb
Release : 1986-01-01
Category : Mathematics
ISBN : 0852748000

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Discrete Fourier Transforms and their Applications, by Vaclav Cizek,Václav Cízek,Václav Čížek Pdf

This text is designed to be a practial handbook on the evaluation and application of one of the major techniques for discrete signal processing. Knowledge of the discrete Fourier transform (DFT) and the ability to construct alogorithms based on the techniques of fast Fourier analysis are essential prerequisites for communications and cybernetics engineers. These methods are also of inestimable value to applied scientists in many other fields. The treatment given here is aimed specifically at such experimentalists and practitioners, and includes only such mathematical development as is necessary to give a feel for the significance of the methods, and to promote proficiency in its use. An introductory discourse on the general theory of Fourier series and transforms is followed by a thorough review of the properties and means of computation of the DFT. The fast Fourier transform is presented as a particularly efficient algorithm for DFT evaluation, and is described in some detail. Some applications of DFT's are discussed, and the book is rounded off with an introduction to discrete Hilbert transforms. Examples are provided throughout the text, and a full bibliography provides the basis for further study of the mathematical theory and specific areas of application.

Author : Brad G. Osgood
Publisher : American Mathematical Soc.
Page : 689 pages
File Size : 43,5 Mb
Release : 2019-01-18
Category : Fourier transformations
ISBN : 9781470441913

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Lectures on the Fourier Transform and Its Applications by Brad G. Osgood Pdf

This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques—all of which are important in many areas of engineering and science—the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.

Author : Richard Tolimieri,Myoung An,Chao Lu
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461219484

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Mathematics of Multidimensional Fourier Transform Algorithms by Richard Tolimieri,Myoung An,Chao Lu Pdf

Developing algorithms for multi-dimensional Fourier transforms, this book presents results that yield highly efficient code on a variety of vector and parallel computers. By emphasising the unified basis for the many approaches to both one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimising implementations. It will thus be of great interest not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers working on signal and image processing.

Author : Charles Van Loan
Publisher : SIAM
Page : 285 pages
File Size : 43,9 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 9780898712858

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Computational Frameworks for the Fast Fourier Transform by Charles Van Loan Pdf

The author captures the interplay between mathematics and the design of effective numerical algorithms.

Author : H.J. Nussbaumer
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 51,7 Mb
Release : 2013-03-08
Category : Mathematics
ISBN : 9783662005514

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Fast Fourier Transform and Convolution Algorithms by H.J. Nussbaumer Pdf

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.

Author : Richard Tolimieri,Myoung An,Chao Lu
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 53,5 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9781475727678

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Algorithms for Discrete Fourier Transform and Convolution by Richard Tolimieri,Myoung An,Chao Lu Pdf

This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines. It thus bridges the gap between digital signal processing algorithms and their implementation on a variety of computing platforms. The mathematical concept of tensor product is a recurring theme throughout the book, since these formulations highlight the data flow, which is especially important on supercomputers. Because of their importance in many applications, much of the discussion centres on algorithms related to the finite Fourier transform and to multiplicative FFT algorithms.