Fast Fourier Transform And Convolution Algorithms
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Fast Fourier Transform And Convolution Algorithms
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Author : H.J. Nussbaumer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Fast Fourier Transform And Convolution Algorithms written by H.J. Nussbaumer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Mathematics categories.
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.
Algorithms For Discrete Fourier Transform And Convolution
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Author : Richard Tolimieri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Algorithms For Discrete Fourier Transform And Convolution written by Richard Tolimieri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Technology & Engineering categories.
This book is based on several courses taught during the last five years at the City College of the City University of New York and at Fudan University, Shanghai, China in the Summer, 1986. It was originally our intention to present to a mixed audience of electrical engineers, mathematicians and computer scientists at the graduate level, a collection of algorithms which would serve to represent the vast array of algorithms designed over the last twenty years for com puting the finite Fourier transform (FFT) and finite convolution. However, it was soon apparent that the scope of the course had to be greatly expanded. For researchers interested in the design of new algorithms, a deeper understanding of the basic mathematical con cepts underlying algorithm design was essential. At the same time, a large gap remained between the statement of an algorithm and the implementation of the algorithm. The main goal of this text is to describe tools which can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural lan guage and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algorithms. This belief is reenforced by the complex and time-consumming effort required to write code for recently available parallel and vector machines. A significant part of this text is devoted to establishing rules and precedures which reduce and at times automate this task. In Chapter 1, a survey is given of basic algebra.
Fast Fourier Transform And Convolution Algorithms
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Author : Henri J Nussbaumer
language : en
Publisher:
Release Date : 1982-09-01
Fast Fourier Transform And Convolution Algorithms written by Henri J Nussbaumer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-09-01 with categories.
Dft Fft And Convolution Algorithms And Implementation
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Author : C. S. Burrus
language : en
Publisher: Wiley-Interscience
Release Date : 1985-01-18
Dft Fft And Convolution Algorithms And Implementation written by C. S. Burrus and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-18 with Technology & Engineering categories.
This readable handbook provides complete coverage of both the theory and implementation of modern signal processing algorithms for computing the Discrete Fourier transform. Reviews continuous and discrete-time transform analysis of signals and properties of DFT, several ways to compute the DFT at a few frequencies, and the three main approaches to an FFT. Practical, tested FORTRAN and assembly language programs are included with enough theory to adapt them to particular applications. Compares and evaluates various algorithms.
Fast Fourier Transform Algorithms And Applications
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Author : K.R. Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-21
Fast Fourier Transform Algorithms And Applications written by K.R. Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-21 with Mathematics categories.
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.
Digital Signal Processing Algorithms
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Author : Hari Krishna
language : en
Publisher:
Release Date : 2017
Digital Signal Processing Algorithms written by Hari Krishna and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
"Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing. It demonstrates the importance of computational number theory in the design of digital signal processing algorithms and clearly describes the nature and structure of the algorithms themselves. The book has two primary focuses: first, it establishes the properties of discrete-time sequence indices and their corresponding fast algorithms; and second, it investigates the properties of the discrete-time sequences and the corresponding fast algorithms for processing these sequences. Digital Signal Processing Algorithms examines three of the most common computational tasks that occur in digital signal processing; namely, cyclic convolution, acyclic convolution, and discrete Fourier transformation. The application of number theory to deriving fast and efficient algorithms for these three and related computationally intensive tasks is clearly discussed and illustrated with examples. Its comprehensive coverage of digital signal processing, computer arithmetic, and coding theory makes Digital Signal Processing Algorithms an excellent reference for practicing engineers. The authors' intent to demystify the abstract nature of number theory and the related algebra is evident throughout the text, providing clear and precise coverage of the quickly evolving field of digital signal processing."--Provided by publisher.
The Fast Fourier Transform
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Author : E. Oran Brigham
language : en
Publisher: Prentice Hall
Release Date : 1974
The Fast Fourier Transform written by E. Oran Brigham and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
The fourier transform; Fourier transform properties; Convolution and correlation; Fourier series and sampled waveforms; The discrete fourier transform; Discrete convolutiion and correlation; Applying the discrete fourier transform.
Fast Transforms Algorithms Analyses Applications
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Author : Douglas F. Elliott
language : en
Publisher: Elsevier
Release Date : 1983-03-09
Fast Transforms Algorithms Analyses Applications written by Douglas F. Elliott and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-03-09 with Mathematics categories.
This book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it.
Fast Fourier Transforms
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Author : C. Sidney Burrus
language : en
Publisher: Lulu.com
Release Date : 2012-11-30
Fast Fourier Transforms written by C. Sidney Burrus and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-30 with Technology & Engineering categories.
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.