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Fast Fourier transform and convolution algorithms

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Published by Springer-Verlag in Berlin, New York .
Written in English

Subjects:

  • Fourier transformations -- Data processing.,
  • Convolutions (Mathematics) -- Data processing.,
  • Digital filters (Mathematics)

Book details:

Edition Notes

StatementHenri J. Nussbaumer.
SeriesSpringer series in information sciences ;, 2
Classifications
LC ClassificationsQA403.5 .N87
The Physical Object
Paginationx, 248 p. :
Number of Pages248
ID Numbers
Open LibraryOL4103517M
ISBN 100387101594
LC Control Number80018096

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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. 1 Introduction.- Introductory Remarks.- Notations.- The Structure of the Book.- 2 Elements of Number Theory and Polynomial Algebra.- Elementary Number Theory.- Divisibility of Integers.- Congruences .   Lausanne HENRI J. NUSSBAUMER April Preface to the First Edition 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 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 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 . Introduction --Elements of number theory and polynomial algebra --Fast convolution algorithms --The fast Fourier transform --Linear filtering computation of discrete Fourier transforms --Polynomial transforms --Computation of discrete Fourier transforms by polynomial transforms --Number theoretic transforms. Series Title. Improvements and Related Algorithms Discrete Fourier Transform Based Algorithms Algorithms Based on Extension Fields Algorithms for Multidimensional Cyclic Convolution Algorithms for Two-Dimensional Cyclic Convolution in Finite Integer Rings Validity of Fast Algorithms over Different Number Systems Introduction Mathematical Preliminaries. $\begingroup$ Well, that's because of 1. a lot of things in applications can be couched in terms of Fourier transforms, and 2. there exists a speedy algorithm called the "fast Fourier transform" (FFT), and if you have a sleek-looking hammer, you tend to start looking for nails $\endgroup$ – J. M. isn't a mathematician Nov 21 '10 at

The Fast Fourier Transform (FFT) Algorithm. The FFT is a fast algorithm for computing the DFT. If we take the 2-point DFT and 4-point DFT and generalize them to 8-point, point, , 2r-point, we get the FFT algorithm. To computetheDFT of an N-point sequence usingequation (1) would takeO.N2/mul- .   This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in hardware, theory and applications continue to keep them important and exciting. Digital Signal Processing Algorithms: Number Theory, Convolution, Fast Fourier Transforms, and Applications (Computer Science & Engineering Book 9) - Kindle edition by Krishna, Hari. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Digital Signal Processing Algorithms: Number Theory, Convolution 5/5(1). The Paperback of the Fast Fourier Transform and Convolution Algorithms by Henri J. Nussbaumer at Barnes & Noble. FREE Shipping on $35 or more! Due to COVID, orders may be delayed.