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Fast Fourier Transform and Convolution Algorithms

  • Book
  • © 1981

Overview

Authors:
  1. Henri J. Nussbaumer

    1. IBM Centre d’Etudes et Recherches, La Gaude, Alpes-Maritimes, France

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Part of the book series: Springer Series in Information Sciences (SSINF, volume 2)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Henri J. Nussbaumer
    Pages 1-3

  3. Elements of Number Theory and Polynomial Algebra

    • Henri J. Nussbaumer
    Pages 4-31

  4. Fast Convolution Algorithms

    • Henri J. Nussbaumer
    Pages 32-79

  5. The Fast Fourier Transform

    • Henri J. Nussbaumer
    Pages 80-111

  6. Linear Filtering Computation of Discrete Fourier Transforms

    • Henri J. Nussbaumer
    Pages 112-150

  7. Polynomial Transforms

    • Henri J. Nussbaumer
    Pages 151-180

  8. Computation of Discrete Fourier Transforms by Polynomial Transforms

    • Henri J. Nussbaumer
    Pages 181-210

  9. Number Theoretic Transforms

    • Henri J. Nussbaumer
    Pages 211-240

  10. Back Matter

    Pages 241-250
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Keywords

About this book

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.

Authors and Affiliations

  • IBM Centre d’Etudes et Recherches, La Gaude, Alpes-Maritimes, France

    Henri J. Nussbaumer

Bibliographic Information

  • Book Title: Fast Fourier Transform and Convolution Algorithms

  • Authors: Henri J. Nussbaumer

  • Series Title: Springer Series in Information Sciences

  • DOI: https://doi.org/10.1007/978-3-662-00551-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1981

  • eBook ISBN: 978-3-662-00551-4Published: 08 March 2013

  • Series ISSN: 0720-678X

  • Edition Number: 1

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Numerical Analysis

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