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Fast Fourier Transform and Convolution Algorithms

  • Henri J. Nussbaumer

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

Table of contents

  1. Front Matter
    Pages I-XII
  2. Henri J. Nussbaumer
    Pages 1-3
  3. Henri J. Nussbaumer
    Pages 4-31
  4. Henri J. Nussbaumer
    Pages 32-79
  5. Henri J. Nussbaumer
    Pages 80-111
  6. Henri J. Nussbaumer
    Pages 151-180
  7. Henri J. Nussbaumer
    Pages 211-240
  8. Back Matter
    Pages 241-276

About this book

Introduction

In the first edition of this book, we covered in Chapter 6 and 7 the applications to multidimensional convolutions and DFT's of the transforms which we have introduced, back in 1977, and called polynomial transforms. Since the publication of the first edition of this book, several important new developments concerning the polynomial transforms have taken place, and we have included, in this edition, a discussion of the relationship between DFT and convolution polynomial transform algorithms. This material is covered in Appendix A, along with a presentation of new convolution polynomial transform algorithms and with the application of polynomial transforms to the computation of multidimensional cosine transforms. We have found that the short convolution and polynomial product algorithms of Chap. 3 have been used extensively. This prompted us to include, in this edition, several new one-dimensional and two-dimensional polynomial product algorithms which are listed in Appendix B. Since our book is being used as part of several graduate-level courses taught at various universities, we have added, to this edition, a set of problems which cover Chaps. 2 to 8. Some of these problems serve also to illustrate some research work on DFT and convolution algorithms. I am indebted to Mrs A. Schlageter who prepared the manuscript of this second edition. Lausanne HENRI J. NUSSBAUMER April 1982 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.

Keywords

Algorithms Digitales Filter Faltung (Math.) Fourier Fourier-Transformation convolution

Authors and affiliations

  • Henri J. Nussbaumer
    • 1
  1. 1.Department d’ElectricitéEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-81897-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1982
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-11825-1
  • Online ISBN 978-3-642-81897-4
  • Series Print ISSN 0720-678X
  • Buy this book on publisher's site
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