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Multiplicative Complexity, Convolution, and the DFT

  • Michael T. Heideman

Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Michael T. Heideman
    Pages 1-4
  3. Michael T. Heideman
    Pages 27-60
  4. Michael T. Heideman
    Pages 61-75
  5. Michael T. Heideman
    Pages 108-118
  6. Back Matter
    Pages 119-155

About this book

Introduction

This book is intended to be a comprehensive reference to multiplicative com­ plexity theory as applied to digital signal processing computations. Although a few algorithms are included to illustrate the theory, I concentrated more on the develop­ ment of the theory itself. Howie Johnson's infectious enthusiasm for designing efficient DfT algorithms got me interested in this subject. I am grateful to Prof. Sid Burrus for encouraging and supporting me in this effort. I would also like to thank Henrik Sorensen and Doug Jones for many stimulating discussions. lowe a great debt to Shmuel Winograd, who, almost singlehandedly, provided most of the key theoretical results that led to this present work. His monograph, Arithmetic Complexity o/Computations, introduced me to the mechanism behind the proofs of theorems in multiplicative complexity. enabling me to return to his earlier papers and appreciate the elegance of his methods for deriving the theory. The second key work that influenced me was the paper by Louis Auslander and Winograd on multiplicative complexity of semilinear systems defined by polynomials. After reading this paper, it was clear to me that this theory could be applied to many impor­ tant computational problems. These influences can be easily discerned in the present work.

Keywords

Mathematica complexity discrete Fourier transform organization proof

Authors and affiliations

  • Michael T. Heideman
    • 1
  1. 1.Etak IncorporatedMenlo ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-3912-3
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8399-7
  • Online ISBN 978-1-4612-3912-3
  • Series Print ISSN 1431-7893
  • Buy this book on publisher's site