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Algorithms for Discrete Fourier Transform and Convolution

  • R. Tolimieri
  • Myoung An
  • Chao Lu
  • C. S. Burrus

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. R. Tolimieri, Myoung An, Chao Lu
    Pages 1-35
  3. R. Tolimieri, Myoung An, Chao Lu
    Pages 36-71
  4. R. Tolimieri, Myoung An, Chao Lu
    Pages 72-93
  5. R. Tolimieri, Myoung An, Chao Lu
    Pages 94-118
  6. R. Tolimieri, Myoung An, Chao Lu
    Pages 119-131
  7. R. Tolimieri, Myoung An, Chao Lu
    Pages 132-175
  8. R. Tolimieri, Myoung An, Chao Lu
    Pages 176-186
  9. R. Tolimieri, Myoung An, Chao Lu
    Pages 187-197
  10. R. Tolimieri, Myoung An, Chao Lu
    Pages 198-221
  11. R. Tolimieri, Myoung An, Chao Lu
    Pages 222-245
  12. R. Tolimieri, Myoung An, Chao Lu
    Pages 246-261
  13. R. Tolimieri, Myoung An, Chao Lu
    Pages 262-279
  14. R. Tolimieri, Myoung An, Chao Lu
    Pages 280-294
  15. R. Tolimieri, Myoung An, Chao Lu
    Pages 295-321
  16. R. Tolimieri, Myoung An, Chao Lu
    Pages 322-347
  17. Back Matter
    Pages 348-350

About this book

Introduction

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.

Keywords

algebra algorithms bridge digital signal processing discrete Fourier transform fast Fourier transform (FFT) signal processing

Authors and affiliations

  • R. Tolimieri
    • 1
  • Myoung An
    • 1
  • Chao Lu
    • 1
  1. 1.Center for Large Scale ComputingCity University of New YorkNew YorkUSA

Editors and affiliations

  • C. S. Burrus
    • 1
  1. 1.Department of Electrical and Computer EngineeringRice UniversityHoustonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3854-4
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-3856-8
  • Online ISBN 978-1-4757-3854-4
  • Series Print ISSN 1431-7893
  • Buy this book on publisher's site