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Algorithms for Discrete Fourier Transform and Convolution

  • Richard Tolimieri
  • Chao Lu
  • Myoung An

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Richard Tolimieri, Chao Lu, Myoung An
    Pages 1-25
  3. Richard Tolimieri, Chao Lu, Myoung An
    Pages 27-54
  4. Richard Tolimieri, Chao Lu, Myoung An
    Pages 55-70
  5. Richard Tolimieri, Chao Lu, Myoung An
    Pages 71-90
  6. Richard Tolimieri, Chao Lu, Myoung An
    Pages 91-100
  7. Richard Tolimieri, Chao Lu, Myoung An
    Pages 101-135
  8. Richard Tolimieri, Chao Lu, Myoung An
    Pages 137-145
  9. Richard Tolimieri, Chao Lu, Myoung An
    Pages 147-154
  10. Richard Tolimieri, Chao Lu, Myoung An
    Pages 155-172
  11. Richard Tolimieri, Chao Lu, Myoung An
    Pages 173-191
  12. Richard Tolimieri, Chao Lu, Myoung An
    Pages 193-202
  13. Richard Tolimieri, Chao Lu, Myoung An
    Pages 203-215
  14. Richard Tolimieri, Chao Lu, Myoung An
    Pages 217-227
  15. Richard Tolimieri, Chao Lu, Myoung An
    Pages 229-248
  16. Richard Tolimieri, Chao Lu, Myoung An
    Pages 249-264
  17. Back Matter
    Pages 265-267

About this book

Introduction

This book is based on several courses taught during the years 1985-1989 at the City College of the City University of New York and at Fudan Univer­ sity, Shanghai, China, in the summer of 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 that would serve to represent the vast array of algorithms designed over the last twenty years for computing 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 concepts 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 that can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural language and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algo­ rithms. This belief is reinforced by the complex and time-consuming effort required to write code for recently available parallel and vector machines. A significant part of this text is devoted to establishing rules and procedures that reduce and at times automate this task.

Keywords

Fourier transform Permutation convolution discrete Fourier transform fast Fourier transform fast Fourier transform (FFT) signal processing

Authors and affiliations

  • Richard Tolimieri
    • 1
  • Chao Lu
    • 2
  • Myoung An
    • 3
  1. 1.Department of Electrical EngineeringCity College of CUNYNew YorkUSA
  2. 2.Department of Computer and Information SciencesTowson State UniversityTowsonUSA
  3. 3.A.J. Devaney AssociatesAllstonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2767-8
  • Copyright Information Springer-Verlag New York 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3115-3
  • Online ISBN 978-1-4757-2767-8
  • Series Print ISSN 1431-7893
  • Buy this book on publisher's site
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