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Algorithms for Discrete Fourier Transform and Convolution

  • Book
  • © 1989

Overview

Authors:
  1. R. Tolimieri

    1. Center for Large Scale Computing, City University of New York, New York, USA

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  2. Myoung An

    1. Center for Large Scale Computing, City University of New York, New York, USA

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  3. Chao Lu

    1. Center for Large Scale Computing, City University of New York, New York, USA

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Editors:
  1. C. S. Burrus

    1. Department of Electrical and Computer Engineering, Rice University, Houston, USA

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Introduction to Abstract Algebra

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 1-35

  3. Tensor Product and Stride Permutation

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 36-71

  4. Cooley-Tukey FFT Algorithms

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 72-93

  5. Variants of FFT Algorithm and Their Implementations

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 94-118

  6. Good-Thomas PFA

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 119-131

  7. Linear and Cyclic Convolution

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 132-175

  8. Agarwal-Cooley Convolution Algorithm

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 176-186

  9. Introduction to Multiplicative Fourier Transform Algorithm (MFTA)

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 187-197

  10. MFTA: The Prime Case

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 198-221

  11. MFTA: Product of Two Distinct Primes

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 222-245

  12. MFTA: Transform Size N = Mr M-Composite Integer and r-Prime

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 246-261

  13. MFTA: Transform Size N = p 2

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 262-279

  14. Periodization and Decimation

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 280-294

  15. Multiplicative Characters and the FFT

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 295-321

  16. Rationality

    • R. Tolimieri, Myoung An, Chao Lu
    Pages 322-347

  17. Back Matter

    Pages 348-350
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Keywords

About this book

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.

Authors, Editors and Affiliations

  • Department of Electrical and Computer Engineering, Rice University, Houston, USA

    C. S. Burrus

  • Center for Large Scale Computing, City University of New York, New York, USA

    R. Tolimieri, Myoung An, Chao Lu

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