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Mathematics of Multidimensional Fourier Transform Algorithms

  • Book
  • © 1997

Overview

Authors:
  1. Richard Tolimieri

    1. Department of Electrical Engineering, City College of CUNY, New York, USA

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  2. Myoung An

    1. A.J. Devaney Associates, Allston, USA

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  3. Chao Lu

    1. Department of Computer and Information Sciences, Towson State University, Towson, 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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  • Appeals not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers - Uses a unifying approach to explore both one-dimensional and multidimensional Fourier transforms

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Tensor Product

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 1-23

  3. Multidimensional Tensor Product and FFT

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 25-36

  4. Finite Abelian Groups

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 37-50

  5. Fourier Transform of Finite Abelian Groups

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 51-61

  6. Cooley—Tukey and Good—Thomas

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 63-69

  7. Lines

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 71-89

  8. Duality of Lines and Planes

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 91-104

  9. Reduced Transform Algorithms

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 105-124

  10. Field Algorithm

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 125-140

  11. Implementation on RISC Architectures

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 141-160

  12. Implementation on Parallel Architectures

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 161-183

  13. Back Matter

    Pages 185-187
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Keywords

About this book

Fourier transforms of large multidimensional data sets arise in many fields --ranging from seismology to medical imaging. The rapidly increasing power of computer chips, the increased availability of vector and array processors, and the increasing size of the data sets to be analyzed make it both possible and necessary to analyze the data more than one dimension at a time. The increased freedom provided by multidimensional processing, however, also places intesive demands on the communication aspects of the computation, making it difficult to write code that takes all the algorithmic possiblities into account and matches these to the target architecture. This book develops algorithms for multi-dimensional Fourier transforms that yield highly efficient code on a variety of vector and parallel computers. By emphasizing the unified basis for the many approaches to one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimizing implementations. This book will be of interest not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers working on signal and image processing. Topics covered include: tensor products and the fast Fourier transform; finite Abelian groups and their Fourier transforms; Cooley- Tukey and Good-Thomas algorithms; lines and planes; reduced transform algorithms; field algorithms; implementation on Risc and parallel

Authors, Editors and Affiliations

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

    C. S. Burrus

  • Department of Electrical Engineering, City College of CUNY, New York, USA

    Richard Tolimieri

  • A.J. Devaney Associates, Allston, USA

    Myoung An

  • Department of Computer and Information Sciences, Towson State University, Towson, USA

    Chao Lu

Bibliographic Information

  • Book Title: Mathematics of Multidimensional Fourier Transform Algorithms

  • Authors: Richard Tolimieri, Myoung An, Chao Lu

  • Editors: C. S. Burrus

  • Series Title: Signal Processing and Digital Filtering

  • DOI: https://doi.org/10.1007/978-1-4612-1948-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1997

  • Hardcover ISBN: 978-0-387-98260-1Published: 18 July 1997

  • Softcover ISBN: 978-1-4612-7352-3Published: 23 October 2012

  • eBook ISBN: 978-1-4612-1948-4Published: 06 December 2012

  • Series ISSN: 1431-7893

  • Edition Number: 2

  • Number of Pages: XI, 187

  • Topics: Engineering, general

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