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Mathematics of Multidimensional Fourier Transform Algorithms

  • Book
  • © 1993

Overview

Authors:
  1. Richard Tolimieri

    1. Aware, Inc., Cambridge, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Myoung An

    1. Aware, Inc., Cambridge, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Chao Lu

    1. Dept. of Computer and Information Sciences, Towson State University, Towson, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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-xiv
    Download chapter PDF

  2. Tensor Product

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 1-28

  3. Multidimensional Tensor Product and FFT

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 29-43

  4. Finite Abelian Groups

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 45-62

  5. Fourier Transform of Finite Abelian Groups

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 63-76

  6. Cooley—Tukey and Good—Thomas

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 77-87

  7. Lines

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 89-113

  8. Duality of Lines and Planes

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 115-133

  9. Reduced Transform Algorithms

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 135-157

  10. Field Algorithm

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 159-177

  11. Implementation on RISC Architectures

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 179-202

  12. Implementation on Parallel Architectures

    • Richard Tolimieri, Myoung An, Chao Lu
    Pages 203-229

  13. Back Matter

    Pages 231-233
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Keywords

About this book

The Fourier transform of large multidimensional data sets is an essen­ tial computation in many scientific and engineering fields, including seismology, X-ray crystallography, radar, sonar and medical imaging. Such fields require multidimensional arrays for complete and faithful modelling. Classically, a set of data is processed one dimension at a time, permitting control over the size of the computation and calling on well-established I-dimensional programs. The rapidly increasing availability of powerful computing chips, vector processors, multinode boards and parallel machines has provided new tools for carrying out multidimensional computations. Multidimensional processing offers a wider range of possible implementations as compared to I-dimensional the greater flexibility of movement in the data in­ processing, due to dexing set. This increased freedom, along with the massive size data sets typically found in multidimensional applications, places intensive demands on the communication aspects of the computation. The writ­ ing of code that takes into account all the algorithmic possibilities and matches these possibilities to the communication capabilities of the tar­ get architecture is an extremely time-consuming task. A major goal of this text is to provide a sufficiently abstra

Authors and Affiliations

  • Aware, Inc., Cambridge, USA

    Richard Tolimieri, Myoung An

  • Dept. of Computer and Information Sciences, Towson State University, Towson, USA

    Chao Lu

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