Mathematics of Multidimensional Fourier Transform Algorithms

  • Richard Tolimieri
  • Myoung An
  • Chao Lu

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Richard Tolimieri, Myoung An, Chao Lu
    Pages 1-28
  3. Richard Tolimieri, Myoung An, Chao Lu
    Pages 29-43
  4. Richard Tolimieri, Myoung An, Chao Lu
    Pages 45-62
  5. Richard Tolimieri, Myoung An, Chao Lu
    Pages 63-76
  6. Richard Tolimieri, Myoung An, Chao Lu
    Pages 77-87
  7. Richard Tolimieri, Myoung An, Chao Lu
    Pages 89-113
  8. Richard Tolimieri, Myoung An, Chao Lu
    Pages 115-133
  9. Richard Tolimieri, Myoung An, Chao Lu
    Pages 135-157
  10. Richard Tolimieri, Myoung An, Chao Lu
    Pages 159-177
  11. Richard Tolimieri, Myoung An, Chao Lu
    Pages 179-202
  12. Richard Tolimieri, Myoung An, Chao Lu
    Pages 203-229
  13. Back Matter
    Pages 231-233

About this book

Introduction

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

Keywords

algorithms fast Fourier transform (FFT) image processing

Authors and affiliations

  • Richard Tolimieri
    • 1
  • Myoung An
    • 1
  • Chao Lu
    • 2
  1. 1.Aware, Inc.CambridgeUSA
  2. 2.Dept. of Computer and Information SciencesTowson State UniversityTowsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0205-6
  • Copyright Information Springer-Verlag New York 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0207-0
  • Online ISBN 978-1-4684-0205-6
  • Series Print ISSN 1431-7893
  • About this book