Mathematics of Multidimensional Fourier Transform Algorithms

  • Richard Tolimieri
  • Myoung An
  • Chao Lu
  • C. S. Burrus

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Richard Tolimieri, Myoung An, Chao Lu
    Pages 1-23
  3. Richard Tolimieri, Myoung An, Chao Lu
    Pages 25-36
  4. Richard Tolimieri, Myoung An, Chao Lu
    Pages 37-50
  5. Richard Tolimieri, Myoung An, Chao Lu
    Pages 51-61
  6. Richard Tolimieri, Myoung An, Chao Lu
    Pages 63-69
  7. Richard Tolimieri, Myoung An, Chao Lu
    Pages 71-89
  8. Richard Tolimieri, Myoung An, Chao Lu
    Pages 91-104
  9. Richard Tolimieri, Myoung An, Chao Lu
    Pages 105-124
  10. Richard Tolimieri, Myoung An, Chao Lu
    Pages 125-140
  11. Richard Tolimieri, Myoung An, Chao Lu
    Pages 141-160
  12. Richard Tolimieri, Myoung An, Chao Lu
    Pages 161-183
  13. Back Matter
    Pages 185-187

About this book

Introduction

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

Keywords

Fourier transform algorithms computer fast Fourier transform fast Fourier transform (FFT) image processing mathematics sets

Authors and affiliations

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

Editors and affiliations

  • C. S. Burrus
    • 1
  1. 1.Department of Electrical and Computer EngineeringRice UniversityHoustonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1948-4
  • Copyright Information Springer-Verlag New York, Inc. 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7352-3
  • Online ISBN 978-1-4612-1948-4
  • Series Print ISSN 1431-7893
  • About this book