Skip to main content
SpringerLink
Log in

Cooley—Tukey and Good—Thomas

  • Chapter
Mathematics of Multidimensional Fourier Transform Algorithms

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

  • 150 Accesses

Abstract

The abstract definition of the Fourier transform and the statement of Fourier transform duality as expressed by the periodization-decimation results of Chapter 4 provide a unifying principal underlying most 1-dimensional and multidimensional FFT. The C-T FFT of Chapters 1 and 2 are expressions of this duality. In [1], a vector-radix FFT was derived extending this duality relative to groups of affine motions on indexing set. This class of FFT is highly parallelizable.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. An, M., Gertner, I., Rofheart, M. and Tolimieri, R. (1991), “Discrete Fast Fourier Transform Algorithms: A Tutorial Survey,” Advances in Electronics and Electron Physics 80.

    Google Scholar 

  2. Burrus, C.S. (1981), “A New Prime Factor FFT Algorithms,” Proc. 1981 IEEE Int. Conf. ASSP, Atlanta, GA, 335–338.

    Google Scholar 

  3. Burrus, C.S. and Eschenbacher, P.W. (1981), “ An In-Place In- Order Prime Factor FFT Algorithm,” IEEE Trans. ASSP 29, 806–817.

    Article  MATH  Google Scholar 

  4. Good, I.J. (1958), “The Interaction Algorithm and Practical Fouriei Analysis,” J. Roy. Stat. Soc. Ser. B 20, 361–372.

    Google Scholar 

  5. Good, I.J. (1971), “The Relationship between Two Fourier Transforms,” IEEE Trans. Comput. C-20, 310–317.

    Google Scholar 

  6. Temperton, C. (1985), “Implementation of a Self-Sorting In-Place Prime Factor FFT Algorithm,” J. Comput. Phys. 58, 283–299.

    Google Scholar 

  7. Temperton, C. (1988), “Implementation of a Prime Factor FFT Algorithm on the Cray-1,” Parallel Comput. 6, 99–108.

    Article  MathSciNet  MATH  Google Scholar 

  8. Weil, A. (1953), L’Integration dans les Groupes et ses Applications Topologique, Hermann, Paris.

    Google Scholar 

  9. Weil, A. (1964), “Sur Certaines Groupes D’operateurs Unitaires,” Acta Math. 111, 143–211.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aware, Inc., One Memorial Drive, 02142, Cambridge, MA, USA

    Richard Tolimieri & Myoung An

  2. Dept. of Computer and Information Sciences, Towson State University, 21204, Towson, MD, USA

    Chao Lu

Authors
  1. Richard Tolimieri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Myoung An
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chao Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Tolimieri, R., An, M., Lu, C. (1993). Cooley—Tukey and Good—Thomas. In: Mathematics of Multidimensional Fourier Transform Algorithms. Signal Processing and Digital Filtering. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0205-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0205-6_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-0207-0

  • Online ISBN: 978-1-4684-0205-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation