Skip to main content

Fast Fourier Transform

  • Chapter
  • First Online:

Part of the book series: High-Performance Computing Series ((HPC,volume 2))

Abstract

This chapter introduces the definition of the DFT and the basic idea of the FFT. Then, the Cooley–Tukey FFT algorithm, bit-reversal permutation, and Stockham FFT algorithm are explained. Finally, FFT algorithm for real data is described.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Bergland, G.D.: A fast Fourier transform algorithm for real-valued series. Commun. ACM 11, 703–710 (1968)

    Article  Google Scholar 

  2. Brigham, E.O.: The Fast Fourier Transform and Its Applications. Prentice-Hall, Englewood Cliffs, NJ (1988)

    Google Scholar 

  3. Cochran, W.T., Cooley, J.W., Favin, D.L., Helms, H.D., Kaenel, R.A., Lang, W.W., Maling, G.C., Nelson, D.E., Rader, C.M., Welch, P.D.: What is the fast Fourier transform? IEEE Trans. Audio Electroacoust. 15, 45–55 (1967)

    Article  Google Scholar 

  4. Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daisuke Takahashi .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Takahashi, D. (2019). Fast Fourier Transform. In: Fast Fourier Transform Algorithms for Parallel Computers. High-Performance Computing Series, vol 2. Springer, Singapore. https://doi.org/10.1007/978-981-13-9965-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-9965-7_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-9964-0

  • Online ISBN: 978-981-13-9965-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics