Skip to main content
SpringerLink
Log in

Fast Fourier Transform Algorithms

  • Chapter
Transforms and Fast Algorithms for Signal Analysis and Representations

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

  • 666 Accesses

Abstract

This chapter is devoted to the fast algorithms for various types of discrete Fourier transforms (DFTs).

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Bi and Y. Q. Chen, Fast DFT algorithms for length N = q x 2m, IEEE Trans. Circuits Systems II, vol. 45, no. 6, 685–690, 1998.

    Article  MATH  Google Scholar 

  2. G. Bi and Y. Q. Chen, Split-radix algorithm for the 2D DFT, Electron. Lett., vol. 33, no. 3, 203–305, 1997.

    Article  Google Scholar 

  3. G. Bi, Fast algorithms for DFT of composite sequence lengths, Signal Processing, Else-vier, 70, 139–145, 1998.

    Article  MATH  Google Scholar 

  4. G. Bi and Y. Q. Chen, Fast generalized DFT and DHT algorithms, Signal Processing, Elsevier, 65, 383–390, 1997.

    Article  Google Scholar 

  5. G. Bonnerot and M. Bellanger, Odd-time odd-frequency discrete Fourier transform for symmetric real valued series, Proc. IEEE, vol. 64, no. 3, 392–393, 1976.

    Article  Google Scholar 

  6. S. C. Chan and K. L. Ho, Split vector radix fast Fourier transform, IEEE Trans. Signal Process., vol. 40, no. 8, 2029–2039, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Duhamel, Implementation of split-radix FFT algorithms for complex, real, and real-symmetric data, IEEE Trans. Acoustics, Speech, Signal Process., vol. 34, no. 4, 285–295, 1986.

    Article  MathSciNet  Google Scholar 

  8. P. Duhamel and M. Vetterli, Improved Fourier and Hartley transform algorithm: appli-cation to cyclic convolution of real data, IEEE Trans. Acoustics, Speech, Signal Process., vol. 35, no. 6, 818–824, 1987.

    Article  Google Scholar 

  9. D. F. Elliott and K. R. Rao, Fast Transforms: Algorithms, Analyses, Applications, Academic Press, Inc., New York, 1982.

    MATH  Google Scholar 

  10. O. K. Ersoy, Fourier-Related Transforms, Fast Algorithms and Applications, Prentice- Hall International, Inc., Upper Saddle River, NJ, 1997.

    Google Scholar 

  11. O. K. Ersoy, Semisystolic array implementation of circular, skew-circular, and linear convolutions, IEEE Trans. Comput, 34, no. 2, 190–194, 1985.

    Article  Google Scholar 

  12. I. J. Good, The relationship between two fast Fourier transforms, IEEE Trans. Comput., vol. 20, 310–317, 1977.

    Article  Google Scholar 

  13. M. T. Heideman, C. S. Burrus and H. W Johnson, Prime-factor FFT algorithm for real-valued series, Int. Conf. ASSP, 28A.7.1–28A.7.4, 1984.

    Google Scholar 

  14. N. Hu and O. K. Ersoy, Fast computation of real discrete Fourier transform for any number of data points, IEEE Trans. Circuits Syst II, vol. 38, no. 11, 1280–1292, 1991.

    MATH  Google Scholar 

  15. D. P. Kolba and T. W. Parks, A prime factor FFT algorithm using high-speed convolution, IEEE Trans., vol. 25, 90–103, 1977.

    Google Scholar 

  16. Z. J. Mou and P. Duhamel, In-place butterfly-style FFT of 2-D real sequences, IEEE Trans. Acoustics, Speech, Signal Process., vol. 36, no. 10, 1642–1650, 1988.

    Article  MATH  Google Scholar 

  17. H. J. Nussbaumer and P. Quandalle, Computation of convolutions and discrete Fourier transforms by polynomial transform, IBM J. Res. Develop., vol. 22, no. 2, 1978.

    Google Scholar 

  18. S. C. Pei and Tzyy-Liang Luo, Split-radix generalized fast Fourier transform, Signal Processing, vol. 54, 137–151, 1996.

    Article  MATH  Google Scholar 

  19. L. R. Rabiner and B. Gold, Theory and Application of Digital Aignal Processing, Prentice- Hall, Englewood Cliffs, NJ, 1975.

    Google Scholar 

  20. C. M. Rader, Discrete Fourier transforms when the number of data sample is prime, Proc. IEEE., vol. 56, 1107–1108, 1968.

    Article  Google Scholar 

  21. V. Sorensen, M. T. Heideman, and C. S. Burreu, On computing the split-radix FFT, IEEE Trans. Acoustics, Speech, Signal Process., vol. 34, no. 2, 152–156, 1986.

    Article  Google Scholar 

  22. R. Stasinski, Radix-K FFT’s using K-point convolutions, IEEE Trans. Signal Process., vol. 42, no. 4, 743–750, 1994.

    Article  Google Scholar 

  23. Y. Suzuki, T. Sone and K. Kido, A new algorithm of radix 3, 6, and 12, IEEE Trans. Acoustics, Speech, Signal Process., vol. 34, no. 2, 389–383, 1986.

    Article  MathSciNet  Google Scholar 

  24. R. Tolimieri, M. An and C. Liu, Algorithms for Discrete Fourier Transform and Con-volution, Springer-Verlag, New York, 1989.

    Google Scholar 

  25. M. Vetterli and P. Duhamel, Split-radix algorithms for length p m DFT’s, IEEE Trans. Acoustics, Speech, Signal Process., vol. 37, no. 1, 57–64, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  26. S. Winograd, On computing the discrete Fourier transform, Math. Comput., 32, 175–199, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  27. H. R. Wu and F. J. Paoloni, On the two-dimensional vector-radix FFT algorithm, IEEE Trans. Acoustics, Speech, Signal Process., vol. 37, no. 8, 1302–1304, 1989.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technical University, Singapore, 63798, Singapore

    Guoan Bi

  2. Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong

    Yonghong Zeng

Authors
  1. Guoan Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yonghong Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bi, G., Zeng, Y. (2004). Fast Fourier Transform Algorithms. In: Transforms and Fast Algorithms for Signal Analysis and Representations. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8220-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-0-8176-8220-0_3

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6499-6

  • Online ISBN: 978-0-8176-8220-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation