Fast Fourier Transform Algorithms

  • Guoan Bi
  • Yonghong Zeng
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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


Discrete Fourier Transform Fast Algorithm Arithmetic Operation Input Sequence Real Multiplication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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.MATHCrossRefGoogle Scholar
  2. 2.
    G. Bi and Y. Q. Chen, Split-radix algorithm for the 2D DFT, Electron. Lett., vol. 33, no. 3, 203–305, 1997.CrossRefGoogle Scholar
  3. 3.
    G. Bi, Fast algorithms for DFT of composite sequence lengths, Signal Processing, Else-vier, 70, 139–145, 1998.MATHCrossRefGoogle Scholar
  4. 4.
    G. Bi and Y. Q. Chen, Fast generalized DFT and DHT algorithms, Signal Processing, Elsevier, 65, 383–390, 1997.CrossRefGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.MathSciNetMATHCrossRefGoogle Scholar
  7. 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.MathSciNetCrossRefGoogle Scholar
  8. 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.CrossRefGoogle Scholar
  9. 9.
    D. F. Elliott and K. R. Rao, Fast Transforms: Algorithms, Analyses, Applications, Academic Press, Inc., New York, 1982.MATHGoogle Scholar
  10. 10.
    O. K. Ersoy, Fourier-Related Transforms, Fast Algorithms and Applications, Prentice- Hall International, Inc., Upper Saddle River, NJ, 1997.Google Scholar
  11. 11.
    O. K. Ersoy, Semisystolic array implementation of circular, skew-circular, and linear convolutions, IEEE Trans. Comput, 34, no. 2, 190–194, 1985.CrossRefGoogle Scholar
  12. 12.
    I. J. Good, The relationship between two fast Fourier transforms, IEEE Trans. Comput., vol. 20, 310–317, 1977.CrossRefGoogle Scholar
  13. 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. 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.MATHGoogle Scholar
  15. 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. 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.MATHCrossRefGoogle Scholar
  17. 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. 18.
    S. C. Pei and Tzyy-Liang Luo, Split-radix generalized fast Fourier transform, Signal Processing, vol. 54, 137–151, 1996.MATHCrossRefGoogle Scholar
  19. 19.
    L. R. Rabiner and B. Gold, Theory and Application of Digital Aignal Processing, Prentice- Hall, Englewood Cliffs, NJ, 1975.Google Scholar
  20. 20.
    C. M. Rader, Discrete Fourier transforms when the number of data sample is prime, Proc. IEEE., vol. 56, 1107–1108, 1968.CrossRefGoogle Scholar
  21. 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.CrossRefGoogle Scholar
  22. 22.
    R. Stasinski, Radix-K FFT’s using K-point convolutions, IEEE Trans. Signal Process., vol. 42, no. 4, 743–750, 1994.CrossRefGoogle Scholar
  23. 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.MathSciNetCrossRefGoogle Scholar
  24. 24.
    R. Tolimieri, M. An and C. Liu, Algorithms for Discrete Fourier Transform and Con-volution, Springer-Verlag, New York, 1989.Google Scholar
  25. 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.MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    S. Winograd, On computing the discrete Fourier transform, Math. Comput., 32, 175–199, 1978.MathSciNetMATHCrossRefGoogle Scholar
  27. 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.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Guoan Bi
    • 1
  • Yonghong Zeng
    • 2
  1. 1.School of Electrical and Electronic EngineeringNanyang Technical UniversitySingaporeSingapore
  2. 2.Department of Electrical and Electronic EngineeringThe University of Hong KongHong Kong

Personalised recommendations