Cooley-Tukey FFT Algorithms

  • R. Tolimieri
  • Myoung An
  • Chao Lu
Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)


In the following two chapters, we will concentrate on algorithms for computing FFT of size a composite number N. The main idea is to use the additive structure of the indexing set Z/N to define mappings of the input and output data vectors into 2-dimensional arrays. Algorithms are then designed, transforming 2-dimensional arrays which, when combined with these mappings, compute the N-point FFT. The stride permutations of chapter 2 play a major role.


Fast Fourier Transform Vector Operation Fast Fourier Trans Twiddle Factor Commutation Theorem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Cochran, W. T. et al., ”What is the Fast Fourier Transform?,” IEEE Trans. Audio Electroacoust., vol. 15, 1967, pp.45–55.CrossRefGoogle Scholar
  2. [2]
    Cooley, J. W., Tuckey, J. W. ”An Algorithm for the machine Calculation of complex Fourier Series,” Math. Comp., vol. 19, 1965, pp.297–301.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Gentleman, W. M., Sande, G. ”Fast Fourier Transform for Fun and Profit,” Proc.AFIPS, Joint Computer Conference, vol.29,1966, pp.563–578.Google Scholar
  4. [4]
    Korn, D.J., Lambiotte, J.J. ”Computing the Fast Fourier Transform on a vector computer,” Math. Comp., vol.33, 1979, pp.977–992.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Pease, M. C. ”An Adaptation of the Fast Fourier Transform for Parallel Processing,” J. ACM, vol 8, 1971, pp.843–846.Google Scholar
  6. [6]
    Burrus, C.S. ”Bit Reverse Unscrambling for a Radix 2m FFT”, IEEE Trans. on ASSP, vol. 36, July, 1988.Google Scholar
  7. [7]
    Singleton, R. C. ”An Algorithm for Computing the Mixed-Radix Fast Fourier Transform,” IEEE Trans.Audio Electroacoust., vol.17, 1969, pp.93–103.CrossRefGoogle Scholar
  8. [8]
    Swartztrauber, P. N. ”FFT algorithms for vector computers,” Parallel Computing, vol.1, North Holland, 1984, pp.45–63.CrossRefGoogle Scholar
  9. [9]
    Temperton, C. ”Self-Sorting Mixed-Radix Fast Fourier Transforms,” J. of Compt.Phys., 52(1), 1983 pp.198–204.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Burrus, C.S. and Park, T.W. DFT/FFT and Convolution Algorithms New York: John Wiley and Sons, 1985.Google Scholar
  11. [11]
    Oppenheim, A.V. and Schafer, R.W. Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1975.MATHGoogle Scholar
  12. [12]
    Nussbaumer, H.J. Fast Fourier Transform and Convolution Algorithms, Berlin, Heidelberg and New York, Springer-Verlag, 1981.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • R. Tolimieri
    • 1
  • Myoung An
    • 1
  • Chao Lu
    • 1
  1. 1.Center for Large Scale ComputingCity University of New YorkNew YorkUSA

Personalised recommendations