Advertisement

Cooley-Tukey FFT Algorithms

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

Abstract

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.

Keywords

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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