MFTA: Transform Size N = p2

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


In chapters 8 to 11, multiplicative algorithms were designed for the FFT of transform sizes N, N a prime, a product of distinct primes and a product of relatively primes. These algorithms start with the multiplicative ring-structure of the indexing set, in the spirit of the Good-Thomas PFA and compute the resulting factorization by combining Rader and Winograd small FFT algorithms. The basic factorization is
$$F\pi =CA$$
where C is a block diagonal matrix with small skew-circulant blocks (rotated Winograd cores) and tensor product of these small skew-circulant blocks, and A is a pre-addition matrix with all its entries being 0, 1 or −1.


Discrete Fourier Transform Unit Group Permutation Matrix Real Matrix Block Diagonal Matrix 
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]
    Blahut, R. E. Fast Algorithms for Digital Signal Processing, Chapter 4 and 8. Addison-Wesley, Reading, Mass., 1985.zbMATHGoogle Scholar
  2. [2]
    Heideman, M. T. Multiplicative Complexity, Convolution, and the DFT, Chapter 5. Springer-Verlag, 1988.Google Scholar
  3. [3]
    Lu, Chao: Fast Fourier Transform Algorithms For Special N’s and The Implementations On VAX. Ph.D. Dissertation. Jan. 1988, the City University of New York.Google Scholar
  4. [4]
    Lu, Chao and Tolimieri, R: “Extension of Winograd Multiplicative Algorithm to Transform Size N=p 2 q, p 2 qr and Their Implementation”, Proceeding of ICASSP 89, 19.D.3. Scotland.Google Scholar
  5. [5]
    Nussbaumer, H. J. Fast Fourier Transform and Convolution Algorithms, Second Edition, Springer-Verlag, 1982.Google Scholar
  6. [6]
    Tolimieri, R. Lu, Chao and Johnson, W. R.: “Modified Winograd FFT Algorithm and Its Variants for Transform Size N=p k and Their Implementations” accepted for publication by Advances in Applied Mathematics.Google Scholar
  7. [7]
    Winograd, S. “On Computing the Discrete Fourier Transform”, Proc. Nat. Acad. Sci. USA., vol. 73. no. 4,(April 1976):1005–1006.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Winograd, S. “On Computing the Discrete Fourier Transform”, Math, of Computation, Vol.32, No. 141, (Jan. 1978):pp 175–199.MathSciNetzbMATHCrossRefGoogle 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