Multiplicative Fourier Transform Algorithm
The Cooley-Tukey FFT algorithm and its variants depend upon the existence of nontrivial divisors of the transform size N. These algorithms are called additive algorithms since they rely on the subgroups of the additive group structure of the indexing set. A second approach to the design of FT algorithms depends on the multiplicative structure of the indexing set. We applied the multiplicative structure previously, in chapter 5, in the derivation of the Good-Thomas PFA.
KeywordsDiscrete Fourier Transform Permutation Matrice Fast Fourier Transform Algorithm Multiplicative Structure Multiplicative Complexity
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- Blahut, R. E. Fast Algorithms for Digital Signal Processing, Addison-Wesley, 1985, Chapter 8.Google Scholar
- Temperton, C. “Implementation of Prime Factor FFT Algorithm on Cray-1”, to be published.Google Scholar
- Agarwal, R. C. and Cooley, J. W. “Vectorized Mixed Radix Discrete Fourier Transform Algorithms”, IEEE Proc., 75 (9), Sep. 1987.Google Scholar
- Heideman, M. T. Multiplicative Complexity, Convolution, and the DFT, Springer-Verlag, 1988.Google Scholar
- Lu, C. Fast Fourier Transform Algorithms For Special N’s and The Implementations On VAX, Ph.D. Dissertation, The City University of New York, Jan. 1988.Google Scholar
- Tolimieri, R., Lu, C. 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
- Lu, C. and Tolimieri, R. “Extension of Winograd Multiplicative Algorithm to Transform Size N = p 2 q, p 2 qr and Their Implementation”, Proc. ICASSP 89, Scotland, May 22–26.Google Scholar
- Gertner, I. “A New Efficient Algorithm to Compute the Two-Dimensional Discrete Fourier Transform”, IEEE Trans. Acoust., Speech and Signal Proc., 36 (7), July 1988.Google Scholar