Introduction to Multiplicative Fourier Transform Algorithm (MFTA)
The Cooley-Tukey FFT algorithm and its variants depend upon the existence of non-trivial 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 appealed to the multiplicative structure previously, in chapter 5, in the derivation of the Good-Thomas PFA.
KeywordsDiscrete Fourier Transform Real Multiplication Signal Proc Fast Fourier Transform Algorithm Multiplicative Structure
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- Kolba, D. P. and Parks, T. W. “Prime Factor FFT Algorithm Using High Speed Convolution”, IEEE Trans. Acoust., Speech and Signal Proc. ASSP-25(1977):281-294.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. vol 75, no.9, Sep., 1987.Google Scholar
- Heideman, M. T.: Multiplicative Complexity, Convolution, and the DFT, Springer-Verlag 1988.Google Scholar
- 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
- 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
- Lu, Chao and Tolimieri, R.:“Extension of Winograd Multiplicative Algorithm to Transform Size N=p 2q, p 2 qr and Their Implementation”, Proceeding of ICASSP 89, Scotland, May 22-26.Google Scholar
- Gertner, Izidor: “A New Efficient Algorithm to Compute the Two-Dimensional Discrete Fourier Transform” IEEE Trans, on ASSP, Vol. 36, No. 7, July 1988.Google Scholar
- Johnson, R.W., Lu, Chao and Tolimieri, R.:Fast Fourier Algorithms for the Size of Product of Distinct Primes and Implementations on VAX. Submitted to IEEE Trans. Acout., Speech, Signal Proc.Google Scholar
- Johnson, R. W., Lu, Chao and Tolimieri, R.:“Fast Fourier Algorithms for the Size of 4p and 4pq and Implementations on VAX”. Submitted to IEEE Trans.Acout., Speech, Signal Proc.Google Scholar