Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Rader, C. M. “Discrete Fourier Transforms When the Number of Data Samples Is Prime”, Proc. IEEE 56 (1968): 1107–1108.
Winograd, S. “On Computing the Discrete Fourier Transform”, Proc. Nat. Acad. Sct. USA., vol. 73. no. 4,(April 1976):1005–1006.
Winograd, S. “On Computing the Discrete Fourier Transform”, Math. of Computation, Vol.32, No. 141, (Jan. 1978):pp 175–199.
Temperton, C. “A Note on Prime Factor FFT Algorithms”. J. Comp. Phys., 52, (1983): 198–204.
Blahut, R. E. Fast Algorithms for Digital Signal Processing, Chapter 8. Addison-Wesley, Reading, Mass., 1985.
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.
Temperton, C. “Implementation of Prime Factor FFT Algorithm on Cray-1”, to be published.
Agarwal, R.C. and Cooley, J. W. “Fourier Transform and Convolution Subroutines for the IBM 3090 Vector Facility”, IBM J. Res. Devel., vol.30 pp 145–162. Mar., 1986.
Agarwal, R.C. and Cooley, J.W. “Vectorized Mixed Radix Discrete Fourier Transform Algorithms”, IEEE Proc. vol 75, no.9, Sep., 1987.
Heideman, M. T.: Multiplicative Complexity, Convolution, and the DFT, Springer-Verlag 1988.
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.
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.
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.
Gertner, Izidor: “A New Efficient Algorithm to Compute the Two-Dimensional Discrete Fourier Transform” IEEE Trans, on ASSP, Vol. 36, No. 7, July 1988.
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.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tolimieri, R., An, M., Lu, C. (1989). Introduction to Multiplicative Fourier Transform Algorithm (MFTA). In: Burrus, C.S. (eds) Algorithms for Discrete Fourier Transform and Convolution. Signal Processing and Digital Filtering. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3854-4_8
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3854-4_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3856-8
Online ISBN: 978-1-4757-3854-4
eBook Packages: Springer Book Archive