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Introduction to Multiplicative Fourier Transform Algorithm (MFTA)

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Algorithms for Discrete Fourier Transform and Convolution

Part of the book series: Signal Processing and Digital Filtering ((SIGNAL PROCESS))

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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.

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References

  1. Rader, C. M. “Discrete Fourier Transforms When the Number of Data Samples Is Prime”, Proc. IEEE 56 (1968): 1107–1108.

    Article  Google Scholar 

  2. Winograd, S. “On Computing the Discrete Fourier Transform”, Proc. Nat. Acad. Sct. USA., vol. 73. no. 4,(April 1976):1005–1006.

    Article  MathSciNet  MATH  Google Scholar 

  3. Winograd, S. “On Computing the Discrete Fourier Transform”, Math. of Computation, Vol.32, No. 141, (Jan. 1978):pp 175–199.

    Article  MathSciNet  MATH  Google Scholar 

  4. Temperton, C. “A Note on Prime Factor FFT Algorithms”. J. Comp. Phys., 52, (1983): 198–204.

    Article  MATH  Google Scholar 

  5. Blahut, R. E. Fast Algorithms for Digital Signal Processing, Chapter 8. Addison-Wesley, Reading, Mass., 1985.

    MATH  Google Scholar 

  6. 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 

  7. Temperton, C. “Implementation of Prime Factor FFT Algorithm on Cray-1”, to be published.

    Google Scholar 

  8. 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.

    Article  MathSciNet  Google Scholar 

  9. Agarwal, R.C. and Cooley, J.W. “Vectorized Mixed Radix Discrete Fourier Transform Algorithms”, IEEE Proc. vol 75, no.9, Sep., 1987.

    Google Scholar 

  10. Heideman, M. T.: Multiplicative Complexity, Convolution, and the DFT, Springer-Verlag 1988.

    Google Scholar 

  11. 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 

  12. 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.

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  13. 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 

  14. 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 

  15. 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 

  16. 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 

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© 1989 Springer Science+Business Media New York

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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

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  • 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

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