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Computation of Discrete Fourier Transforms by Polynomial Transforms

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Part of the Springer Series in Information Sciences book series (SSINF, volume 2)

Abstract

As indicated in the previous chapter, polynomial transforms can be used to efficiently map multidimensional convolutions into one-dimensional convolutions and polynomial products. In this chapter, we shall see that polynomial transforms can also be used to map multidimensional DFTs into one-dimensional DFTs. This mapping is very efficient because it is accomplished using ordinary arithmetic without multiplications, and because it can be implemented by FFT-type algorithms when the dimensions are composite.

Keywords

Discrete Fourier Transform Arithmetic Operation Real Multiplication Real Operation Reduction Modulo 
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.

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References

  1. 7.1
    H. J. Nussbaumer, P. Quandalle: Fast computation of discrete Fourier transforms using polynomial transforms. IEEE Trans. ASSP-27, 169–181 (1979)MathSciNetGoogle Scholar
  2. 7.2
    H. J. Nussbaumer, P. Quandalle: “New Polynomial Transform Algorithms for Fast DFT Computation”, in IEEE 1979 Intern. Acoustics, Speech and Signal Processing Conf. Proc., pp. 510–513Google Scholar
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    S. Winograd: On computing the discrete Fourier transform. Math. Comput. 32, 175–199 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
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    H. J. Nussbaumer: DFT computation by fast polynomial transform algorithms. Electron. Lett. 15 701–702 (1979)CrossRefGoogle Scholar
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    H. J. Nussbaumer, P. Quandalle: Computation of convolutions and discrete Fourier transforms by polynomial transforms. IBM J. Res. Dev. 22, 134–144 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
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    R. C. Agarwal, J. W. Cooley: New algorithms for digital convolution. IEEE Trans. ASSP-25, 392–410 (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  1. 1.Department d’ElectricitéEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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