Polynomial Transforms

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


The main objective of this chapter is to develop fast multidimensional filtering algorithms. These algorithms are based on the use of polynomial transforms which can be viewed as discrete Fourier transforms defined in rings of polynomials. Polynomial transforms can be computed without multiplications using ordinary arithmetic, and produce an efficient mapping of multidimensional convolutions into one-dimensional convolutions and polynomial products.


Chinese Remainder Theorem Reduction Modulo Cyclotomic Polynomial Polynomial Transform Circular Convolution 
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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  1. 6.1
    H. J. Nussbaumer: Digital filtering using polynomial transforms. Electron. Lett. 13, 386–387 (1977)CrossRefGoogle Scholar
  2. 6.2
    H. J. Nussbaumer, P. Quandalle: Computation of convolutions and discrete Fourier transforms by polynomial transforms. IBM J. Res. Dev. 22, 134–144 (1978)zbMATHMathSciNetGoogle Scholar
  3. 6.3
    P. Quandalle: “Filtrage numérique rapide par transformées de Fourier et transformées polynômiales—Etude de l’implantation sur microprocesseurs” Thèse de Doctorat de Spécialité, University of Nice, France (18 mai 1979 )Google Scholar
  4. 6.4
    R. C. Agarwal, J. W. Cooley: New algorithms for digital convolution. IEEE Trans. ASSP-25, 392–410 (1977)Google Scholar
  5. 6.5
    B. Arambepola, P. J. W. Rayner: Efficient transforms for multidimensional convolutions. Electron. Lett. 15, 189–190 (1979)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

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

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