On the group algebras' hierarchy pertaining to the parametrization of fast algorithms of Discrete Orthogonal Transforms

  • Vladimir M. Chernov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 970)


The problem of the parametrization of fast algorithms of Discrete Orthogonal Transforms (DOTs) is treated. It has been shown that the general approach the author takes to the problem of synthesizing DOTs that employs associated DOTs with values in group algebras and subsequent interpretation of the result in an initial field forms a structural basis for such a parametrization. As an example, fast algorithms for a real DFT featured by the asymptotic reduction of order of the principal member in the estimate of multiplicative complexity are synthesized.


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  1. 1.
    Blahut R.E. Fast Algorithms for Digital Signal Processing. Addison-Wesley, Readling, Mass., 1985.Google Scholar
  2. 2.
    Elliot D.F., Rao K.R. Fast Transforms. New York: Academic, 1982.Google Scholar
  3. 3.
    Chernov V.M. The FFT algorithms with data representation in algebraic number fields //Automatic Control and Comp. Sci., 1994, N4. pp. 64–69.Google Scholar
  4. 4.
    Chernov V. M. Fast algorithms of discrete orthogonal transforms for data represented in cyclotomic fields //Pattern Recogn. and Image Anal. 1993. V 3. N4. pp. 455–458.Google Scholar
  5. 5.
    Chernov V.M. Arithmetic methods in the theory of discrete orthogonal transforms //Workshop on Digital Image Processing and Computer Graphics. Proceedings SPIE, V 2363, 1994.Google Scholar
  6. 6.
    Chernov V. M. Non-archimedian normalized fields and algorithms for the two-dimensional Fourier transforms //Pattern Recogn. and Image Anal. 1991. V 1. N4. pp.426–429.Google Scholar
  7. 7.
    Lang S. Algebraic Numbers. Addison-Wesley, Readling, Mass., 1964.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Vladimir M. Chernov
    • 1
  1. 1.Image Processing Systems InstituteRASSamaraRussia

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