Convolution on Finite Groups and Fixed-Polarity Polynomial Expressions

  • Radomir S. Stanković
  • Jaakko T. Astola
  • Claudio Moraga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5717)


This paper discusses relationships among convolution matrices and fixed-polarity matrices for polynomial expressions of discrete functions on finite groups. Switching and multiple-valued functions are considered as particular examples of discrete functions on finite groups. It is shown that if the negative literals for variables are defined in terms of the shift operators on domain groups, then there is a relationship between the polarity matrices and convolution matrices. Therefore, the recursive structure of polarity matrices follows from the recursive structure of convolution matrices. This structure is determined by the assumed decomposition of the domain groups for the considered functions.


Convolution Finite groups Polynomial expressions Spectral representations 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Radomir S. Stanković
    • 1
    • 2
  • Jaakko T. Astola
    • 1
    • 2
  • Claudio Moraga
    • 1
    • 2
  1. 1.Dept. of Computer Science, Faculty of Electronics, Niš, Serbia Dept. of Signal ProcessingTampere University of TechnologyTampereFinland
  2. 2.European Centre for Soft Computing, 33600 Mieres, Spain &, Technical University of DortmundDortmundGermany

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