Annals of Combinatorics

, Volume 9, Issue 2, pp 223–243 | Cite as

Symbolic Computation for Moments and Filter Coefficients of Scaling Functions

Original Paper

Abstract.

Algebraic relations between discrete and continuous moments of scaling functions are investigated based on the construction of Bell polynomials. We introduce families of scaling functions which are parametrized by moments. Filter coefficients of scaling functions and wavelets are computed with computer algebra methods (in particular Gröbner bases) using relations between moments. Moreover, we propose a novel concept for data compression based on parametrized wavelets.

AMS Subject Classification.

42C40 65T60 13P10 94A12 05A10 33C45 

Keywords.

scaling functions moments Bell polynomials wavelets Gröbner bases data compression 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria
  2. 2.Department of Computer ScienceUniversity of InnsbruckInnsbruckAustria

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