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Symbolic Computation for Moments and Filter Coefficients of Scaling Functions
Georg Regensburger1 and Otmar Scherzer2
1Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, 4040 A-Linz, Austria
georg.regensburger@oeaw.ac.at
2Department of Computer Science, University of Innsbruck, Techniker Str. 25, A-6020 Innsbruck, Austria
otmar.scherzer@uibk.ac.at
Annals of Combinatorics 9 (2) p.223-243 June, 2005
AMS Subject Classification: 42C40, 65T60, 13P10, 94A12, 05A10, 33C45
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.
Keywords: scaling functions, moments, Bell polynomials, wavelets, Gröbner bases, data compression

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