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Symbolic Computation for Moments and Filter Coefficients of Scaling Functions

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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.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, A-4040, Linz, Austria

    Georg Regensburger

  2. Department of Computer Science, University of Innsbruck, Techniker Str. 25, A-6020, Innsbruck, Austria

    Otmar Scherzer

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  1. Georg Regensburger
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  2. Otmar Scherzer
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Correspondence to Georg Regensburger.

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Received December 15, 2003

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Regensburger, G., Scherzer, O. Symbolic Computation for Moments and Filter Coefficients of Scaling Functions. Ann. Comb. 9, 223–243 (2005). https://doi.org/10.1007/s00026-005-0253-7

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  • DOI: https://doi.org/10.1007/s00026-005-0253-7

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