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Parametrizing compactly supported orthonormal wavelets by discrete moments

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We discuss parametrizations of filter coefficients of scaling functions and compactly supported orthonormal wavelets with several vanishing moments. We introduce the first discrete moments of the filter coefficients as parameters. The discrete moments can be expressed in terms of the continuous moments of the related scaling function. To solve the resulting polynomial equations we use symbolic computation and in particular Gröbner bases. The cases of four to ten filter coefficients are discussed and explicit parametrizations are given.

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Authors and Affiliations

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

    Georg Regensburger

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  1. Georg Regensburger
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Correspondence to Georg Regensburger.

Additional information

This work was supported by the Austrian Science Fund (FWF) under the SFB grant F1322.

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Regensburger, G. Parametrizing compactly supported orthonormal wavelets by discrete moments. AAECC 18, 583–601 (2007). https://doi.org/10.1007/s00200-007-0054-9

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  • DOI: https://doi.org/10.1007/s00200-007-0054-9

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