Multifilters and prefilters: Uniqueness and algorithmic aspects

Authors:
Mariantonia Cotronei;Maria Laura Lo Cascio;Tomas Sauer
Affiliations:
DIMET - Dipartimento di Informatica, Matematica, Elettronica e Trasporti, Universití degli Studi "Mediterranea" di Reggio Calabria, Via Graziella, loc. Feo di Vito, I-89122 Reggio Calabria, I ...;Dip. Me.Mo.Mat., Universití degli Studi di Roma "La Sapienza", Via Antonio Scarpa, I-00161 Roma, Italy;Lehrstuhl für Numerische Mathematik, Justus-Liebig-Universität Gieíen, Heinrich-Buff-Ring 44, D-35392 Gieíen, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper we study the structure of prefilters which ensure a certain approximation order of a given multifilter system. We show how all prefilters can be obtained from the generic one and that in general these prefilters are necessarily rational filters, but point out how a judicious choice of parameters can be used to obtain FIR filters for the approximation orders 1,2,3. Moreover, we illustrate the results by giving prefilters for the standard examples of multiwavelets.