Orthogonal polynomial wavelets

Bernd Fischer; Woula Themistoclakis

doi:10.1023/A:1015689418605

Orthogonal polynomial wavelets

Bernd Fischer^*, Woula Themistoclakis

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Mathematik

Univ. degli Studi della Basilicata

9 Zitate (Scopus)

Abstract

Recently Fischer and Prestin presented a unified approach for the construction of polynomial wavelets. In particular, they characterized those parameter sets which lead to orthogonal scaling functions. Here, we extend their results to the wavelets. We work out necessary and sufficient conditions for the wavelets to be orthogonal to each other. Furthermore, we show how these computable characterizations lead to attractive decomposition and reconstruction schemes. The paper concludes with a study of the special case of Bernstein-Szegö weight functions.

Originalsprache	Englisch
Zeitschrift	Numerical Algorithms
Jahrgang	30
Ausgabenummer	1
Seiten (von - bis)	37-58
Seitenumfang	22
ISSN	1017-1398
DOIs	https://doi.org/10.1023/A:1015689418605
Publikationsstatus	Veröffentlicht - 01.12.2002

Fördermittel

The second author is grateful for the warm-hearted support she had in visiting the Institute of Mathematics at the Medical University of Lübeck. She also thanks the Department of Mathematics of the University of Basilicata for financial support.

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10.1023/A:1015689418605

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abstract = "Recently Fischer and Prestin presented a unified approach for the construction of polynomial wavelets. In particular, they characterized those parameter sets which lead to orthogonal scaling functions. Here, we extend their results to the wavelets. We work out necessary and sufficient conditions for the wavelets to be orthogonal to each other. Furthermore, we show how these computable characterizations lead to attractive decomposition and reconstruction schemes. The paper concludes with a study of the special case of Bernstein-Szeg{\"o} weight functions.",

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Orthogonal polynomial wavelets

Abstract

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