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System theory and orthogonal multi-wavelets

In this paper we provide a complete and unifying characterization of compactly supported univariate scalar orthogonal wavelets and vector-valued or matrix-valued orthogonal multi-wavelets. This characterization is based on classical results from system theory and basic linear algebra. In particular,...

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Bibliographic Details
Published in:Journal of approximation theory 2019-02, Vol.238, p.85-102
Main Authors: Charina, Maria, Conti, Costanza, Cotronei, Mariantonia, Putinar, Mihai
Format: Article
Language:English
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Summary:In this paper we provide a complete and unifying characterization of compactly supported univariate scalar orthogonal wavelets and vector-valued or matrix-valued orthogonal multi-wavelets. This characterization is based on classical results from system theory and basic linear algebra. In particular, we show that the corresponding wavelet and multi-wavelet masks are identified with a transfer function F(z)=A+Bz(I−Dz)−1C,z∈D={z∈C:|z|
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2017.09.004