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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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Published in: | Journal of approximation theory 2019-02, Vol.238, p.85-102 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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| |
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ISSN: | 0021-9045 1096-0430 |
DOI: | 10.1016/j.jat.2017.09.004 |