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Abstract:
In this paper, we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets with arbitrary integer dilation factor m. A necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets is derived by virtue of paraunitary vector filter bank theory. An algorithm for constructing compactly supported m-scale orthogonal matrix-valued wavelets is presented. The notion of orthogonal matrix-valued wavelet packets is proposed. Their properties are investigated by means of time-frequency method, operator theory and matrix theory. In particular, it is shown how to construct various orthonormal bases of space L(2) (R, C(rxr)) from these wavelet packets, and the orthogonal decomposition relation is also given. (C) 2007 Elsevier Ltd. All rights reserved.
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Source :
CHAOS SOLITONS & FRACTALS
ISSN: 0960-0779
Year: 2008
Issue: 1
Volume: 37
Page: 75-86
2 . 9 8
JCR@2008
5 . 9 4 4
JCR@2020
ESI Discipline: PHYSICS;
JCR Journal Grade:2
CAS Journal Grade:3
Cited Count:
WoS CC Cited Count: 24
SCOPUS Cited Count: 29
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 0
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