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Matrix spectral factorization for SA4 multiwavelet

Authors
  • Kolev, Vasil1
  • Cooklev, Todor2
  • Keinert, Fritz3
  • 1 Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, Bl. 2 Acad. G. Bonchev St., Sofia, 1113, Bulgaria , Sofia (Bulgaria)
  • 2 Indiana University – Purdue University, Wireless Technology Center, Fort Wayne, IN, 46805, USA , Fort Wayne (United States)
  • 3 Iowa State University, Department of Mathematics, Ames, IA, 50011, USA , Ames (United States)
Type
Published Article
Journal
Multidimensional Systems and Signal Processing
Publisher
Springer US
Publication Date
Aug 22, 2017
Volume
29
Issue
4
Pages
1613–1641
Identifiers
DOI: 10.1007/s11045-017-0520-x
Source
Springer Nature
Keywords
License
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Abstract

In this paper, we investigate Bauer’s method for the matrix spectral factorization of an r-channel matrix product filter which is a half-band autocorrelation matrix. We regularize the resulting matrix spectral factors by an averaging approach and by multiplication by a unitary matrix. This leads to the approximate and exact orthogonal SA4 multiscaling functions. We also find the corresponding orthogonal multiwavelet functions, based on the QR decomposition.

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