From filters to wavelets via direct limits. II: Wavelet-packet bases
type: Item
instance of: scholarly article
title: From filters to wavelets via direct limits. II: Wavelet-packet bases
zbMATH Open document ID: 1190.42022
author: Iain Raeburn
published in: Acta Applicandae Mathematicae
publication date: 2010-01-18T00:00:00Z
review text: The author, together with \textit{N. Larson} [in: Operator theory, operator algebras, and applications. Proceedings of the 25th Great Plains Operator Theory Symposium, University of Central Florida, FL, USA, June 7--12, 2005. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 414, 35--40 (2006; Zbl 1151.42317)], identified a particular direct limit of Hilbert spaces that links to the Mallat's wavelet construction from quadrature mirror filters. In this paper, the author shows that the same direct-limit framework works for wavelet-packet bases.
reviewed by: Qiyu Sun
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5659965
zbMATH Keywords: wavelet
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: wavelet packet
zbMATH Keywords: Cuntz family
zbMATH Keywords: direct limit
zbMATH Keywords: Hilbert space
MaRDI profile type: Publication
full work available at URL: s10440-008-9425-x
OpenAlex ID: W2134868051
cites work: Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale \(N\)
cites work: Q3408823
cites work: Q3414349
cites work: Projective multi-resolution analyses arising from direct limits of Hilbert modules
cites work: Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
cites work: Projective multi-resolution analyses for \(L^2(\mathbb R^2)\)
cites work: Q4681774
cites work: Q4320129
DOI: 10.1007/S10440-008-9425-X
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description: scientific article; zbMATH DE number 5659965