Non-translation-invariance and the synchronization problem in wavelet sampling

Title: Non-translation-invariance and the synchronization problem in wavelet sampling
Creator: Hogan, Jeffrey; Lakey, Joseph
Relation: Acta Applicandae Mathematicae Vol. 107, Issue 1-3, p. 373-398
Publisher Link: http://dx.doi.org/10.1007/s10440-009-9480-y
Publisher: Springer
Resource Type: journal article
Date: 2009
Description: One of the major differences between Paley-Wiener spaces of bandlimited signals and the principal shift-invariant (PSI) spaces of wavelet theory is that the latter, although shift-invariant, are in general not translation-invariant. In this paper we study the extra difficulties non-translation-invariance creates for the sampling theory of PSI and multiresolution spaces. In particular it is shown that sampling in PSI spaces requires an extra initialization step to determine the times at which sampled data is acquired. An algorithm is developed to provide this initialization and its effectiveness shown theoretically and demonstrated on a synthetic data set.
Subject: sampling; principal shift-invariant spaces; multiresolution analysis; Zak transform; scaling functions; quadrature mirror filter
Identifier: http://hdl.handle.net/1959.13/916900
Identifier: uon:8144
Identifier: ISSN:0167-8019
Language: eng
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