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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/916900

Title: Non-translation-invariance and the synchronization problem in wavelet sampling
Author/Creator: Hogan, Jeffrey; Lakey, Joseph
Institution: The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
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.
Relation: Acta Applicandae Mathematicae Vol. 107, Issue 1-3, p. 373-398
Publisher Link: http://dx.doi.org/10.1007/s10440-009-9480-y
Date: 2009
Publisher: Springer
Keyword(s): sampling; principal shift-invariant spaces; multiresolution analysis; Zak transform; scaling functions; quadrature mirror filter
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/916900
Identifier: ISSN:0167-8019

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