Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.acha.2005.09.001
Title: Wavelet frames and shift-invariant subspaces of periodic functions
Authors: Goh, S.S. 
Teo, K.M.
Keywords: Multiresolution analysis
Polyphase splines
Shift-invariant subspaces
Wavelet frames
Issue Date: May-2006
Citation: Goh, S.S., Teo, K.M. (2006-05). Wavelet frames and shift-invariant subspaces of periodic functions. Applied and Computational Harmonic Analysis 20 (3) : 326-344. ScholarBank@NUS Repository. https://doi.org/10.1016/j.acha.2005.09.001
Abstract: A general approach based on polyphase splines, with analysis in the frequency domain, is developed for studying wavelet frames of periodic functions of one or higher dimensions. Characterizations of frames for shift-invariant subspaces of periodic functions and results on the structure of these subspaces are obtained. Starting from any multiresolution analysis, a constructive proof is provided for the existence of a normalized tight wavelet frame. The construction gives the minimum number of wavelets required. As an illustration of the approach developed, the one-dimensional dyadic case is further discussed in detail, concluding with a concrete example of trigonometric polynomial wavelet frames. © 2005 Elsevier Inc. All rights reserved.
Source Title: Applied and Computational Harmonic Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/104461
ISSN: 10635203
DOI: 10.1016/j.acha.2005.09.001
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