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Title: Pairs of dual periodic frames
Authors: Christensen, O.
Goh, S.S. 
Keywords: Dual pairs of frames
Gabor frames
Periodic frames
Trigonometric polynomials
Wavelet frames
Issue Date: Nov-2012
Citation: Christensen, O., Goh, S.S. (2012-11). Pairs of dual periodic frames. Applied and Computational Harmonic Analysis 33 (3) : 315-329. ScholarBank@NUS Repository.
Abstract: The time-frequency analysis of a signal is often performed via a series expansion arising from well-localized building blocks. Typically, the building blocks are based on frames having either Gabor or wavelet structure. In order to calculate the coefficients in the series expansion, a dual frame is needed. The purpose of the present paper is to provide constructions of dual pairs of frames in the setting of the Hilbert space of periodic functions L2(0,2π). The frames constructed are given explicitly as trigonometric polynomials, which allows for an efficient calculation of the coefficients in the series expansions. The generality of the setup covers periodic frames of various types, including nonstationary wavelet systems, Gabor systems and certain hybrids of them. © 2012 Elsevier Inc. All rights reserved.
Source Title: Applied and Computational Harmonic Analysis
ISSN: 10635203
DOI: 10.1016/j.acha.2011.12.003
Appears in Collections:Staff Publications

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