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Title: From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa
Authors: Christensen, O.
Goh, S.S. 
Keywords: Dual frames
Gabor frames
Meyers wavelet
Shannons wavelet
Wavelet frames
Issue Date: Mar-2014
Citation: Christensen, O., Goh, S.S. (2014-03). From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa. Applied and Computational Harmonic Analysis 36 (2) : 198-214. ScholarBank@NUS Repository.
Abstract: We discuss an elementary procedure that allows us to construct dual pairs of wavelet frames based on certain dual pairs of Gabor frames and vice versa. The construction preserves tightness of the involved frames. Starting with Gabor frames generated by characteristic functions the construction leads to a class of tight wavelet frames that include the Shannon (orthonormal) wavelet, and applying the construction to Gabor frames generated by certain exponential B-splines yields wavelet frames generated by functions whose Fourier transforms are compactly supported splines with geometrically distributed knot sequences. On the other hand, the pendant of the Meyer wavelet turns out to be a tight Gabor frame generated by a C (R)function with compact support. Asanapplication of ourresults weshow that foreachgiven pairofbandlimiteddualwaveletframesitispossibletoconstructdualwaveletframesforad esiredscalingandtranslationparameters. © 2013 Elsevier Inc. All rights reserved.
Source Title: Applied and Computational Harmonic Analysis
ISSN: 10635203
DOI: 10.1016/j.acha.2013.03.005
Appears in Collections:Staff Publications

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