Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.acha.2013.03.005
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dc.titleFrom dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa
dc.contributor.authorChristensen, O.
dc.contributor.authorGoh, S.S.
dc.date.accessioned2014-10-28T02:35:34Z
dc.date.available2014-10-28T02:35:34Z
dc.date.issued2014-03
dc.identifier.citationChristensen, 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. https://doi.org/10.1016/j.acha.2013.03.005
dc.identifier.issn10635203
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/103302
dc.description.abstractWe 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.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.acha.2013.03.005
dc.sourceScopus
dc.subjectDual frames
dc.subjectGabor frames
dc.subjectMeyers wavelet
dc.subjectShannons wavelet
dc.subjectWavelet frames
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1016/j.acha.2013.03.005
dc.description.sourcetitleApplied and Computational Harmonic Analysis
dc.description.volume36
dc.description.issue2
dc.description.page198-214
dc.description.codenACOHE
dc.identifier.isiut000330601600002
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