Boundary functions for wavelets and their properties

dc.contributor.advisor Fritz Keinert Alturk, Ahmet
dc.contributor.department Mathematics 2018-08-11T09:34:17.000 2020-06-30T02:31:27Z 2020-06-30T02:31:27Z Thu Jan 01 00:00:00 UTC 2009 2013-06-05 2009-01-01
dc.description.abstract <p>Wavelets and wavelet transforms have been studied extensively since the 1980s. It has been shown that the Discrete Wavelet Transform (DWT) can be applied to an enormous number of applications in virtually every branch of science.</p> <p>The DWT is designed for decomposing and reconstructing infinitely long signals. In practice, we can only deal with finitely long signals. This raises the very important question of handling boundaries. What should be done near the ends?</p> <p>Several approaches have been proposed to deal with this problem. In this dissertation, we consider the boundary function approach. The idea is to alter the DWT by constructing appropriate boundary functions at each end so that finite length signals can be analyzed accurately. This dissertation contains two sets of new results. One is about smoothness and approximation order properties of boundary functions. The other is about finding boundary functions. The results have been elaborated upon for some specific wavelets.</p>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 1825
dc.identifier.contextkey 2807023
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath etd/10848
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 18:29:21 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords boundary functions
dc.subject.keywords discrete multiwavelet tranform
dc.subject.keywords discrete wavelet transform
dc.subject.keywords multiwavelets
dc.subject.keywords wavelets
dc.title Boundary functions for wavelets and their properties
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 dissertation Doctor of Philosophy
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