The continuous wavelet transform: A discrete approximation

dc.contributor.advisorBurrus, C. Sidneyen_US
dc.creatorLewis, James M.en_US
dc.date.accessioned2009-06-04T08:18:18Zen_US
dc.date.available2009-06-04T08:18:18Zen_US
dc.date.issued1998en_US
dc.description.abstractIn this thesis, we develop an approximation to the continuous wavelet transform (CWT) which is unique in that it does not require an exact scaling relationship between the levels of the transform, but asymptotically approaches an irrational scaling ratio of 2$\sp{1/n{\sb0}}$ where $n\sb0$ is related to the number of vanishing moments of the original scaling filter. The autocorrelation sequences of the scaling and wavelet filters associated with the Daubechies family of orthonormal compactly supported wavelets are shown to converge to smooth symmetric wavelets which approximate the Deslauriers and Dubuc limiting functions. We show why this transform is superior to a conventional dyadic wavelet transform for the edge detection application, and analyze its performance in denoising applications.en_US
dc.format.extent91 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS E.E. 1998 LEWISen_US
dc.identifier.citationLewis, James M.. "The continuous wavelet transform: A discrete approximation." (1998) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/17192">https://hdl.handle.net/1911/17192</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/17192en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectElectronicsen_US
dc.subjectElectrical engineeringen_US
dc.titleThe continuous wavelet transform: A discrete approximationen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentElectrical Engineeringen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Scienceen_US
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