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Implementation and representation of the discrete wavelet transform

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Date Issued:
1993
Summary:
This thesis presents a comprehensive analysis of a relatively new transform for discrete time signals, called the Discrete Wavelet Transform (DWT). We find how this transform is connected with the already existing theory of perfect reconstruction filter banks and the recently introduced theory of multiresolution analysis. We use the conditions obtained from these two theories in order to understand the construction of wavelet filters, which also generate continuous functions that prove to constitute an orthonormal basis for the L$\sp2$ space. We also investigate the connection of this transform to the sampled wavelet series of nonorthogonal functions with good time-frequency localization properties. Finally, we see the way that the DWT maps a discrete signal in the phase plane and the applications that such representations incorporate.
Title: Implementation and representation of the discrete wavelet transform.
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Name(s): Efthymoglou, George P.
Florida Atlantic University, Degree grantor
Erdol, Nurgun, Thesis advisor
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 1993
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 119 p.
Language(s): English
Summary: This thesis presents a comprehensive analysis of a relatively new transform for discrete time signals, called the Discrete Wavelet Transform (DWT). We find how this transform is connected with the already existing theory of perfect reconstruction filter banks and the recently introduced theory of multiresolution analysis. We use the conditions obtained from these two theories in order to understand the construction of wavelet filters, which also generate continuous functions that prove to constitute an orthonormal basis for the L$\sp2$ space. We also investigate the connection of this transform to the sampled wavelet series of nonorthogonal functions with good time-frequency localization properties. Finally, we see the way that the DWT maps a discrete signal in the phase plane and the applications that such representations incorporate.
Identifier: 14944 (digitool), FADT14944 (IID), fau:11724 (fedora)
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): College of Engineering and Computer Science
Thesis (M.S.E.)--Florida Atlantic University, 1993.
Subject(s): Wavelets (Mathematics)
Integrals, Singular
Signal processing--Digital techniques
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fcla/dt/14944
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.