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Implementation and representation of the discrete wavelet transform
- 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 |
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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. |
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Subject(s): |
Wavelets (Mathematics) Integrals, Singular Signal processing--Digital techniques |
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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. |