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Non-separable two dimensional wavelets and their filter banks in polar coordinates

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Date Issued:
1995
Summary:
The problems encountered in development and implementation of orthonormal two dimensional wavelet bases and their filter banks in polar coordinates are addressed. These wavelets and filter banks have possible applications in processing signals that are collected by sensors working in the polar coordinate system, such as biomedical and radar generated signals. The relationship between the space of measurable, square-integrable functions on the punctured polar coordinate system L^2(P) and space of measurable, square-integrable functions on the rectangular plane L^2(R^2) is developed. This allows us to develop complete wavelet bases in a more convenient and familiar surrounding of L^2(R^2) and to transport this theory to L^2(P). Corresponding filter banks are also developed. The implementation of wavelet analysis of punctured polar plane is discussed. An example of wavelet bases, filter banks, and implementation is provided.
Title: Non-separable two dimensional wavelets and their filter banks in polar coordinates.
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Name(s): Andric, Oleg.
Florida Atlantic University, Degree grantor
Erdol, Nurgun, Thesis advisor
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 1995
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 111 p.
Language(s): English
Summary: The problems encountered in development and implementation of orthonormal two dimensional wavelet bases and their filter banks in polar coordinates are addressed. These wavelets and filter banks have possible applications in processing signals that are collected by sensors working in the polar coordinate system, such as biomedical and radar generated signals. The relationship between the space of measurable, square-integrable functions on the punctured polar coordinate system L^2(P) and space of measurable, square-integrable functions on the rectangular plane L^2(R^2) is developed. This allows us to develop complete wavelet bases in a more convenient and familiar surrounding of L^2(R^2) and to transport this theory to L^2(P). Corresponding filter banks are also developed. The implementation of wavelet analysis of punctured polar plane is discussed. An example of wavelet bases, filter banks, and implementation is provided.
Identifier: 15190 (digitool), FADT15190 (IID), fau:11962 (fedora)
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): College of Engineering and Computer Science
Thesis (M.S.)--Florida Atlantic University, 1995.
Subject(s): Wavelets (Mathematics)
Coordinates, Polar
Signal processing--Mathematical models
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fcla/dt/15190
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.