Date of Award

Spring 1991

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Electrical Engineering - (Ph.D.)

Department

Electrical and Computer Engineering

First Advisor

Ali N. Akansu

Second Advisor

Rashid Ansari

Third Advisor

Yeheskel Bar-Ness

Fourth Advisor

Erdal Panayirci

Fifth Advisor

John Tavantzis

Abstract

This dissertation aims to emphasize the interrelations and the linkages of the theories of discrete-time filter banks and wavelet transforms. It is shown that the Binomial-QMF banks are identical to the interscale coeffi cients or filters of the compactly supported orthonormal wavelet transform bases proposed by Daubechies.

A generalized, parametric, smooth 2-band PR-QMF design approach based on Bernstein polynomial approximation is developed. It is found that the most regular compact support orthonormal wavelet filters, coiflet filters are only the special cases of the proposed filter bank design technique.

A new objective performance measure called Non-aliasing Energy Ra-tio(NER) is developed. Its merits are proven with the comparative performance studies of the well known orthonormal signal decomposition techniques.

This dissertation also addresses the optimal 2-band PR-QMF design problem. The variables of practical significance in image processing and coding are included in the optimization problem. The upper performance bounds of 2-band PR-QMF and their corresponding filter coefficients are derived.

It is objectively shown that there are superior filter bank solutions available over the standard block transform, DCT. It is expected that the theoretical contributions of this dissertation will find its applications particularly in Visual Signal Processing and Coding.

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