New results on paraunitary filter banks : energy compaction properties, linear phase factorizations and relation to wavelets

Author: Soman, Anand

Year: 1993

Degree: Dissertation (Ph.D.)

Advisor: Vaidyanathan, P. P.

Committee Member: Unknown, Unknown

Option: Electrical Engineering

DOI: 10.7907/tkk3-a559

Abstract

Subband coding schemes have been widely used to encode signals from speech, high quality audio, and image sources. The theory of perfect reconstruction filter banks has also been studied extensively. The purpose of this thesis is to study the properties of the so-called paraunitary systems, and issues pertaining to their applications and implementations.

We will begin by proving several properties of paraunitary filter banks. For example, we will prove that all orthonormal discrete-time wavelets can be generated using paraunitary binary trees. We will also extend this result to arbitrary tree-structures and wavelet packets. Next, we will address the two issues involved in the design of a paraunitary subband coding system. 1) the problem of optimal bit allocation among various channels given a fixed bit-rate, and 2) the problem of finding the optimal filter bank (by optimization) to encode a given signal. We will prove several interesting results in this regard. We will then show how generalized polyphase representations can be used to enhance the coding gain of transform coding systems.

In practical applications, one often imposes several other conditions on the individual filters in a filter bank. For example, the linear phase property is found to be important for encoding image signals, whereas the 'pairwise mirror-image' property generally yields filters with better responses and, therefore, better frequency selectivity. The final part of the thesis deals with the implementions of paraunitary systems having such additional properties. We will obtain factorizations for such systems which will be proved to be minimal as well as complete. These factorizations yield structures which are robust, i.e., all the desired properties are retained in spite of coefficient quantization.

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