Perfect Reconstruction Filter Banks for Adaptive Filtering and Coding
Usevitch, Bryan Edward
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Permalink
https://hdl.handle.net/2142/72008
Description
Title
Perfect Reconstruction Filter Banks for Adaptive Filtering and Coding
Author(s)
Usevitch, Bryan Edward
Issue Date
1993
Doctoral Committee Chair(s)
Cybenko, G.,
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Abstract
This thesis considers the design of perfect reconstruction filter banks (PRFBs) for adaptive filtering and coding applications. The first half of this thesis derives a generalization to the Transform Domain Adaptive Filter (TDAF), which uses filter banks instead of unitary transforms to preprocess input signals. The parametrization for a class of nonparaunitary PRFBs is derived and used to express the minimum mean square error (MMSE) of the Generalized Transform Domain Adaptive Filters, in terms of the filter bank chosen. Using this parametrization, it is shown how to analytically design filter banks to give optimum error and convergence performances given prior knowledge of the adaptive application. Design examples demonstrate the improved error performance of the derived structures relative to the Least Mean Square (LMS) algorithm when prior knowledge is incorporated.
The second half of this thesis compares the energy compacting properties of unitary filters from transform coders and paraunitary filters from subband coders using a cost criterion which is proposed. Stationary processes for which paraunitary filters have better energy compaction than unitary filters are denoted as subband optimal, and all subband optimal processes are analytically characterized for the case of length-4 filters. It is shown analytically for length-4 filters and empirically for longer length filters that Markov-1 processes are subband optimal and that the Daubechies maximally smooth wavelet sequences achieve better energy compaction than the best unitary filters for Markov-1 inputs. A class of processes which is subband optimal for longer filter lengths is shown to have autocovariance matrices with a particular eigenstructure. Sample autocovariance matrices from images are shown to exhibit this structure and are also shown to be subband optimal.
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