Improvements in Adaptive IIR Filtering: Theory and Application
Nayeri, Majid
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https://hdl.handle.net/2142/69400
Description
Title
Improvements in Adaptive IIR Filtering: Theory and Application
Author(s)
Nayeri, Majid
Issue Date
1988
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
Characteristics of the mean-square error surface in adaptive digital filters determine how well a gradient algorithm performs within a given filter structure, i.e., if the surface has steep slopes and contains local minima, a gradient algorithm will have difficulty reaching the global minimum. It is shown that although Stearns' conjecture holds strictly for first- and second-order filters, it is not true in general, and that an additional restriction introduced by Soderstrom is needed for unimodality of the error surface. The adverse effect of overparameterization which can have serious practical implications is shown through an example. Also, it is shown that for certain insufficient order filters, a nonminimum phase characteristic is sufficient for multimodality of the error surface when the unknown system is driven by white noise. A convenient method for finding the stationary points is introduced.
It is also shown how different filter structures of an adaptive filter leads to a change in the characteristics of the corresponding error surface, and consequently, to a change in the corresponding convergence rate and minimum mean square error. A general theory, based on an analysis of stationary points, is presented which shows that whenever a direct form IIR filter with a unimodal MSE surface is transformed into an alternate realization, the MSE surface associated with the new structure may have additional points, which are either new equivalent minima, or saddle points. The general theory is specialized for the parallel and cascade forms.
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