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It is well known that a digital filter can be characterized with different parametrizations and realized with different structures. The main objective of this thesis is two-fold. The first one is to investigate the effects of parametrizations and structures on the performance of adaptive filters, particularly on the stability aspect, and hence to derive new adaptive algorithms. The second one is to examine how a well-designed adaptive algorithm can be degraded when implemented with finite precision considerations. The main contributions in this thesis are summarized as follows. After demonstrating the finite word length (FWL) effects on the adaptive filters using the traditional direct-form-based structures, a simple adaptive state-space filter is derived. This structure is computationally efficient and it is shown that such an adaptive filter yields much better performance than the classical adaptive state-space filters in terms of stability and FWL behavior. It is shown that when an adaptive filter can be implemented with a normal statespace realization, the corresponding adaptive algorithm is bounded-input boundedoutput (BIBO) stable if the instantaneous poles of the filter are all inside the circle |z| < γ with γ a constant satisfying 0 < γ < 1. As one of the applications of this new result, a novel adaptive constrained IIR notch filter is derived, where the filter is parametrized using the frequency vector and implemented in a cascade form with ii ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library

A parametric approach to adaptive IIR filtering : finite precision implementation and stability aspects