On the stability and convergence of Feintuch's algorithm for adaptive IIR filtering

Gradient-descent adaptive algorithms are among the most widely used in current practice, with many different variants that generally fit into two major groups: one group includes algorithms that are especially suited for FIR (or finite-impulse-response) modeling, while the other group includes algorithms that are tailored for IIR (or infinite-impulse-response) modeling. In the first group, the regression (or data) vectors do not depend on the unknown parameters, which leads to convenient linear models that often facilitate the analysis of the algorithms. In the second category, on the other hand, the regression vectors are dependent on the unknown parameters, thus giving rise to nonlinear functionals and to a richer structure that requires a more thorough analysis. This paper focuses on a widely used adaptive IIR algorithm, the so-called Feintuch's (1976) algorithm, and provides a study of its robustness, stability, and convergence properties in a deterministic framework.

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