Performance Analysis of th e Sign Algorithm for an Adaptive IIR Notch Filter with Constrained Poles and Zeros

Gradient-type algorithms for adaptive IIR notch filters are very attractive in terms of both performances and computational requirements. Generally, it is quite difficult to assess their performances analytically. There have been several trials to analyze such adaptive algorithms as the sign and the plain gradient algorithms for some types of adaptive IIR notch filters, but many of them still remain unexplored. Furthermore, analysis techniques used in those trials can not be directly applied to different types of adaptive IIR notch filters. This paper presents a detailed performance analysis of the sign algorithm for a well-known adaptive IIR notch filter with constrained poles and zeros, which can not be done by just applying the related existing analysis techniques, and therefore has not been attempted yet. The steady-state estimation error and mean square error (MSE) of the algorithm are derived in closed forms. Stability bounds of the algorithm are also assessed. extensive simulations are conducted to support the analytical findings.