Statistical properties of a memoryless nonlinear gradient algorithm for an adaptive constrained IIR notch filter

Gradient-type algorithms for adaptive IIR notch filters are very attractive in terms of both performance and computational requirements in real-life applications. This paper presents a statistical analysis of a memoryless nonlinear gradient algorithm developed recently for a well-known second-order adaptive IIR notch filter with constrained poles and zeros. This analysis is based on a proper use of the Taylor series expansion and the nonlinearization of filter output signals. A closed form expression for the steady-state bias is first derived, which is valid for both fast and slow adaptations. An analytical expression for the estimation mean square error is then derived for very slow adaptation. Stability bound of the algorithm is also discussed. Extensive simulations are performed to support the analytical findings