Performance analysis of adaptive IIR notch filters based on least mean p-power error criterion

In this paper, we present the steady state analysis of adaptive IIR notch filters based on the least mean p-power error criterion. We consider the cases when the sinusoidal signal is contaminated with white Gaussian noise and p=3, 4. We first derive two difference equations for the convergence of the mean and the mean square error (MSE) of the adaptive filter's notch coefficient, and then give the steady state estimation bias and MSE. Stability conditions on the step size value are also derived. Simulation experiments are presented to confirm the validity of the obtained analytical results. It is shown that the notch coefficient steady state bias of the p-power algorithm for small step size values is independent of the step size value and is equal for p=1, 2, 3 and 4. However, for larger step size values, the p-power algorithm with p=3 provides the best performance in term of the MSE.