Tracking characteristics of the constrained IIR adaptive notch filter

In this paper, we study the tracking behavior of a constrained IIR notch filter whose coefficients are estimated using a constant step size Gauss-Newton algorithm. Using weak convergence theory and the concept of prescaling, it is shown that the mean behavior of the adaptive filter coefficients can be studied by using an ordinary differential equation (ODE). Approximate and simple closed form results are derived for the tracking behavior of a second order notch filter. Computer simulations are presented to substantiate the analysis.