Mean-squared error analysis of an adaptive notch filter

A mean-square-error analysis of the steady-state coefficient fluctuation of an infinite impulse response (IIR) adaptive notch filter, whose coefficients are estimated by simple gradient and sign gradient algorithms, is presented. Regarding the magnitude and phase responses of the transfer function that is used to realize a second-order IIR adaptive notch filter, it is shown that the filter-coefficient estimation error can be studied by using first-order ordinary difference equations with stochastic input. Simple closed-form results are derived for the mean-square error of the steady-state coefficients. The results of computer experiments are presented to substantiate the analysis