Performance analysis of normalized update algorithm for adaptive digital notch filter

Methods of analyzing the convergence and steady-state characteristics of an adaptive notch filter whose coefficient is estimated by a normalized gradient algorithm are presented. The adaptive detection of a sinusoid with white Gaussian noise is investigated. An expression for the necessary iterations of convergence is derived. The basic idea is the integration of the inverse of the average step size for the coefficient update algorithm. Closed-form expressions for the steady-state mean square error of the variable coefficient are obtained. The results of computer simulations are presented to substantiate the analysis