In this letter, a method to analyze the steady-state characteristics of multirale IIR adaptive notch filter is proposed. A closed-form expression for the steady-state mean square error of variable coefficient has been obtained. The results of computer simulation are shown which confirm the theoretical prediction.

In this paper, methods to analyze the convergence and steady-state characteristics of an adaptive notch filter with two input structure are proposed. The adaptive detection of a sinusoid with additive Gaussian noises has been investigated. Expressions for the necessary iteration of convergence are derived. An analysis of steady-state coefficient error has been also obtained. The analysis of this paper clarifies the effects of colored Gaussian noise and the noise correlation between primary input and reference input. Finally, the results of computer simulations are shown which confirm the theoretical predictions.