Steady-state analysis of a second-order adaptive IIR notch filter using the sign algorithm

This paper presents a method to analyze the steady-state coefficient fluctuation of a second order IIR adaptive notch filter, whose coefficients are estimated by the sign algorithm. The adaptive detection of a sinusoid with additive white Gaussian noise has been investigated. The analytical expressions are derived for the mean-square of coefficients fluctuation at the steady-state. The values of step sizes for the gradient and sign algorithms have been shown such that each algorithm produced the same mean-square error at convergence. Finally, the results of computer simulations are shown which confirm the theoretical predictions.