State-space approach to steady-state analysis of adaptive IIR notch filters

In this paper we propose a novel state-space approach to steady-state analysis of a gradient algorithm (GA) for a second-order adaptive infinite impulse response (IIR) notch filter. A general expression for the sinusoid frequency estimation mean square error (MSE) in terms of state-space matrices of a third-order complex-coefficient system is presented. A closed form expression is then derived from the general expression and computer simulation results are included to confirm its accuracy.