Complex coefficient adaptive IIR notch filter tracking characteristics

This paper investigates tracking characteristics of a complex-coefficient adaptive infinite-impulse response (IIR) notch filter with a gradient-based algorithm. Two cases are investigated, i.e., linear chirp and randomly-varying frequency input complex signals buried in a complex zero-mean white Gaussian noise. First-order real-coefficient difference equations with respect to steady-state instantaneous frequency tracking error are derived. Closed-form expressions for frequency tracking mean square error (MSE) are derived from the difference equations. In addition, closed-form expressions for optimum notch bandwidth coefficient and step size constant are presented. Computer simulations are included to validate the analyses.