Tracking analysis of an adaptive notch filter with constrained poles and zeros

This paper analyzes the asymptotic tracking properties of an adaptive notch filter (ANF) with pole-zero constraints for the cancellation or retrieval of multiple time-varying sine waves in additive noise. The asymptotic mean square error (MSE) is analyzed using the methods of Ljung and Gunnarsson (1990) when the variations in the underlying frequencies are assumed to be sufficiently small. Closed-form expressions for the MSE are derived as functions of the tuning variables of the algorithm. The results give insight into the operational properties of the algorithm and are used in order to minimize the MSE with respect to the tuning variables. Computer simulations confirm the validity of the derived results