A continuous-time adaptive notch filter: Transient and tracking analyses

This paper presents a state-space approach for implementation of a continuous-time adaptive notch filter with a gradient-based algorithm for a single sinusoid frequency estimation. Transient analysis of the proposed algorithm is carried out under the assumption of slow adaptation. Tracking characteristics are also investigated for linear chirp and sinusoidally-varying input signal frequency. Closed-form expressions for frequency tracking error for both cases are derived. Finally, simulation results are presented to verify the validity of the proposed algorithm and derived expressions.