Performance characterization of a non-linear system as both an adaptive notch filter and a phase-locked loop

The behaviour of a non-linear dynamical system is described. The system may be characterized as an adaptive notch filter, or alternatively, as a phase-locked loop. Either way, the system has the inherent capability of directly providing estimates of the parameters of the extracted sinusoidal component of its input signal, namely its amplitude, phase and frequency. The structure and mathematical properties of the system are presented for two cases of fixed-frequency and varying-frequency operation. The effects of parameter setting of the system on its performance are studied in detail using computer simulations. Transient and steady-state behaviour of the system are studied in the presence of noise. Simplicity of structure, high noise immunity and robustness and the capability of direct estimation of amplitude, phase and frequency are the salient features of the system when envisaged as an adaptive notch filter or a phase-locked loop. Copyright (C) 2004 John Wiley Sons, Ltd.