Discrete-time Frequency-Locked-Loop filters for parameters estimation of sinusoidal signals

The paper proposes a novel discretization technique for the design of discrete-time Frequency-Locked-Loop nonlinear (FLL) filters. Continuous-time nonlinear FLL filters have been proposed for their circuital simplicity and ability to provide unbiased estimates of all parameters of a time-varying sinusoidal signal, that is its instantaneous frequency, phase and amplitude. It is shown in the paper that standard discretization techniques fail to provide discrete-time FLL filters that exhibit the same good properties of their continuous-time counterparts. In particular, unlike continuous-time FLL filters, biased estimates are usually produced by these discrete-time FLL filters. In order to overcome this drawback, a Tustin discretization technique equipped with an adaptive pre-warping mechanism consisting of properly adjusting the pre-warping frequency on-line is shown to be sufficient to solve the problem. The properties of the resulting discrete-time FLL filters are fully analyzed. In particular, its semi-global exponential stability and convergence to the true values of the signal parameters has been established. A final example with comparisons with FLL filters synthesized by standard discretization techniques is provided for the assessment of the results.