A direct adaptive method for discriminating sinusoidal components with nearby frequencies

This paper deals with the on-line simultaneous estimation of frequencies, amplitudes, and phases of a pair of sinusoidal signals with values of the frequencies that are close to each other. The proposed nonlinear parametric identification method is based on the interconnection of two quadrature-based adaptive filters, originally conceived for the extraction of a single sinusoidal signal. The distinctive feature of quadrature based filters, inherited by the method under consideration, consists in performing the adaptation in a parametric space having higher dimensions than the number of unknowns. The stability analysis, based on two-time scale averaging arguments, shows the existence of multiple asymptotically stable manifolds corresponding to the simultaneous detection of the two sinusoidal signals.