Generalized Adaptive Notch Smoothers for Real-Valued Signals and Systems

Systems with quasi-periodically varying coefficients can be tracked using the algorithms known as generalized adaptive notch filters (GANFs). GANF algorithms can be considered an extension, to the system case, of classical adaptive notch filters (ANFs). We show that estimation accuracy of the existing algorithms, as well as their robustness to the choice of design parameters, can be considerably improved by means of compensating estimation delay effects which occur in the amplitude tracking and frequency tracking loops of GANF/ANF filters. Apart from the increased computational burden, the price for the achieved improvements is paid in terms of a decision delay-the proposed generalized adaptive notch smoothing (GANS) algorithms must be run on delayed input/output data sequences. Since such delay is acceptable in many signal processing and system identification applications, the proposed solution seems to be an attractive alternative to the currently available trackers.