Self-stabilized adaptive allpass filters for phase equalization and approximation

In this paper, we present a simple adaptive filtering solution to general phase equalization and phase modeling tasks. Our proposed algorithm maintains approximate allpass constraints on the coefficients of an adaptive FIR filter in a self-stabilized manner. An analysis of an idealized IIR version of the technique shows that it converges to a unique stationary point corresponding to the optimal phase relationship between the processed signals. The relationship between the mean-squared error of the estimated phase response and the mean-squared error of the filter coefficients is also derived. Simulations verify that the proposed algorithm performs accurate phase equalization and approximation of unknown systems even in low signal-to-noise ratio conditions