Time-varying modeling of a non-stationary signal

In this paper, a method for modeling a non-stationary signal using time-varying parameters by considering that the signal is generated by a linear, time-varying (LTV) system with a stationary white noise input is presented. This method is based on the Wold-Cramer (W/C) representation of a non-stationary signal. Because the relationship between the generalized transfer function of an LTV system and the time-varying coefficients of the difference equation of a discrete-time system is not addressed so far in literature, therefore, in this paper a solution to this problem is proposed. A simple relationship between the system generalized transfer function and the time-varying parameters of the system is derived, then an MLS algorithm is developed to solve for the system time-varying parameters. Computer simulation illustrating the effectiveness of our algorithm is presented.