Wiener filtering of nonstationary signals based on spectral density functions

This paper deals with a large class of nonstationary stochastic processes generated by passing white noise through a general linear time-varying filter. It is shown that such processes can be characterized in terms of a family of jointly wide-sense stationary processes. This formulation is used to define the spectral density function for the nonstationary processes considered in the paper. Then the spectral density function is used to give a suboptimal solution to the nonstationary Wiener filtering problem. This suboptimal solution is shown to be nearly optimal under conditions corresponding to a sufficiently small rate of variation. A numerical example compares this suboptimal Wiener filter solution to an optimal solution.