Evolutionary analysis of non-stationary signals

The Wold-Cramer representation of non-stationary signals made possible the development of the evolutionary spectral methods pioneered by Priestley (1981) and Melard (1989). We show that by considering such a model a practical non-stationary signal analysis is achievable. Estimating the kernel of the Wold-Cramer representation allows us to develop time-varying estimators for the mean, the autocorrelation and the spectrum of the signal. As a specific application of the evolutionary analysis, we consider the analysis and implementation of the Wiener filtering of nonstationary processes. Applying the orthogonality principle generalized normal equations can be obtained and then realized using a maximum-entropy spectral estimator for the Wold-Cramer kernels. An examples illustrating the filtering is given.