Non-stationary Wiener filtering based on evolutionary spectral theory

We consider solutions to the non-stationary Wiener filtering problem using the evolutionary spectral theory. Two cases of interest result from the fact that the desired signal and the noise is uncorrelated. One constrains the support of the generating kernels of the signals and the other imposes orthogonality on their innovation processes. The latter condition is more general and our solution coincides with the one presented previously by Abdrabbo and Priestley (1969). For the first case, we develop a new solution that depends directly on the Wold-Cramer models of the desired and noisy processes. Implementation is achieved in both cases by estimating the kernels for the Wold-Cramer representations from the spectra using the evolutionary maximum entropy spectral estimation. An example illustrating the filtering is given