The relationship between Wigner-Ville and evolutionary spectra for frequency modulated random processes

TWo major candidates for ´time-frequency´ spectral characterisation of nonstationary processes are the Wigner-Ville spectrum and Priestley´s evolutionary spectral density. There has been much general discussion on the relative merits of these two spectra, but little on specific comparisons. This is probably because it is difficult to construct theoretical evolutionary spectra for realistic examples. This paper is concerned with illustrating a theoretical relationship between these spectra by a series of examples. The examples include both uniformly and nonuniformly modulated cases. The nonuniformly modulated examples include a nonstationary process Which is ´frequency modulated´ in form for which the principle of ´covariance equivalence´ allows the description of the evolutionary spectrum.