Wigner-Ville and evolutionary spectra for covariance equivalent nonstationary random processes

TWO methods of ´time-frequency´ spectral characterisation of nonstationary random processes are the Wigner-Ville spectrum and the evolutionary spectral density. This paper compares Wigner-Ville and evolutionary spectra for a particular class of nonstationary processes, namely those that exhibit a ´frequency modulated´ structure (e.g., acoustic signals for which the Doppler effect is significant). Wigner-Ville spectra for such processes are (at least in principle) easy to obtain, but in order to obtain theoretical evolutionary spectral densities for such processes the concept of ´covariance equivalence´ is used. The spectra are computed for the sound perceived by an observer due to a convecting monopole source emitting a random signal.