Covariant estimators of time-frequency descriptors for nonstationary random processes

For a nonstationary random process, the time-time correlation function, frequency-frequency Loeve spectrum, time-frequency Wigner-Ville distribution, and frequency-time Ambiguity Function are each complete theoretical descriptions of second-order behavior: They are complete in the sense that they determine realizations of the random process according to the Cramer-Loeve spectral representation for a harmonizable process. In this paper we derive estimators for these descriptors by requiring them to have the same covariant dependence on time delay and complex modulation as do their theoretical counterparts.