On the spectral correlation measurement of nonstationary stochastic processes

In this paper, the problem of the single sample-path based spectral correlation measurement for a new class of nonstationary stochastic processes is addressed. Processes belonging to this class, referred to as spectrally correlated processes, exhibit a Loeve bifrequency spectrum with spectral masses concentrated on a countable set of support curves in the bifrequency plane and include, as a special case, the almost-cyclostationary processes. The amount of spectral correlation existing between separate spectral components is characterized by the bifrequency spectral correlation density function which is the density of the Loeve bifrequency spectrum along its support curves. It is shown that, in general, when the location of the spectral masses is unknown, a reliable single sample-path based estimate of the bifrequency spectral correlation density function is given by the time-smoothed periodogram, provided that the departure of the nonstationarity from the almost-cyclostationarity is not too big and a sufficiently large smoothing product is considered. Moreover, in general, the estimate performance cannot be improved as wished by increasing the sample size and the spectral resolution.