Some considerations for statistical characterization of nonstationary random processes

In this paper, we cite the use of the time-dependent correlation function for nonstationary discrete-time random processes, its 2D spectral representation, and the relation to other common time-frequency descriptions of nonstationary random processes. We show a simple distinction between a periodic process and a cyclostationary process in terms of the correlation and 2D spectral density function. We further use the time-dependent correlation functions to easily prove properties about linear prediction for general nonstationary periodic processes and cyclostationary processes. Finally we cite the problems inherent in developing general white noise-driven causal linear models (innovations representations) and conjecture about necessary conditions on the 2D spectral density for their realization.