Generalized almost-cyclostationary processes and spectrally correlated processes: Two extensions of the class of the almost-cyclostationary processes

In this paper, two recently introduced classes of nonstationary processes are reviewed: The class of the generalized almost-cyclostationary (GACS) processes and the class of the spectrally correlated (SC) processes. GACS processes exhibit multivariate statistical functions that are almost-periodic functions of time whose Fourier series expansions have coefficients and frequencies that can depend on the lag shifts of the processes. SC processes exhibit spectral components with different frequencies that are correlated. Both GACS and SC processes include as special case the almost-cyclostationary (ACS) processes. GACS and SC processes arise in communications and radar-sonar applications when ACS processes are transmitted and there exists relative motion between transmitter and receiver and/or surrounding scatterers. Problems arising in the statistical function estimation and in sampling continuous-time GACS and SC processes are addressed.