Sampling of Spectrally Correlated Processes

The problem of sampling continuous-time spectrally correlated (SC) processes is addressed. SC processes have Loève bifrequency spectrum with spectral masses concentrated on a countable set of support curves in the bifrequency plane. This class of nonstationary processes extends that of the almost-cyclostationary processes and occurs in wideband mobile communications and spectral analysis with nonuniform spectral resolution. The class of the discrete-time SC processes is introduced and characterized. It is shown that such processes can be obtained by uniformly sampling the continuous-time SC processes. Sampling theorems are presented and sufficient conditions to avoid aliasing are provided. Applications are illustrated with reference to the problem of cross spectral analysis with nonuniform frequency resolution and the propagation of communications signals through MIMO multipath Doppler channels.