Interpolation and decimation of spectrally correlated stochastic processes

The problem of interpolation and decimation of jointly spectrally correlated (SC) discrete-time stochastic processes is addressed. Jointly SC processes have Loève bifrequency cross-spectrum with spectral masses concentrated on a countable set of support curves of the bifrequency plane. Jointly almost-cyclostationary (ACS) processes are obtained as special case when the support curves are lines with unit slope. It is shown that two jointly wide-sense stationary or jointly ACS processes expanded or decimated with different rates give rise to jointly SC processes. In addition, interpolation filtering of jointly SC processes is considered and sufficient conditions for alias-free filtering are provided.