Vector sampling expansion: deterministic and stochastic signals

This work extends Papoulis´ (1977) general sampling expansion to the vector case where N band-limited signals are passed through a multi-input multi-output (MIMO) linear time invariant (LTI) system that generates M (M⩾N) output signals. We find necessary and sufficient conditions for reconstructing the N input signals from the samples of the M output signals, all sampled at N/M the Nyquist rate. A surprising necessary condition is that M/N must be an integer. This condition is no longer necessary when each of the output signals can be sampled at a different rate