Introduction to vector sampling expansion

This work extends Papoulis' General Sampling Expansion to the vector case where N band limited signals are passed through a multi-input multi-output (MIMO) 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.