Generalization of Results on Vector Sampling Expansion

This paper addresses the problem of parsimonious sampling of filtered signals. A vector of bandlimited signals is passed through a multiple-input multiple-output (MIMO) filter and then sampled. Conditions on the sampling rates are presented that allow for perfect reconstruction of the original signals. We extend previous results in two aspects. First, we allow for different bandwidths in signal vector entries while previous results were restricted to the same bandwidth in all entries. Second, we emphasize the parsimonious aspect of the sampling. Namely, in each case, including those previously treated, we highlight the gains which can be made via downsampling.