Minimum rate sampling and reconstruction of signals with arbitrary frequency support

We examine the question of reconstruction of signals from periodic nonunifo rm samples. This involves discarding samples from a uniformly sampled signa l in some periodic fashion. We give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform sampling pattern has been fixed. We give an implicit characterization of the recons truction system, and a design method by which the ideal reconstruction filt ers may be approximated. We demonstrate that for certain spectral supports the minimum rate can be approached or achieved using reconstruction schemes of much lower complexity than those arrived at by using spectral slicing, as in earlier work. Previous work on multiband signals have typically been those for which rest rictive assumptions on the sizes and positions of the bands have been made, or where the minimum rate was approached asymptotically. We show that the class of multiband signals which can be reconstructed exactly is shown to b e far larger than previously considered. When approaching the minimum rate, this freedom allows us, in certain cases to have a far less complex recons truction system.