Efficient Minimum Rate Sampling of Signals with Frequency Support over Non-Commensurable Sets

Abstract

We examine the question of reconstruction of signals from periodic non-uniform samples. This involves discarding samples from a uniformly sampled signal in some periodic fashion. We give a characterization of the signals that can be reconstructed at exactly the minimum rate once a non-uniform sampling pattern has been fixed. We give an implicit characterization of the reconstruction system and a design method by which the ideal reconstruction filters 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 restrictive 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 be far larger than previously considered. When approaching the minimum rate this freedom allows us in certain cases to have a far less complex reconstruction system.