Generalized periodic non-uniform sampling of non-bandlimited signals

A new paradigm for the periodic non uniform sampling of a class of non bandlimited signals was recently proposed. The main idea is to generate the periodic non uniform samples by retaining a select group of samples from a larger set, obtained by oversampling the continuous time signal by an integer factor L. In this paper, we revisit the problem and consider the more challenging case where the sampler operates at L/M time the Nyquist rate with L and M being coprime integers. We derive a new multi-input multi-output (MIMO) discrete-time model, and then use this model to obtain a set of necessary conditions for perfect signal reconstruction with FIR filters. We also show that unlike the case of M = 1, the newly derived conditions are not sufficient for FIR perfect recovery.