Analog compressed sensing

A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. Practical signals often posses a sparse structure so that a large part of the bandwidth is not exploited. In this paper, we consider a framework for utilizing this sparsity in order to sample such analog signals at a low rate. By relying on results developed in the context of compressed sensing (CS) of finite-length vectors, we develop a general framework for low-rate sampling of signals in shift-invariant spaces. In contrast to the problems treated in the context of CS, here we explicitly consider sampling of analog signals for which no underlying finite-dimensional model exists.