Time-based Sampling and Reconstruction of Non-bandlimited Signals

The last two decades have seen a renewed interest in sampling theory, which is concerned with the conversion of continuous-domain signals into discrete sequences. This conversion is traditionally achieved by recording the intensity of the signal at specified time instants. Alternatively, sampling can be based on timing rather than amplitude information. In this paper, we investigate the problem of timing-based sampling of non-bandlimited signals, within the Finite Rate of Innovation (FRI) setting. We show how these signals can be non-uniformly sampled using a compact-support kernel that satisfies the generalised Strang-Fix conditions, and a comparator. We then prove that perfect input estimation is possible using a novel local reconstruction algorithm.