Sampling Classes of Non-Bandlimited Signals Using Integrate-and-Fire Devices: Average Case Analysis

We investigate the use of integrate-and-fire systems to efficiently sample classes of non-bandlimited signals such as bursts of spikes. The sampling in this case is based on storing some timing information about the signal, and no information about its amplitude. We demonstrate that perfect reconstruction of these signals is possible when using proper prefiltering strategies before using a multi-channel integrate-and-fire system. We show that the probability of perfect reconstruction of the bursts of Diracs is high, even when the sufficient conditions for perfect reconstruction are not satisfied.