Event-driven modulo sampling

In contrast to Shannon sampling theory, where measurements are recorded at equally-spaced time instants, event-driven sampling records values at non-uniform instants dependent on the input. However, both sampling schemes are subject to input dynamic range constraints. This represents a fundamental bottleneck, which can only be alleviated via adjustments in the encoder architecture. Here we explore an alternative strategy based on the recent work on Unlimited Sampling theory, which uses a modulo non-linearity to guarantee a predefined input amplitude range. We propose a cascade model comprising a modulo non-linearity in series with an integrate- and-fire (IF) event-driven encoder. The modulo component does not act on inputs within the IF dynamic range, thus our model is fully compatible with the existing IF methodology. For inputs outside the IF dynamic range, the modulo output is discontinuous, and it currently cannot be recovered from the IF output with existing methods. We introduce theoretical conditions for which the input of the proposed cascade model can be recovered with arbitrary precision. Through numerical simulations, we show the performance of the reconstruction algorithm. The proposed methodology paves the way for a new generation of event-driven models suitable for a much wider range of applications.