Modulo Sampling of FRI Signals

An analog-to-digital converter (ADC)’s dynamic range is critical during sampling analog signals. A modulo operation prior to sampling can be used to enhance the effective dynamic range of the ADC. Further, the sampling rate of ADC also plays a crucial role, and it is desirable to reduce it. The finite-rate-of-innovation (FRI) signal model, ubiquitous in many applications, can be used to reduce the sampling rate. In the context of modulo folding for FRI sampling, existing works operate at a very high sampling rate compared to the rate of innovation (RoI) and require a large number of samples compared to the degrees of freedom (DoF) of the FRI signal. Moreover, these approaches use infinite-length filters that are practically infeasible. We consider the FRI sampling problem with a compactly supported kernel under the modulo framework. We derive theoretical guarantees and show that sampling above the RoI could uniquely identify FRI signals. The number of samples for identifiability is equal to the DoF. We propose a practical algorithm to estimate the FRI parameters from the modulo samples. We show that the proposed approach has the lowest error in estimating the FRI parameters while operating with the lowest number of samples and sampling rates compared to existing techniques. The results help design cost-effective, high-dynamic-range ADCs for FRI signals.