Unlimited Sampling of FRI Signals Independent of Sampling Rate

To achieve High Dynamic Range (HDR) sensing, the Unlimited Sampling Framework (USF) was recently proposed. In the USF, modulo encoding of the continuous-time input signal prevents the analog-to- digital converter (ADC) from saturation. For recovering the HDR signal from folded samples, reconstruction algorithms are utilized. Current USF pipeline is highly focused on bandlimited signal classes and requires considerable oversampling. In contrast, in this paper, we consider non-bandlimited signals, in particular, sparse inputs with finite-rate-of-innovation (FRI). By devising a novel, dual-channel modulo sampling architecture we show that, surprisingly, sparse signal recovery from modulo samples can be performed independent of the sampling rate. We validate the effectivity of our sampling scheme and show that perfect signal reconstruction is achieved up to machine precision.