Unlimited Sampling of FRI Signals with Dithered One-Bit Quantization

Recent research in sampling theory suggests utilizing unlimited sampling with one-bit quantization time-varying threshold (UNO) for bandlimited signals. The UNO framework addresses the problems associated with the finite dynamic range and limited quantization levels in conventional ADCs. However, the input signal in many engineering applications is not bandlimited. Of particular interest are the finite rate of innovation (FRI) signals that are characterized by finitely many samples per unit of time and need not be bandlimited. In this work, leveraging upon the generalized FRI sampling theory, we introduce a novel sampling approach for FRI signals that utilizes low-cost one-bit ADCs. We extend this one-bit generalized FRI (OBi-GeFRI) sampling to include unlimited sampling for FRI signals in the form of a new unlimited one-bit FRI (UNOFRI) framework. We rely on the highly efficient random Kaczmarz algorithm, a linear feasibility problem solver, for signal reconstruction in both OBi-GeFRI and UNOFRI. Our numerical examples illustrate the viability of these sampling techniques to tackle the shortcomings of the state-of-the-art.