Deep Learning for Modulo Sampling of FRI Signals

The finite rate of innovation (FRI) of certain signal classes allows for sub-Nyquist sampling, while modulo folding enables sampling signals with dynamic ranges beyond that of an analog-to-digital converter (ADC). Combining these techniques enables sampling at sub-Nyquist rates using an ADC with a lower dynamic range than the signal. Current signal recovery techniques use algorithmic approaches with high oversampling factors (OFs) and constraints on the signal parameters. In this paper, we introduce a deep learning method to modulo unfolding and combine it with an annihilating filter approach for signal parameter recovery. Our method significantly improves unfolding accuracy and reduces error compared to the state-of-the-art, and performs well at OFs as low as 2 times the rate of innovation, with no constraints on the signal parameters. This approach offers a practical tool for signal recovery from modulo sampled FRI signals, potentially reducing the hardware demands of measurement devices.