Frequency Estimation via Sub-Nyquist Unlimited Sampling

The problem of frequency estimation from sub-Nyquist samples has numerous applications across various disciplines and has been extensively studied in signal processing literature. Despite the existence of several algorithmic approaches, the full potential of these methods has not been realized due to the limitations of analog-to-digital converters (ADCs). In particular, accurately estimating frequency for high-dynamic-range signals that may saturate the ADC is still an interesting problem, regardless of the sub-Nyquist aspect. On a different note, the Unlimited Sensing Framework (USF) focuses on recovering large signals from folded samples but requires oversampling. In this paper, we propose a hardware-software co-design approach that allows for frequency estimation from folded samples at sub-Nyquist rates. Our key insight is that temporal redundancy can be eliminated by introducing channel redundancy. Surprisingly, our recovery guarantees are independent of the sampling rate. To achieve this, we introduce a novel multi-channel sampling pipeline coupled with a reconstruction algorithm. Beyond numerical experiments, we build customized hardware and validate our approach through lab experiments. This demonstrates the capabilities of our method in real-world scenarios while opening up new questions for the field.