"On Unlimited Sampling: Recovering Functions from Fractional-Part of Measurements"Bhandari, AyushThe Unlimited Sensing Framework (USF) is a recently introduced digital acquisition method that aims at recovering functions from the fractional-part or modulo-folded measurements, in a mathematically guaranteed fashion. In doing so, the USF circumvents the fundamental bottlenecks in the Shannon-Nyquist sampling method that led to the "Digital Revolution." Notably, USF prevents signal saturation or clipping by utilizing radically different modulo analog-to-digital converters and achieves higher digital resolution within a given bit budget. In the first part of this talk, we survey recent results in this area and present a sampling theorem akin to the Shannon-Nyquist criterion. Despite the non-linearity in the sensing pipeline, the required sampling rate depends only on the signal's bandwidth. Then, we address the problem of sampling arbitrary exponential sums (Prony's method). Here, we demonstrate a perhaps surprising result: K complex exponentials can be recovered from 6K+4 modulo samples. Throughout the talk, we provide experimental verification of our results using our patented modulo ADC hardware. |
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