On Unlimited Sampling and Reconstruction

Shannon's sampling theorem, at the heart of digital signal processing, is well understood and explored. However, its practical realization still suffers from a fundamental bottleneck due to dynamic range limitations underlying analog-to-digital converters (ADCs). This results in clipping or saturation for amplitudes exceeding their maximum recordable voltage thus leading significant information loss. In this paper, we develop an alternative paradigm sensing recovery, called Unlimited Sampling Framework. The key observation that applying modulo operation before ADC prevents saturation; instead, one encounters different type Such setup can be implemented, example, via so-called folding self-reset ADCs, as proposed various contexts circuit design literature. challenge new loss recover bandlimited samples. We derive conditions when perfect recovery possible complement them with stable algorithm. required density independent depends on bandwidth only. Our guarantees extend measurements affected by bounded noise, which includes round-off quantization. Numerical experiments validate our approach. For it functions orders magnitude higher than ADC's threshold quantized samples up unavoidable quantization error. Applications unlimited found number fields such communication imaging.