Reconstruction Condition of Quantized Signals in Unlimited Sampling Framework

TL;DR

This paper investigates the reconstruction of signals from quantized modulo samples in the unlimited sampling framework, establishing a new minimum sampling rate requirement that depends on signal bandwidth and quantization bits.

Contribution

It introduces a novel lower bound on the sampling rate for exact signal recovery in quantized unlimited sampling systems, considering practical quantization effects.

Findings

Exact recovery at the new minimum sampling rate in the presence of quantization noise.

Verification of the theoretical minimum sampling rate through numerical simulations.

Analysis of trade-offs between sampling rate, quantization bits, and computational complexity.

Abstract

The latest theoretical advances in the field of unlimited sampling framework (USF) show the potential to avoid clipping problems of analog-to-digital converters (ADC). To date, most of the related works have focused on real-valued modulo samples, but little has been reported about the impact of quantization. In this paper, we study more practical USF system where modulo samples are quantized to a finite number of bits. In particular, we present a new requirement about the lower bound of sampling rate to ensure exact recovery of original signals from quantized modulo samples. The minimum sampling rate is jointly determined by signal bandwidth and quantization bits. Numerical results show that in the presence of quantization noise, signals with different waveforms and bandwidths are recovered perfectly at the new minimum sampling rate while the recovery fails at minimum sampling rate before modification, which also verifies the correctness of the theory. The trade-offs of sampling rates, quantization bits and computational complexity of recovery algorithm are also given for practitioners to weigh.