Modulo Sampling and Recovery with Unknown and Time-Varying Folding Parameter

Abstract

Sampling signals with a high dynamic range (DR) poses significant challenges in analog-to-digital conversion (ADC), where the DR of the ADC must exceed that of the input signal to prevent information loss. Modulo sampling offers a promising solution to this problem by reducing the DR of the signal prior to sampling. In this paper, we address the modulo recovery problem in scenarios where the folding parameter is unknown and potentially time-varying, motivated by practical hardware limitations that make it difficult to maintain a constant and precise folding parameter. We provide a theoretical guarantee for the unique recovery of band-limited (BL) signals from modulo samples without requiring knowledge of the folding parameter. Additionally, we develop a robust recovery algorithm specifically for scenarios with a constant but unknown folding parameter. The algorithm’s performance is evaluated through simulations under various conditions, including different oversampling rates and noise levels. The results demonstrate that our method achieves high accuracy in signal recovery, even in challenging environments.