Modulo Sampling in Shift-Invariant Spaces: Recovery and Stability Enhancement

TL;DR

This paper extends modulo sampling techniques to shift-invariant signals, enabling accurate recovery from modulo samples through analog preprocessing and filtering, even under noisy conditions, thus broadening its practical applicability.

Contribution

It introduces a novel modulo sampling framework for shift-invariant signals using analog preprocessing, enhancing recovery and stability beyond bandlimited signals.

Findings

Successful reconstruction of SI signals from modulo samples with minimal oversampling

Effective noise robustness demonstrated across various noise levels

Analog preprocessing with a mixer improves stability and recovery accuracy

Abstract

Sampling shift-invariant (SI) signals with a high dynamic range poses a notable challenge in the domain of analog-to-digital conversion (ADC). It is essential for the ADC's dynamic range to exceed that of the incoming analog signal to ensure no vital information is lost during the conversion process. Modulo sampling, an approach initially explored with bandlimited (BL) signals, offers a promising solution to overcome the constraints of dynamic range. In this paper, we expand on the recent advancements in modulo sampling to encompass a broader range of SI signals. Our proposed strategy incorporates analog preprocessing, including the use of a mixer and a low-pass filter (LPF), to transform the signal into a bandlimited one. This BL signal can be accurately reconstructed from its modulo samples if sampled at slightly above its Nyquist frequency. The recovery of the original SI signal from this BL representation is then achieved through suitable filtering. We also examine the efficacy of this system across various noise conditions. Careful choice of the mixer plays a pivotal role in enhancing the method's reliability, especially with generators prone to instability. Our approach thus broadens the framework of modulo sampling's utility in efficiently recovering SI signals, pushing its boundaries beyond BL signals while sampling only slightly above the rate needed for a SI signal.