Sub-Nyquist Sampling: Bridging Theory and Practice

TL;DR

This paper reviews sub-Nyquist sampling strategies, connecting theoretical models with practical hardware implementations to reduce ADC rates below the Nyquist limit, aiming to advance digital signal processing.

Contribution

It bridges the gap between theoretical sub-Nyquist sampling models and practical hardware applications, fostering further research and development.

Findings

Sub-Nyquist strategies can effectively reduce ADC sampling rates.

Theoretical models like union of subspaces inform practical system design.

Bridging theory and practice enhances potential for real-world applications.

Abstract

Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level. In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.