On the Acquisition of Stationary Signals Using Uniform ADCs

TL;DR

This paper investigates optimal strategies for acquiring stationary signals with uniform ADCs, focusing on minimizing mean-squared error through joint filter optimization, revealing that sub-Nyquist sampling can be optimal under certain rate constraints.

Contribution

It provides a closed-form solution for minimal TMSE and demonstrates that optimal pre-sampling filters avoid aliasing and discard weak frequencies, especially at low rate budgets.

Findings

Optimal pre-sampling filters omit aliasing.

Sub-Nyquist sampling can minimize TMSE under tight rate budgets.

Closed-form expressions for minimal TMSE are derived.

Abstract

In this work, we consider the acquisition of stationary signals using uniform analog-to-digital converters (ADCs), i.e., employing uniform sampling and scalar uniform quantization. We jointly optimize the pre-sampling and reconstruction filters to minimize the time-averaged mean-squared error (TMSE) in recovering the continuous-time input signal for a fixed sampling rate and quantizer resolution and obtain closed-form expressions for the minimal achievable TMSE. We show that the TMSE-minimizing pre-sampling filter omits aliasing and discards weak frequency components to resolve the remaining ones with higher resolution when the rate budget is small. In our numerical study, we validate our results and show that sub-Nyquist sampling often minimizes the TMSE under tight rate budgets at the output of the ADC.