  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.
