  In task-based quantization, a multivariate analog signal is transformed into
a digital signal using a limited number of low-resolution analog-to-digital
converters (ADCs). This process aims to minimize a fidelity criterion, which is
assessed against an unobserved task variable that is correlated with the analog
signal. The scenario models various applications of interest such as channel
estimation, medical imaging applications, and object localization. This work
explores the integration of analog processing components -- such as analog
delay elements, polynomial operators, and envelope detectors -- prior to ADC
quantization. Specifically, four scenarios, involving different collections of
analog processing operators are considered: (i) arbitrary polynomial operators
with analog delay elements, (ii) limited-degree polynomial operators, excluding
delay elements, (iii) sequences of envelope detectors, and (iv) a combination
of analog delay elements and linear combiners. For each scenario, the minimum
achievable distortion is quantified through derivation of computable
expressions in various statistical settings. It is shown that analog processing
can significantly reduce the distortion in task reconstruction. Numerical
simulations in a Gaussian example are provided to give further insights into
the aforementioned analog processing gains.
