  This paper develops the fundamental capacity limits of a sampled analog
channel under a sub-Nyquist sampling rate constraint. In particular, we derive
the capacity of sampled analog channels over a general class of time-preserving
sampling methods including irregular nonuniform sampling. Our results indicate
that the optimal sampling structures extract out the set of frequencies that
exhibits the highest SNR among all spectral sets of support size equal to the
sampling rate. The capacity under sub-Nyquist sampling can be attained through
filter-bank sampling, or through a single branch of modulation and filtering
followed by uniform sampling. The capacity under sub-Nyquist sampling is a
monotone function of the sampling rate. These results indicate that the optimal
sampling schemes suppress aliasing, and that employing irregular nonuniform
sampling does not provide capacity gain over uniform sampling sets with
appropriate preprocessing for a large class of channels.
