  For a continuous-time additive white Gaussian noise (AWGN) channel with
possible feedback, it has been shown that as sampling gets infinitesimally
fine, the mutual information of the associative discrete-time channels
converges to that of the original continuous-time channel. We give in this
paper more quantitative strengthenings of this result, which, among other
implications, characterize how over-sampling approaches the true mutual
information of a continuous-time Gaussian channel with bandwidth limit. The
assumptions in our results are relatively mild. In particular, for the
non-feedback case, compared to the Shannon-Nyquist sampling theorem, a widely
used tool to connect continuous-time Gaussian channels to their discrete-time
counterparts that requires the band-limitedness of the channel input, our
results only require some integrability conditions on the power spectral
density function of the input.
