Shannon meets Nyquist: Capacity limits of sampled analog channels

We explore several fundamental questions at the intersection of sampling theory and information theory. In particular, we study how capacity is affected by a given sampling mechanism below the channel's Nyquist rate, and what sampling strategy should be employed to maximize capacity. Two classes of sampling mechanisms are investigated: uniform sampling with filtering and uniform sampling with a filter bank. Optimal filters that maximize capacity are identified for both cases. We also highlight connections between capacity and minimum mean squared error (MMSE) estimation from sampled data. Our results indicate that maximizing capacity of sampled analog channels is a joint optimization problem over both the transmission strategy and the sampling technique.