Sampling is key in all fields where the world is analog, but computation is
digital. The question is: When does a countable set of measurements allow a
perfect and stable representation of a class of signals? 

We review sampling of finite rate of innovation (FRI) signals, which are
non-bandlimited continuous-time signals with a finite parametric
representation.
This leads to sharp results on sampling and reconstruction and performance
bounds on retrieving sparse continuous-time signals buried in noise. 

We then look at sampling problems where physics plays a central role. We
consider the wave equation, and review the fact that wave fields are
essentially
bandlimited in space-time domain. This can be used in acoustic source
localization problems. Then, in a diffusion equation scenario, so