Uniform Sampling of Band-limited Signals

Abstract

This master thesis presents a short introduction into the field of sampling of functions of one variable. It is not meant to come up with any new theory, just to give an overview over known material, and to prove most of the background theory. The main focus is on bandlimited functions, i.e. L2-functions f whose Fourier transform vanishes outside a bounded set, called the spectrum of f. We will also consider the larger class of Bernstein functions, which are not necessarily square-integrable.