  We develop a unified sampling theory based on sheaves and show that the
Shannon-Nyquist theorem is a cohomological consequence of an exact sequence of
sheaves. Our theory indicates that there are additional cohomological
obstructions for higher-dimensional sampling problems. Using these
obstructions, we also present conditions for perfect reconstruction of
piecewise linear functions on graphs, a collection of non-bandlimited functions
on topologically nontrivial domains.
