The Nyquist theorem for cellular sheaves
Algebraic Topology
2013-07-30 v1
Abstract
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.
Cite
@article{arxiv.1307.7212,
title = {The Nyquist theorem for cellular sheaves},
author = {Michael Robinson},
journal= {arXiv preprint arXiv:1307.7212},
year = {2013}
}
Comments
Sampling Theory and Applications 2013