The Nyquist theorem for cellular sheaves

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.

Sampling Theory and Applications 2013

References in corpus (1)

• Inverse problems in geometric graphs using internal measurements

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