Causal Linear Topological Filters over a 2-Simplex
Signal Processing
2021-10-07 v1
Abstract
Topological filters via sheaves generalize the classical linear translation-invariant filter theory by attaching the filter computation locally to a simplicial topological space. This paper develops topological filters for causal signal flow over a 2-simplex. Our construction retains the established construction for 1-simplices and we show how an apparent conflict in the sheaf assignment can be resolved by a concurrent extension, which introduces an auxiliary 1-simplex that computes the resolution. Furthermore, we discuss how singularities formed by double cone connections can be resolved.
Cite
@article{arxiv.2110.02362,
title = {Causal Linear Topological Filters over a 2-Simplex},
author = {Georg Essl},
journal= {arXiv preprint arXiv:2110.02362},
year = {2021}
}
Comments
5 pages, 4 figures, submitted to IEEE ICASSP 2022