Causal Linear Topological Filters Over A 2-Simplex

Georg Essl

ICASSP 2022accepted0 citations

Causal Linear Topological Filters Over A 2-Simplex

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.

BibTeX

@inproceedings{icassp2022_causallineartopo,
  title = {Causal Linear Topological Filters Over A 2-Simplex},
  author = {Georg Essl},
  booktitle = {ICASSP 2022},
  year = {2022}
}