<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This article gives an overview of the applications of algebraic topology methods in signal processing. We explain how the notions and invariants such as (co)chain complexes and (co)homology of simplicial complexes can be used to gain insight into higher-order interactions of signals. The discussion begins with some basic ideas in classical circuits, continues with signals over graphs and simplicial complexes, and culminates with an overview of sheaf theory and the connections between sheaf cohomology and signal processing.</p>
</abstract>

This article gives an overview of the applications of algebraic topology methods in signal processing. We explain how the notions and invariants such as (co)chain complexes and (co)homology of simplicial complexes can be used to gain insight into higher-order interactions of signals. The discussion begins with some basic ideas in classical circuits, continues with signals over graphs and simplicial complexes, and culminates with an overview of sheaf theory and the connections between sheaf cohomology and signal processing.

Topological Methods in Signal Processing

B&H Electrical Engineering

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Topological Methods in Signal Processing"}

This article gives an overview of the applications of algebraic topology methods in signal processing. We explain how the notions and invariants such as...

Topological Methods in Signal Processing

Published Online: Nov 01, 2022

Page range: 14 - 25

Received: May 01, 2020

Accepted: Jun 01, 2020

DOI: https://doi.org/10.2478/bhee-2020-0002

Keywords
signal processing, graph, simplicial complex, chain complex, homology, cohomology, sheaf, Laplacian, spectral analysis

© 2020 Ismar Volić, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Topological Methods in Signal Processing

Published Online: Nov 01, 2022

Page range: 14 - 25

Received: May 01, 2020

Accepted: Jun 01, 2020

DOI: https://doi.org/10.2478/bhee-2020-0002

Keywordssignal processing, graph, simplicial complex, chain complex, homology, cohomology, sheaf, Laplacian, spectral analysis

© 2020 Ismar Volić, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
signal processing, graph, simplicial complex, chain complex, homology, cohomology, sheaf, Laplacian, spectral analysis