<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

Data publikacji: 01 lis 2022

Zakres stron: 14 - 25

Otrzymano: 01 maj 2020

Przyjęty: 01 cze 2020

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

Słowa kluczowe
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

Data publikacji: 01 lis 2022

Zakres stron: 14 - 25

Otrzymano: 01 maj 2020

Przyjęty: 01 cze 2020

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

Słowa kluczowesignal 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.

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