This article is a lecture note from DAFx 2023, discussing the application of combinatorial Hodge theory in digital signal processing and sound synthesis. It’s an extension of a previous lecture at DAFx 2022. The article delves into the application of topology in digital signal processing, finite element methods, and other areas. It explains the combinatorial construction of topological spaces and uses linear algebra to explain the concepts. It also explains the use of matrices to capture connectivity information in graphs and how to algebraize these graphs. The article then discusses the simplicial complex as a generalization of graphs.
Publication date: 8 Nov 2023
Project Page: https://arxiv.org/abs/2311.03469
Paper: https://arxiv.org/pdf/2311.03469
