Topological Filters - A Toolbox for Processing Dynamic Signals - Michael Robinson
Explore topological filters as a powerful toolbox for processing dynamic signals in this comprehensive lecture from the Workshop on Topology: Identifying Order in Complex Systems. Delve into the fundamentals of overlap constructs, sheaf theory, and finite topologies derived from partial orders. Learn how changing overlaps affects topology and discover the concept of consistency in sheaves. Examine practical applications, including separating sinusoids from noise and flight tracking, to understand the excellent performance of sheaf-based approaches. Investigate discrete-time LTI filters, comparing standard adaptive filters with topological filters like OPLPF. Gain insights into the application of these techniques in extracting musical structure from Afro-Cuban drumming. Presented by Michael Robinson from American University, this 53-minute talk offers a deep dive into advanced signal processing techniques using topological methods.