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Topological Filters - A Toolbox for Processing Dynamic Signals - Michael Robinson
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- 1 Intro
- 2 Overlap constructs topology
- 3 Changing overlaps changes the topology
- 4 Sheaves are about consistency
- 5 Finite topologies from partial orders
- 6 Topologizing a partial order
- 7 A sheaf on a poset is...
- 8 An assignment is...
- 9 A global section is...
- 10 Consistency radius is...
- 11 The space of global sections
- 12 Separating sinusoids from noise
- 13 Sheaves deliver excellent performance
- 14 More complex example: flight tracking
- 15 Sheaf model of the sensors . We can forma partial order of the sensors and
- 16 Known flight path
- 17 Minor RDF angle error
- 18 Major flight path error
- 19 Discrete-time LTI filters
- 20 Proof sketch: Input sheaf
- 21 Proof sketch: The internal state
- 22 OPLPF block diagram
- 23 How is this a topological filter?
- 24 Compare: standard adaptive filter
- 25 Filter performance comparison - OPLPF combines good noise removal with signal envelope stability
- 26 Context: Afro-Cuban drumming
- 27 Extracting musical structure
- 28 Some instruments are less clear
