Outline: 0:37 - Overview of graph signal processing 4:25 - Local filters 5:59 - Review of graphs 8:09 - Adjacency matrix 9:46 - Matrix representation of local linear filters 12:50 - Support of a matrix 14:25 - Motivation of distributed and local filters 16:04 - Review of Fourier transform in classical signal processing 23:08 - Abstract view of Fourier transform as projection of signal to an orthogonal complete basis 29:00 - Fourier bases are eigen-functions of the shift operator 33:00 - For directed path graph, shift matrix is the same as the adjacency matrix 37:40 - Generalize of shift matrix idea to non-path and undirected graphs 39:29 - Graph Fourier transform 44:40 - Low-pass/high-pass/band-pass filter 47:57 - Other choices of shift matrices Correction: 3:35 - I didn't distinguish local filters from distributed filters and it is not quite precise. Local filters are more restrictive (only take inputs from neighbors) and can be considered as building blocks of distributed filters. Please watch for more precise definition. 48:16 - Laplacian matrix should be D - A instead. ... https://www.youtube.com/watch?v=yXJDufjeLHs

... https://www.youtube.com/watch?v=qNScZM0fsK0