Signal Processing for Time-Series Functions on a Graph

Previous research introduced signal processing on graphs, an approach to generalize signal processing tools such as filtering to functions supported on graphs. These methods can be applied to scalar functions with a domain that can be described by a fixed weighted undirected graph. We consider here time-series functions supported on a fixed, weighted, undirected graph and show that an extension to the approach of Shuman et al. does not generalize to this problem, but rather suffers from a catastrophic loss of temporal information in the signal during convolution operations. Finally, we propose alternative signal processing approaches to time-series functions on a fixed graph.