stationary graph signals

While conventional discrete signals are represented over grids, we currently deal with a number of signal types for which no well-defined grid is applicable; data related to social networks is among the examples. an alternative way for representing such signals is to assume a graph, where each node plays the role of a grid point. in other words, each node contains a part of the whole signal and based on the connections in the graph, these parts could be thought of as related to each other. in contrast to the conventional 1d discrete signals where each signal tap is adjacent to its predecessor and successor taps, in graph signals, the adjacency of a signal tap is not necessarily limited to 2 other taps. obviously, there are more degrees of freedom in graph signals, which makes them a more versatile modeling platform. the downside is that the processing techniques which are well-studied for decades for conventional discrete signals shall be revisited and redefined. as we will see in this talk, some of the equivalent processes and definitions in the graph signal domain are quite non-trivial.