Stationary Graph Signals

While conventional discrete signals are represented over grids, we currently dealwith a number of signal types for which no well-defined grid is applicable; data relatedto social networks is among the examples. An alternative way for representing suchsignals is to assume a graph, where each node plays the role of a grid point. In otherwords, each node contains a part of the whole signal and based on the connections inthe graph, these parts could be thought of as related to each other. In contrast to theconventional ۱D discrete signals where each signal tap is adjacent to its predecessor andsuccessor taps, in graph signals, the adjacency of a signal tap is not necessarily limitedto ۲ other taps. Obviously, there are more degrees of freedom in graph signals, whichmakes them a more versatile modeling platform. The downside is that the processingtechniques which are well-studied for decades for conventional discrete signals shall berevisited and redefined. As we will see in this talk, some of the equivalent processesand definitions in the graph signal domain are quite non-trivial.