Stationary Graph Signals using an Isometric Graph Translation

Abstract : In this communication, we extend the concept of stationary temporal signals to stationary graph signals. We introduce the concept of strict sense stationary and wide sense stationary graph signals as a statistical invariance through an isometric graph translation. Using these definitions, we propose a spectral characterisation of WSS graph signals allowing to study stationarity using only the spectral components of a graph signal. Finally, we apply this characterisation a synthetic graph in order to study a few important stochastic graph signals. Also, using geographic data, we study weather readings on the graph of weather stations and show evidence of stationarity in the temperature readings.