Stationary graph signals using an isometric graph translation

We extend the concept of stationary temporal signals to stationary graph signals. Doing so, we introduce the concept of strict sense stationary and wide sense stationary graph signals as a statistical invariance through an isometric graph translation operator. 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 on a synthetic graph in order to study a few important stochastic graph signals. Also, using geographic data, we study weather readings on a graph of weather stations and show evidence of stationarity in the temperature readings.