Stationary graph signals using an isometric graph translation
Benjamin Girault · 2015
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.