Stationary graph processes: Nonparametric spectral estimation

Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides in more irregular graph domains. The contribution in this paper is twofold. First, we propose several equivalent notions of weak stationarity for random graph signals, all taking into account the structure of the graph where the random process takes place. Second, we analyze the properties of the induced power spectral density along with nonparametric approaches to estimate it, including average and window-based periodograms.