Fig. 1
The joint stationarity hypothesis is more general than assuming either (standard) VWSS and TWSS or VWSS on a (Cartesian) product graph. The figure presents three examples of PSDs plotted as 2-dimensional function of λ1,λ2 that, for simplicity, corresponds to the eigenvalues of two graphs. The second graph (time) is a ring. In the separable case (left), the PSD has to satisfy h(λ1,λ2)=h1(λ1)h2(λ2), making it unable to capture any dependencies between λ1 and λ2. Using VWSS (middle) limits the PSD to h(λ1,λ1)=h(λ1+λ2) leading to constant values along the diagonal line λ1+λ2=c. Joint stationarity (right) can encode any PSD h(λ1,λ2), as exemplified here