The Spectral-Domain $\mathcal{W}_2$ Wasserstein Distance for Elliptical Processes and the Spectral-Domain Gelbrich Bound

In this short note, we introduce the spectral-domain $\mathcal{W}_2$ Wasserstein distance for elliptical stochastic processes in terms of their power spectra. We also introduce the spectral-domain Gelbrich bound for processes that are not necessarily elliptical.