Uncertainty and concentration inequalities for nonstationary random processes and time-frequency energy spectra

Abstract

We provide various sharp uncertainty inequalities for nonstationary random processes. These inequalities relate the temporal and spectral energy concentration of a process to the effective rank of its correlation operator. Similar inequalities are established for the time-frequency (TF) concentration of a wide range of TF energy spectra. We further identify TF energy spectra that feature maximum TF concentration and illustrate our results for the practically important class of underspread random processes.