Time-varying spectra for underspread and overspread nonstationary processes

We introduce an extended concept of underspread and overspread nonstationary random processes and show its importance for time-varying spectral analysis. We consider two classes of time-varying power spectra that comprise most existing spectra, including Wigner-Ville and evolutionary spectra. For underspread processes, all spectra are shown to yield similar results. For overspread processes, the spectra may yield very different results and contain oscillatory "cross-terms" indicating time-frequency correlations. These cross-terms can be attenuated via smoothing techniques.