Generalized evolutionary spectral analysis and the Weyl spectrum of nonstationary random processes

Abstract

The evolutionary spectrum (ES) is a "time-varying power spectrum" of nonstationary random processes. Starting from an innovations system interpretation of the ES, we introduce the generalized evolutionary spectrum (GES) as a novel family of time-varying power spectra. The GES contains the ES and the transitory evolutionary spectrum as special cases. We consider the problem of finding an innovations system for a process characterized by its correlation function, and we discuss the connection between GES analysis and the class of underspread processes. Furthermore, we show that another special case of the GES-a novel time-varying power spectrum that we call the Weyl spectrum-has substantial advantages over all other members of the GES family. The properties of the Weyl spectrum are discussed, and its superior performance is verified experimentally for synthetic and real-data processes.