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

|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 recently introduced transitory evolutionary spectrum as special cases. We consider the problem of nding 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. We furthermore show that another special case of the GES, a novel time-varying power spectrum that we call 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 veriied experimentally for synthetic and real-data processes.