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 i nterpretation of the ES, we introduce the generalized evolutionary spe ctrum (GES) as a novel family of time-varying power spectra, The GES c ontains the ES and the recently introduced transitory evolutionary spe ctrum as special cases. We consider the problem of finding an innovati ons system for a process characterized by its correlation function, an d we discuss the connection between GES analysis and the class of unde rspread processes. Furthermore, we show that another special case of t he GES-a novel time-varying power spectrum that we call Weyl spectrum- has substantial advantages over all other members of the GES family, T he properties of the Weyl spectrum are discussed, and its superior per formance is verified experimentally for synthetic and real-data proces ses.