Spectral characteristics of nonstationary random processes - a critical review

This article analyzes the approaches to defining "spectral characteristics" derived from the spectral functions of nonstationary random processes. The processes considered are those for which an evolutionary power spectrum as designated by Priestley can be defined. Two basic approaches to defining s pectral characteristics are reviewed. The first, characterized as geometric , leads to Vanmarke's spectral moments, which have proven to be very useful characteristics for stationary processes. However, these moments may be in finite for nonstationary processes, which creates problems for applications . The second approach, viewed as nongeometric, is based on Di Paola's pre-e nvelope covariances. The advantages and deficiencies of both approaches are discussed. Pt is also shown that the nongeometric spectral characteristics can be directly defined from the frequency domain as integrals of the one- sided auto- and cross-spectra of the evolutionary process and its derivativ es. These nongeometric spectral characteristics are then used in defining p ara-meters that characterize the central frequency and the bandwidth of evo lutionary processes. To this end, the probability distributions of the proc ess envelope are analyzed. It is demonstrated that suitable central frequen cies and bandwidth factors can be defined from the probability density func tions of the derivatives of the envelope and the phase. (C) 1999 Elsevier S cience Ltd. All rights reserved.