Spectral Moments and Pre-Envelope Covariances of Nonseparable Processes

Abstract

A critical review of the definition of the spectral moments of a stochastic process in the nonstationary case is presented. An adequate time-domain representation of the spectral moments in the stationary case is first established, showing that the spectral moments are related to the variances of the stationary analytical pre-envelope processes. The extension to the nonstationary case is made in the time domain evaluating the covariances of the nonstationary pre-envelope showing the differences between the proposed definition and the classical one made introducing the evolutionary power.