Covariance equivalent forms and evolutionary spectra for nonstationary random processes

Abstract

Many nonstationary random processes exhibit a "frequency modulated" structure. In this paper a method of modelling such processes as the output of a time variable filter driven by white noise is described. The basis of the method relies on producing a process that is "covariance equivalent" to the process under consideration. This particular formulation makes it possible to predict the evolutionary (time-frequency) spectral density of the process.

The theoretical basis of the method is explained and this is followed by a detailed example which illustrates the theory. The example is concerned with the prediction of the evolutionary spectral density of the motion of a vehicle accelerating over rough terrain. The terrain is described as a spatially homogeneous random process and the nonstationarity of the response arises because of the variable velocity of the vehicle.

The covariance equivalent formulation is quite general and other applications (which include problems in acoustics) are noted.