Power spectral analysis of non-stationary random processes

Abstract

The problem of power spectral analysis for non-stationary processes is discussed from the point of view of physical and engineering applications. The author's theory of “evolutionary power spectra” is explained in intuitive terms, with emphasis on the problem of defining a non-stationary spectrum whose physical interpretation is similar to that of a stationary spectrum. It is shown that evolutionary (i.e. time-dependent) spectra have a physical interpretation as local energy distributions over frequency, and that, under certain conditions, the evolutionary spectrum at each instant of time may be estimated from a single realization of the process. In this way, it is possible to study processes with continuously changing “spectral patterns”. Methods of estimating evolutionary power spectra are discussed, and detailed formulae for sampling fluctuations are included.