ABSTRACT
In Chapter 12, we considered window-based methods for analyzing nonstationary processes with time-varying frequencies (TVF). These include shortterm Fourier transforms (Gabor), along with Wigner-Ville and wavelet representations. In this chapter, we introduce an altogether different approach for analyzing TVF data in which we extend the definition of stationarity to the class of generalized stationary (or G-stationary) processes. This approach allows us to transform the time index ofmany nonstationary processes to an index set upon which they are stationary. The presentation here will be introductory in nature, and no effort will be
made to cover this topic in detail. Our approach is to include sufficient information to give the reader a basic understanding of this methodology. Most of the developments in this area have only recently appeared in the literature, and these references are given here as a source of further details.
Definition 13.1 Let {X(t) : t 2 S} be a stochastic process defined on S R, let u ¼ g(t) be a mapping onto a set Rg R, and let g1 denote a specified inverse. Then X(t) is a G-stationary process if
