Time-dependent spectral analysis of nonstationary time series

Modeling of nonstationary stochastic time series has found wide applications in speech processing, biomedical signal processing, seismology, and failure detection. Data from these fields have often been modeled as piecewise stationary processes with abrupt changes, and their time-varying spectral features have been studied with the help of spectrograms. A general class of piecewise locally stationary processes is introduced here that allows both abrupt and smooth changes in the spectral characteristics of the nonstationary time series. It is shown that this class of processes behave as approximately piecewise stationary processes and can be used to model various naturally occuring phenomena. An adaptive segmentation method of estimating the time-dependent spectrum is proposed for this class of processes. The segmentation procedure uses binary trees and windowed spectra to nonparametrically and adaptively partition the data into approximately stationary intervals. Results of simulation studies demonstrate that the method has excellent ability to adapt to the rate at which the spectrum is changing. Applications of the method to speech signals and earthquake data are considered.