Many biological and physical signals are non-stationary in nature. For
example, brain waves recorded during an epileptic seizure have waveforms
whose amplitude (variance) and oscillatory behavior (spectral
distribution) change over time. This talk will address some of the
interesting statistical problems for analyzing non-stationary signals,
namely, (i.) estimation of the time-varying spectrum and coherence and
(ii.) extraction and selection of localized spectral features for
classification and discrimination.
I will present an overview of a coherent and unified body of statistical models and methods for analyzing non-stationary signals. These methods are based on the SLEX (smooth localized complex exponentials) library which is a collection of orthogonal bases; each basis consists of time-localized Fourier waveforms that have dyadic multi-resolution support. Thus, the SLEX library provides a rich, systematic and efficient way of extracting transient spectral and cross-spectral features. In addition, the SLEX methods are able to handle massive data sets because they utilize computationally efficient algorithms. Finally, as a matter of practical importance, the SLEX methods give results that are easy to understand because they are time-dependent analogues of the classical Fourier methods for stationary signals. The SLEX methods will be applied to some data sets, namely, brain waves that were recorded during an epileptic seizure, a speech signal and seismic waves recorded during earthquake and explosion events. Finally, limitations of the current research and future directions for enhancements will be discussed.