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.