### Yale University

Department of Statistics

Seminar

#### Monday February 26, 1996

Sudeshna Adak

Department of Statistics

Stanford University

#### Title: 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. The problem of defining a time-dependent spectrum
for a general class of nonstationary processes is discussed in the context
of problems in geophysics and speech processing.
An appropriate definition of time-dependent spectra is proposed for a class
of nonstationary processes that are locally stationary. A tree-based
segmentation algorithm of estimating the time-dependent spectrum is
proposed for this class of locally stationary processes. A cross-validation
procedure is suggested for an optimal bias-variance tradeoff in the
procedure.
This method of time-frequency analysis is compared and contrasted with
wavelets, matching pursuit, and Priestley's evolutionary spectra. Different
examples of locally stationary processes are considered to demonstrate the
algorithm's excellent ability to adapt to the rate at which the spectrum is
changing.
Applications of this method to signals arising from speech recognition,
earthquakes, and electrocardiograms will be considered together with their
scientific implications.
#### Seminar to be held in Room 107, 24 Hillhouse at 11:30 pm