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Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Winter 2007 Seminar Series
Presents
Distances and Riemannian Metrics in Spectral
Analysis
Tryphon Georgiou
University of Minnesota
Friday, March 9th, 2007 3:00pm-4:00pm ESB 2001
Abstract:
From radar to medical imaging, and from speech processing to communications and system identi-
fication, many technological advances rely on new efficient ways to estimate a power frequency dis-
tribution from recorded signals. Robustness and accuracy are of at most importance, yet there is no
universal agreement on how these are to be quantified. The focus of the talk is on intrinsic notions of
distance between power spectral distributions.
We will discuss alternatives and present natural notions of distance motivated by problem in predic-
tion and smoothing of time-series. More specifically, a power spectral distribution allows constructing
an optimal predictor for a corresponding time-series. If the actual power spectral distribution of the
time-series differs from the one used in designing the predictor, a degradation of the prediction-error
variance is to be expected. This degradation of predictive performance allows us to quantify distances
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