Tryphon T. Georgiou was born in Athens, Greece, in 1956. He received the Diploma in Mechanical and Electrical Engineering from the National Technical University of Athens, Greece, in 1979, and the Ph.D. degree from the University of Florida, Gainesville, in 1983. He has served on the faculty of Florida Atlantic (1983-1986) and Iowa State (1986-1989) Universities. Since 1989 he has been with the University of Minnesota where he is a Professor of Electrical and Computer Engineering, a co-director of the Control Science and Dynamical Systems Center (1990-present), and holds the Vincentine Hermes-Luh chair of Electrical Engineering. He has served as an Associate Editor for the IEEE Trans. on Automatic Control, the SIAM Journal on Control and Optimization, and the Systems and Control Letters. He is a Fellow of the IEEE and has also served as an elected member of the Board of Governors of the Control Systems Society (2002-2005). His research interests lie in the areas of control engineering, systems, information theory, and applied mathematics. He is a co-recipient of the George Axelby Outstanding Paper awards of the IEEE Control Systems Society for the years 1992 and 1999, for joint works with M.C. Smith (Univ. of Cambridge), and for 2003, for joint work with C.I. Byrnes (Washington Univ., St. Louis) and A. Lindquist (KTH, Stockholm).
The analysis of signals into constituent harmonics and the estimation of their power distribution are considered fundamental to systems engineering. Due to its significance in modeling and identification, spectral analysis is in fact a "hidden technology" in a wide range of application areas, and a variety of sensor technologies, ranging from radar to medical imaging, rely critically upon efficient ways to estimate the power distribution from recorded signals. Robustness and accuracy are of at most importance, yet there is no universal agreement on how these are to be quantified. Thus, in this talk we will motivate the need for ways to compare power spectral distributions.
Metrics, in any field of scientific endeavor, must relate to physically meaningful properties of the objects under consideration. In this spirit, we will discuss certain natural notions of distance between power spectral densities. These will be motivated by problems in prediction theory and related properties of time-series. Analogies will be drawn with an old subject of a similar vein, that of quantifying distances between probability distributions, which has given rise to information geometry. The contrast and similarities between metrics will be highlighted by analyzing mechanical vibrations, speech, and visual tracking.