ECE Colloquium - Dr. Louis Scharf, Colorado State University

Wed, 11/15/2017 - 10:00am
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CoRE Lecture Hall
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ECE Department
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Title: Coherence as an Organizing Principle in Statistical Signal Processing

Abstract: In this talk we will begin with a few rudimentary ideas for the representation of signals in the standard Euclidean and Fourier bases, and then talk about filtering in the language of linear algebra. This will establish a framework for talking about coherence as an organizing principle for signal processing. We will demonstrate that many problems in signal processing lead to coherence. For example, coherence illuminates multiple correlation coefficients and the Cramer-Rao bound. It solves a subspace detection problem, and the problem of detecting dependence between signals measured at co-located or distributed sensors. It leads to a defensible definition of broadband spectral coherence among a multiplicity of time series. There will be some statistics thrown into the mix, as we establish that many coherence statistics are distributed as products of beta-distributed random variables. Throughout the talk, linear algebraic ideas will be clarified with geometrical pictures and insights.

Bio: Louis Scharf received his Ph.D. from the University of Washington, Seattle. He is currently Research Professor of Mathematics and Emeritus Professor of Electrical and Computer Engineering, with a joint appointment in Statistics at Colorado State University. Prof. Scharf has made contributions to matched and adaptive subspace detection for radar, sonar, and hyperspectral imaging; invariance theories for detection and estimation in subspaces; multi-channel coherence for space-time signal processing; and modal analysis in power systems. He has authored three books: L.L. Scharf, "Statistical Signal Processing: Detection, Estimation, and Time Series Analysis," Addison-Wesley, 1991; L.L. Scharf, "A First Course in Electrical and Computer Engineering," Addison-Wesley, 1998; and P.J. Schreier and L.L. Scharf, "Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals," Cambridge University Press, 2010. Prof. Scharf has received several awards for his work, including an IEEE Third Millennium Medal, the Technical Achievement and Society Awards from the IEEE Signal Processing Society (SPS), the Donald W. Tufts Award for Underwater Acoustic Signal Processing, a 2016 Diamond Award from the University of Washington (Seattle), and the 2016 IEEE Jack S. Kilby Signal Processing Medal, endowed by Texas Instruments. He is a Life Fellow of IEEE.