Spring 2019

Thurs, Apr 25th 2019, 12:00PM, Venue: Porter B9
Louis Scharf, Colorado State

Title: Coherence as an Organizing Principle in Signal Processing

Abstract: In this talk we will establish a framework for talking about coherence as an organizing principle for signal processing. We will demonstrate that many problems in detection, estimation, and space-time signal processing may be analyzed with coherence statistics. 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, and it illuminates the problems of beamforming and spectrum analysis. There will be some statistics thrown into the mix, as we establish that many coherence statistics are distributed as products of independent beta-distributed random variables. Throughout the talk, linear algebraic ideas will be clarified with geometrical pictures and insights.

Bio: Louis Scharf is Research Professor of Mathematics and Emeritus Professor of Electrical and Computer Engineering at Colorado State University, Fort Collins, CO. His research interests are in statistical signal processing and machine learning, as it applies to adaptive array processing for radar, sonar, and communication; modal analysis for electric power monitoring; and image processing for classification. He has made original contributions to matched and adaptive subspace detection, invariance theories for signal processing, and reduced-rank signal processing. He has co-authored the books, L.L. Scharf, "Statistical Signal Processing: Detection, Estimation, and Time Series Analysis," Addison-Wesley, 1991, 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. Professor Scharf has received several awards for his professional service and his contributions to statistical signal processing, including the Technical Achievement and Society Awards from the IEEE Signal Processing Society (SPS); the Donald W. Tufts Award for Underwater Acoustic Signal Processing, the Diamond Award from the University of Washington, and the 2016 IEEE Jack S. Kilby Medal for Signal Processing. He is a Life Fellow of IEEE.
link to video