COL+UNIV+2012+SPRING+ELEN+E4815+SYLLABUS-+16+JAN+2012-1

COL+UNIV+2012+SPRING+ELEN+E4815+SYLLABUS-+16+JAN+2012-1 - 1...

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Random Signals and Noise ELEN E4815 Columbia University Spring Semester 2012 Syllabus 16 January 2012 Professor I. Kalet The course is designed to give the student an introduction to the important subject of random signals and noise. Random processes play a very important role in the fields of communication, signal processing, and control, as well as in many other fields as far-fetched as the stock market, the economy (who wants to talk about that now in an election year?) and biological sciences. The course will begin with a brief review of probability theory. The random process will then be defined. This will be followed by a discussion of stationary processes, correlation functions and power spectral densities. The effect of linear (and non-linear) operations on random signals will also be discussed. We will define important random processes such as gaussian processes (including white gaussian noise) and bandlimited random processes, and some of their important properties. We will also discuss some practical analysis applications of random processes and noise in different fields, e.g., calculating signal-to-noise ratios in communication systems. After these topics, we will discuss Wiener-Hopf filtering. We will also consider parameter estimation, the estimation of time functions and the Cramer-Rao bounds on estimation. If time permits we will describe the Kharhunen-Loeve expansion at the end of
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This note was uploaded on 02/28/2012 for the course ELEN E4815 taught by Professor I during the Spring '12 term at Columbia.

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