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Unformatted text preview: EEL 5544 - Noise in Linear Systems (Should be called “Probability and Random Processes for Electrical Engineers”) July 15, 2011 SYLLABUS 1. Catalog Description: (3 credits) Passage of electrical noise and signals through linear systems. Statistical representation of random signals, electrical noise, and spectra. Instructor’s clarification: This course starts from the fundamentals of probability and covers probability, random variables, random vectors, and random processes. The focus is on the mathematical tools required to quantify random phenomena. 2. Pre-requisite: No course pre-requisite. Pre-requisite knowledge for success in this course: Very strong mathematical skills. Solid understanding of systems theory, including convolution, Fourier transforms, and impulse functions. Knowledge of basic linear algebra, including matrix properties and eigen-decomposition. 3. Course Objectives: Upon completion of this course, the student should be able to • Recite the axioms of probability; use the axioms and their corrolaries to give reasonable answers • Determine probabilities based on counting (lottery tickets, etc.) • Calculate probabilities of events from the density or distribution functions for random variables • Classify random variables based on their density or distribution functions • Know the density and distribution functions for common random variables • Determine random variables from definitions based on the underlying probability space • Determine the density and distribution functions for functions of random variables using several different techniques presented in class • Calculate expected values for random variables • Determine whether events, random variables, or random processes are statistically independent • Use inequalities to find bounds for probabilities that might otherwise be difficult to evaluate S-2 • Use transform methods to simplify solving some problems that would otherwise be difficult • Evaluate probabilities involving multiple random variables or functions of multiple random variables • Classify random processes based on their time support and value support • Simulate random variables and random processes • Classify random processes based on stationarity • Evaluate the mean, autocovariance, and autocorrelation functions for random processes at the output of a linear filter • Evaluate the power spectral density for wide-sense stationary random processes • Give the matched filter solution for a simple signal transmitted in additive white Gaussian noise • Determine the steady state probabilities for a Markov chain 4. Contribution of course to meeting the professional component: Does not apply 5. Relationship of course to program outcomes: Does not apply 6. Instructor: Dr. John M. Shea (a) Office: 439 NEB (b) Phone: 352.575.0740 (c) Email: [email protected] (d) Web site (personal): http://wireless.ece.ufl.edu/jshea (e) Office hours: Monday and Thursday, 2 PM – 4PM (subject to change)...
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- Spring '11
- Probability, Probability theory, ISBN, Random Processes