ECE Course Syllabus
ECE6601 Course Syllabus
Random Processes (3-0-3)
- Technical Interest
- ECE 3075
- Catalog Description
- To develop the theoretical framework for the processing of random signals and data.
- Papoulis, Pillai, Probability, Random Variables, and Stochastic Processes (4th edition), McGraw Hill, 2002. ISBN 9780072817256 (required) (comment: Book also published under ISBN: 9780073660110)
SPIs are a subset of the abilities a student will be able to demonstrate upon successfully completing the course.
- Topical Outline
Review of Probability and Random Variables Axioms and Properties of Probability Conditional Probability, Independence Random Variables, Density Functions, Expectation Moments, Normal (Gaussian) Random Variables Two Random Variables Joint Density and Computation of Probability Independence, Correlation Linear Mean Square Estimation Random Sequences Conditional Densities, Chapman-Kolmogorov Equation Normal Sequences, Sample Mean Markov and Chebychev Inequalities Convergence of Sequences, Laws of Large Numbers, Central Limit Random Processes Definition, Mean, Autocorrelation, Autocovariance Examples: Random Phase Sinusoid, Poisson Process, Telegraph Signal, Random Walk, Wiener Process Stationarity Strict Sense, Wide Sense, Stationary Increments, Cyclostationarity Properties of Auto- and Cross-correlation Functions Power Spectral Density Definition, Relation to Fourier Transform Discrete-Time vs Continuous-Time White Noise, Spectral Estimation Response of Linear Systems to Random Inputs Time Doman Analysis Mean and Autocorrelation of Output, Crosscorrelation of Input with Output Frequency Domain Analysis Bandpass Signals and Filters Shot Noise, ARMA Models Ergodicity Mean Ergodicity, Generally and for Wide Sense Stationary RP's Correlation and Distribution Ergodicity Expansions of Random Processes Sampling Karhunen-Loeve Markov Processes General Definition Poisson Revisited Queues Discrete-Time, Discrete-State; Homogeneity, Reducibility, Recurrence Continuous-Time, Discrete-State; Diffusion Equations Simulation of Random Processes Mean Square Estimation Orthogonality Principle for N Observations, Whitening Linear and Nonlinear Estimation Rank Reduction Continuous-Time Observations, Wiener Filter
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