ECE Course Outline


Random Signals and Applications (3-0-3)

ECE 3084 [min C] and (ECE 3077 or CEE/ISYE/MATH/ 3770)
Catalog Description
Introduction to random signals and processes with emphasis on applications in ECE. Includes basic estimation theory, linear prediction, and statistical modeling.
Stark & Woods, Probability, Statistics, and Random Processes for Engineers (4th edition), Prentice Hall, 2011. ISBN 0132311232, ISBN 978-0132311236 (required)

Topical Outline
1.	Random Vectors
   a.	joint distributions and transformation of random vectors
   b.	mean vector and covariance matrix
   c.	Gaussian random vectors
   d.	estimating the mean vector and covariance matrix
   e.	linear estimation and least-squares
   f.	minimum mean-square error estimation

2.	Discrete-time random signals
   a.	Bernoulli trials and random walks
   b.	random sequences and discrete-time linear systems
   c.	wide-sense stationary sequences and the power spectral density
   d.	Markov processes
   e.	hidden Markov models

3.	Introduction to statistical DSP
   a.	discrete-time linear prediction
   b.	the Wiener filter
   c.	sequences of random vectors, state evolution and the Kalman filter

4.	Continuous-time random signals
   a.	Poisson processes
   b.	digital modulation
   c.	Brownian motion
   d.	Markov processes
   e.	wide-sense stationary processes, the autocorrelation function, and the power spectral density
   f.	continuous-time systems with random inputs

5.	Further topics
   a.	graphical models
   b.	Bayesian inference
   c.	the expectation-maximization algorithm

Applications will be discussed alongside of general mathematical techniques.  Applications will include, but not be limited to, speech processing, tracking, modulation and detection for digital communications, radar, sigma-delta quantization, and financial modeling.