# ## ECE Course Outline

#### Random Processes (3-0-3)

Prerequisites
ECE 3075
Corequisites
None
Catalog Description
To develop the theoretical framework for the processing of random signals and data.
Textbook(s)
Papoulis, Pillai, Probability, Random Variables, and Stochastic Processes (4th edition), McGraw Hill, 2002. ISBN 9780072817256 (required) (comment: Book also published under ISBN: 9780073660110)

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
``` Georgia Institute of Technology
North Avenue, Atlanta, GA 30332
Phone: 404-894-2000