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# ## ECE Course Syllabus

### ECE6601 Course Syllabus

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

Lab Hours
0 supervised lab hours and 0 unsupervised lab hours

Technical Interest
Group
Telecommunications

Course Coordinator
Weitnauer,Mary Ann

Prerequisites
ECE 3077

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)

Strategic
Performance
Indicators (SPIs)
SPIs are a subset of the abilities a student will be able to demonstrate upon successfully completing the course.

```Outcome 1 (Students will demonstrate expertise in a subfield of study chosen from the fields of electrical engineering or computer engineering):
1.	Characterize a random process in terms of its autocorrelation function, distribution, and in the case of wide sense stationary processes, the power spectral density.

Outcome 2 (Students will demonstrate the ability to identify and formulate advanced problems and apply knowledge of mathematics and science to solve those problems):
1.	Determine the dependence or independence of random variables, based on the properties of the joint probability density function.
2.	Apply the properties of minimum mean squared error estimation.
3.	Apply the properties of Markov Chains.

Outcome 3 (Students will demonstrate the ability to utilize current knowledge, technology, or techniques within their chosen subfield):

```

Topical Outline
``` 1. Review of Probability and Random Variables
a. Axioms and Properties of Probability
b. Conditional Probability, Independence
c. Random Variables, Density Functions, Expectation
d. Moments, Normal (Gaussian) Random Variables
2. Two Random Variables
a. Joint Density and Computation of Probability
b. Independence, Correlation
c. Linear Mean Square Estimation
3. Random Sequences
a. Conditional Densities, Chapman-Kolmogorov Equation
b. Normal Sequences, Sample Mean
i. Markov and Chebychev Inequalities
ii. Convergence of Sequences, Laws of Large Numbers, Central Limit
4. Random Processes
a. Definition, Mean, Autocorrelation, Autocovariance
b. Examples: Random Phase Sinusoid, Poisson Process, Telegraph Signal,
i. Random Walk, Wiener Process
5. Stationarity
a. Strict Sense, Wide Sense, Stationary Increments, Cyclostationarity
b. Properties of Auto- and Cross-correlation Functions
6. Power Spectral Density
a. Definition, Relation to Fourier Transform
b. Discrete-Time vs Continuous-Time
c. White Noise, Spectral Estimation
7. Response of Linear Systems to Random Inputs
a. Time Doman Analysis
b. Mean and Autocorrelation of Output, Crosscorrelation of Input with Output
c. Frequency Domain Analysis
d. Bandpass Signals and Filters
e. Shot Noise, ARMA Models
8. Ergodicity
a. Mean Ergodicity, Generally and for Wide Sense Stationary RP's
b. Correlation and Distribution Ergodicity
9. Expansions of Random Processes
a. Sampling
b. Karhunen-Loeve
10. Markov Processes
a. General Definition
b. Poisson Revisited
c. Queues
d. Discrete-Time, Discrete-State; Homogeneity, Reducibility, Recurrence
e. Continuous-Time, Discrete-State; Diffusion Equations
11. Simulation of Random Processes
12. Mean Square Estimation
a. Orthogonality Principle for N Observations, Whitening
b. Linear and Nonlinear Estimation
c. Continuous-Time Observations, Wiener Filter``` Georgia Institute of Technology
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