Semester and Year: Fall term annually.

Credit Hours: 3.

Lecture: TF: 10:00-11:20AM .

** Pre-requisites: **ESCE-2410: Signals and
Systems (or equivalent), and, ESCE-2500: Probability (or equivalent).

Instructor

Prof. Alhussein Abouzeid

Email: abouzeid@ecse.rpi.edu

Course Description

This course introduces probability from an axiomatic and measure-theoretic perspective with applications in communication, sensing and imaging, pattern recognition and other signal processing systems. The course covers concepts of stochastic processes, wide sense stationarity, spectral decomposition, Brownian motion, Poisson processes, Markov processes; and other advanced topics.

Student Learning Outcomes

1. Develop an in-depth knowledge of the theory of probability and stochastic processes.

2. Be able to apply probability and stochastic process theory to model and analyze typical electrical and computer engineering systems.

3. Be able to evaluate the performance of engineering systems with uncertainty.

Course Content

1. Review of Probability Axioms and Random Variable

2. Convergence and limit theorems

3. Stochastic Processes

4. Poisson, Wiener and Markov Processes

5. Stationary Processes

6. Autocorrelation

7. Spectral Density

8. Effects of Filtering

9. Cyclo-stationary Processes*

10. Stochastic Derivatives and Integrals

11. Karhunen-Loeve Expansion*

12. Markov Chains*, Random Walks, and Other Applications

13. Filter Design, Weiner and Kalman* Filters

13. Applications in Computer Networking and Statistical Signal Processing

*Items with “*” will be covered if time permits. *

Course Text(s)

1. A. Papoulis and S.U. Pillai, Probability, Random Variables, and Stochastic Processes, Fourth Edition, McGraw Hill, 2002.

(Very comprehensive, but new students might get lost in it.)

Optional Additional References

1. Bruce Hajek, *Random
Processes For Engineers*, Cambridge University Press, 2015.

Pre-production copy of this book is available for free for educational use at: http://hajek.ece.illinois.edu/Papers/randomprocJuly14.pdf

(Very comprehensive and in-depth. May be too dense/sophisticated for students new to stochastic processes.)

2. A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed., Prentice Hall, 1993.

(Easy to follow, but not comprehensive enough in some topics.)

3. S. Ross,
Stochastic Processes, 2^{nd} ed., Wiley, 1995.

(Easy to follow, particularly useful for discrete & CS applications. Not much coverage for continuous time processes.)

4. R. Gallager, Stochastic Processes: Theory for Applications, Cambridge University Press, 2014.

(Easy to follow, particularly useful for continuous & EE communications applications. Detailed description of Gaussian processes. Not enough coverage for discrete time.)

5. R.D. Yates and D.J. Goodman,* *Probability and Stochastic Processes: A
Friendly Introduction for Electrical and Computer Engineers, Second Edition,
Wiley, 2004.

(Easy to follow, good for probability review, but does not cover enough of advanced topics.)

6. Probability, Random Processes, and Estimation Theory for Engineers, 3rd Edition, H. Stark and J. W. Woods, 2002.

(Rigorous, not quite easily accessible for starting students, focuses on continuous time.)

Course Assessment Measures

Three Exams, 25% each

Homeworks 25%

In-class problems +5%