Cleveland State University Department of Electrical Engineering and Computer Science

EEC 512 And Stochastic Processes

Catalog Data: EEC 512 - Probability and Stochastic Processes(4 credits) Prerequisite(s): Graduate standing. General concepts of probability and random variables, including random experiments, inequalities, joint distributions, functions of random variables, expectations, and the . Basic concepts of random processes and their properties are introduced. Markov process, linear systems with stochastic inputs, and power spectra are presented.

Textbook: Probability, Random Variables, and Stochastic Processes, by Athanasios Papoulis, Fourth Edition, McGraw Hill, 2004.

References:  An Introduction to Probability and Stochastic Processes, by James L. Melsa and Andrew P. Sage, Prentice Hall, 1973.  Introduction to Random Processes, by William A. Gardner, Second Edition, McGraw Hill, 1990.  Probability and Random Processes for Electrical Engineering, by Alberto Leon- Garcia, Addison-Wesley, 1989.  Digital Modulation Techniques, by Fuqin Xiong, Artech House, 2000

Instructor: Dr. Murad Hizlan, Office: FH338, Tel: 216-687-4526 Email: [email protected]

Course Objectives: This course introduces students to , random variables, and stochastic processes. At the end of this course, the students should understand probabilistic space, events and their probabilities, random variables and their probability densities, functions of random variables, expectations, correlation functions and power spectral densities of stochastic processes, and their applications. The students also should be able to derive or compute probabilities, densities, expectations, correlations, and power spectral densities. This course provides the fundamental background for communications, computer communications networks, controls, and signal processing.

Grading Policy: Midterm Test I: 30%,Midterm Test II: 30%, Final Exam: 30%, Homework 10%.

Remarks: As graduate students you are required to read the text before the lecture and after the lecture.Homework will be assined and graded. Answers will be provided.

Course Outline:

Session Topics Reading (sections) Assignments

1 The meaning of probability, , 1-1 to 1-3, 2-1,2-2 , probability axioms 2 , Baye’s theorem, 2-3, 2- independence 2,4,8,9,12,14,17 3 Labor Day (Sept.-1) 4 Bernoulli trails, , 3-1 to 3-3 Demoivre-Laplace Theorem 5 The law of large numbers, Poisson theorem 3-3, 3-4 3-4,5,8,11,12,13 and random points 6 Random variables, distribution and density 4-1, 4-2 functions, 7 Important densities, conditional 4-3,4-4 4-4,8,9,12,19,20 distributions 8 Function of one , 5-1 to 5-2 fundamental theorem, examples 9 Mean and variance, moments, characteristic 5-3 to 5-5 5- function 1,2,18,21,22,26 10 Review 11 Midterm Test I Chapters 1 to 5 12 Two random variables, joint distribution 6-1 and density, probability mass 13 One function of two random variables 6-2 14 Two functions of two random variables, 6-3 6-2,4,6,7,8,9 applications 15 Continuing discussion of functions of two 7-1,7-2 random variables: joint moments, correlation, independence, joint characteristic function 16 Conditional distributions, Baye’s theorem, 7-3,7-4 7-1,3,4,7,8,16 conditional expected values 17 Sequences of random variables, 8-1,8-2 independence, correlation matrix, conditional densities 18 Stochastic convergence and limit theorems 8-4, 8-5 8-4,5,12,30,31 19 Stochastic processes and their 10-1 20 Correlation functions, stationary processes 10-1 21 Review 22 Midterm Test II Chapters 6 to 8,10-1 23 Systems with stochastic inputs, 10-2 24 Spectra of stochastic processes, 10-3 Output of a linear system 25 Discrete-time processes 10-4 10- 1,3,22,27,33,35, 41 26 PSD of bandpass signals Appendix A (F. Xiong) 27 PSD of baseband digital signals Appendix A (F. Xiong) 28 PSD of digitally modulated carrier signals Appendix A (F. Xiong) 29 PSD of digitally modulated carrier signals Appendix A (F. (continue) Xiong) 30 FINAL EXAM Chapters 10 and PSD

Note: Class starts at 8-25 and ends on 12-3 (Wed.). Final exam is on 12-8 (Mon.) There are total of 15 weeks for classes. September 1 (Mon.) is Labor day, a University holiday. So there are a total 29 class times.