EEE 554: Random Signal Theory, Fall 2007

 

Meeting: Tue/Thu, 4:40 pm – 5:55 pm, SCOB 252

Instructor: Prof. Gang Qian, GWC 454, 965-3704 / 727-8742, gang.qian@asu.edu

Office Hours: Tuesday, Thursday, 3:30-4:30 pm

 

TA: Adarsh Bangalore Narasimhamurthy, GWC 276, anbangal@asu.edu

TA Office Hours: Monday, 3 – 5 pm; Wednesday, 9am – 12 pm

 

Course website: http://www.public.asu.edu/~gqian/EEE554-F07.htm (course syllabus, homework assignments, solutions)

Textbook: A. Papoulis and S. U. Pillai. Probability, Random Variables and Stochastic Processes. 4th edition, McGraw-Hill, 2002.  The textbook web site is here, where you can find the textbook errata sheet, and supplementary material includes power point and pdf lectures, and a detailed list of errata and homework solution hints.

 

Other Useful References:

·        Alberto Leon-Garcia, Probability and Random Processes for Electrical Engineering, Addison-Wesley, 1994.

·        S. Ross. A First Course in Probability, 6th Edition, Prentice-Hall, 2002.

·        H. Stark and J. W. Woods Probability, Random Processes and Estimation Theory for Engineers, 2nd Edition, Prentice-Hall, 2002

Course Objectives: This course is intended to have the students develop a concrete understanding of probability theory and random processes so that the students are well prepared for other specific courses and research areas in various fields of electrical engineering, such as communications, signal processing, information theory, and estimation and detection theory. The study of the course is mathematical in nature with many examples of the application of these concepts to engineering problems.

Prerequisites: This course requires a sound background in calculus, linear algebra and elementary probability.

 

Outline:

·        Introduction and the meaning of probability

·        Axioms of probability

·        Concept of a random variable, probability distributions, conditional distributions, repeated trials

·        Functions of a random variable, transformations, expectation and moments, and characteristic functions

·        A pair of random variables, joint, marginal, and conditional distributions, conditional expectations

·        Sequences of random variables, convergences of random sequences, modes of convergence

·        Stochastic processes, wide- and strict-sense stationarity, power spectral distribution

·        Markov chains in discrete and continuous time, stationary distributions, Poisson process, queueing models

 

Progress:

Lecture

Date 

Section 

Homework Assignment

Homework Solution

 

 

 

 

 

1

08/21

Course Overview, Math Quiz
Ch. 1 Introduction and the meaning of probability

 

 

2

08/23

2.2 Probability space, Axioms of probability

 

 

3

08/28

2.3 Conditional probability, Total prob. and the Bayes’ theorem, Independence

HW #1: 2.{21, 22, 24, 25},

Due Sept/06/2007

Hint: Read example 2-18 before working on problem 2.25.

 Solution to HW #1 &

Grading method

 

4

08/30

4.1 Random variable, 4.2 Distribution and density functions,

 

 

5

09/04

4.2 Distribution and density functions,

 

 

6

09/06

4.2 Distribution and density functions, 4.3 Specific random variables

HW #2: 4.{4, 13, 15, 16,  26, 30}, 

Due Sept/13/2007

Note: In 4.26, the total number of components should be 1000, instead of 100.

 

7

09/11

4.3 Specific random variables

 

 

8

09/13

4.4 Conditional distributions

HW #3: 4.{18, 19, 20, 22}, 

Due Sept/20/2007

Solution to HW #2 &

Grading method

9

09/18

Ch. 3: Repeated trials

 

 

10

09/20

Repeated trials (First midterm is set on Oct. 4th.)

HW #4: 3.{1, 2, 6, 7}, 

Due Sept/27/2007

Solution to HW #3 &

Grading method

11

09/25

Ch. 5: Functions of one random variable

 

 

12

09/27

5.2 Distribution of g(x), Fundamental theorem of transformation of one r.v.

HW #5: 5.{ 6, 9, 11,15} plus two additional problems, 

Hint: 5.11, assume that in the Cauchy distribution \mu=0.

Due Oct/9/2007

Solution to HW #4 &

Grading method

13

10/02

Inverse problem,

 

 

14

10/04

Midterm 1: Chapters 1-4

-         closed-book, closed-note,

-         calculator allowed,

-         one page double-sided, letter (A-4) sized formula sheet allowed

 

Solution to midterm 1

15

10/09

5.3 Mean and variance

 

 

16

10/11

Inequalities,

HW #6: 5.{26, 27, 28, 34, 38 (a), (b)}

Due Oct/18/2007

Solution to HW #5 &

Grading method

17

10/16

Characteristic functions, moment generating functions

 

 

18

10/18

Ch. 6. Two random variables

HW #7- Part I

Due Oct/30/2007

 

19

10/23

Functions of two random variables

HW #7-PartII: 6 {2, 3, 5, 8, 20, 24}

Due Oct/30/2007

Solution to HW #6 &

Grading method

20

10/25

Functions of two random variables,

 

 

21

10/30

Joint moments

 

Solution to HW #7 &

Grading method

22

11/01

Conditional distribution

HW #8: 6.{47, 49, 57, 64, 65, 71, 72}

Due 11/06/2007

Solution to HW #8

23

11/06

Ch. 7: Sequences of random variables

 

 

24

11/08

Sequences of random variables, minimum mean square error estimation,

 

 

25

11/13

Midterm 2: Chapters 1-6, with emphasis on Ch. 5 and 6

-         closed-book, closed-note,

-         calculator allowed,

-         one page double-sided, letter (A-4) sized formula sheet allowed

Important points: pdf/cdf of functions of r.v., the 3-step procedure introduced in the class, characteristic functions, moments/moment generating function, expectation of a function, linearity of expectation, marginal pdf/cdf given joint functions, uncorrelated/independent/orthogonal, conditional distribution/expectation

 

26

11/15

Stochastic convergence

HW #9:   7 {11, 16}

Due Nov/20/2007

 

27

11/20

Stochastic convergence

 

Solution to HW #9 &

Grading method

28

11/22

No class, Thanksgiving Day

 

 

29

11/27

Stochastic convergence

 

Solution to midterm 2

30

11/29

Stochastic processes: general concepts,

Exercise #1 : 7{13, 14,  28,  29, 30}, 9.{4, 8}

Solution to exercise #1

31

12/04

Stochastic processes: systems with stochastic inputs

Exercise #2:  9.{13, 22}

Solution to exercise #2

 

12/11

 

4:40 – 6:35 pm

Final:  Comprehensive

-         closed-book, closed-note,

-         calculator allowed,

-         Up to 3 pages double-sided, letter (A-4) sized formula sheet(s) allowed

 

 

 

* You may want to check out some homework solution hints.

 

Exams/Grading:

·        Homework assignments will be made approximately weekly or biweekly. Homework papers are collected at the beginning of class on the date specified at the time of assignment.

·        Three closed-book exams: two midterm exams and one final exam

·        No make-up exams will be granted, except approved in advance by the instructor or in the case of a legitimate unforeseen emergency. If unable to attend for any reason, contact the instructor at least one week before the exam.

·        Homework: 10%; Midterm 1: 25%; Midterm 2: 25%; Final: 40%

Course Policies:

·         You are strongly encouraged to attend the classes and to participate in the class discussions. We will not cover the entire text book section by section. It will be very difficult to follow the course if you miss the class meetings.

·         You are allowed to discuss with your friends about the homework assignments. Nevertheless you must do your own work. Doing your own homework will definitely serve you well in exams and help you secure good grades. Copying homework from others will not be tolerated. Both parties are responsible.

·         No cheating allowed. Any form of cheating will result in an immediate failure of the course.