EE320/650 – Random Signal Analysis
Last Updated: March 27, 2008

Course Content
The elements of probability theory: continuous and discrete random variables, characteristic functions and central limit theorem. Stationary random processes: auto correlation, cross correlation, power density spectrum of a stationary random process and system analysis with random signals.
Prerequisite: EE302 (or equivalent). 3 credit hours.

Instructor:    

Jeffrey N. Denenberg

Phone: (203) 268-1021

Fax: (509) 471-2831

Email: [email protected]

Web: doctord.webhop.net

Office Hrs: 4:30-5:30 pm, Thurs. B239

Classroom: Buckman Hall - B232

Note: Winter trimester

Class Hrs: 6:00-9:00 pm Thurs.

Textbook:      G. Cooper, C. McGillem, Probabilistic Methods of Signal and System Analysis, Oxford University Press, 1999, ISBN 0-19-512354-9.

References:    Textbook Cross References Table

  1. H. Hsu, Probability, Random Variables, and Random Processes, McGraw Hill, 1997
    (Schaum’s Outline Series – Strongly suggested)
  2. A. Papoulis and Pillai, Probability, Random Variables and Stochastic Processes, 4th Edition,
    McGraw-Hill, New York, 2003,  ISBN 0-07-366011-6 (0-07-112256-7).
  3. Matlab Tutorial by B. Aliane – University of New Haven
  4. Grinstead/Snell, Introduction to Probability, Second Edition (A Free PDF Textbook)
  5. R. M. Gray, Introduction to Statistical Signal Processing – Stanford (A Free PDF Textbook)
  6. Random Processes by Nick Kingsbury – University of Cambridge

Homework:                As shown on the schedule, each assignment id due the following week.  Late homework is generally not accepted.

Computer Usage:      Assignment of homework exercises to be completed using MatLab. 

Tutorials on the web:

Noise Tutorial – www.rfic.co.uk,

Results:                      EE320 (Final Grades)
EE650 (Final Grades)

Grading Policy:         Exams I and II             40%
Homework                  20%
Final Exam                 40%

Prepared by: Jeffrey N. Denenberg

Course Objectives: This course is tailored to provide an introductory treatment of probability and random signals relevant to undergraduate and graduate electrical and computer engineering students.

Course outcomes:     At the completion of this course students should:

 

1.

Recite the axioms of probability; use the axioms and their corollaries to give reasonable answers. 

2.

Determine probabilities based on counting (lottery tickets, etc.)

3.

Calculate probabilities of events from the density or distribution functions for random variables

4.

Classify random variables based on their density or distribution functions

5.

Know the density and distribution functions for common random variables

6.

Determine random variables from definitions based on the underlying probability space.

7.

Determine the density and distribution functions for functions of random variables using several different techniques presented in class.

8.

Calculate expected values for random variables.

9.

Determine whether events, random variables, or random processes are statistically independent.

10.

Use inequalities to find bounds for probabilities that might otherwise be difficult to evaluate.

11.

Use transform methods to simplify solving some problems that would otherwise be difficult.

12.

Evaluate probabilities involving multiple random variables or functions of multiple random variables.

13.

Simulate random variables and random processes.

14.

Classify random processes:

  • based on their time support and value support.
  • based on stationarity.

15.

Evaluate:

  • the mean, autocovariance, and autocorrelation functions for random processes at the output of a linear filter
  • the power spectral density for wide-sense stationary random processes

Schedule:

Date

Topic

Aliane

Shea

Stensby

HW

1/2

Ch. 1 - Introduction To and Overview of Probability and Noise

Probability:
Definitions - Relative Frequency, Axiomatic
Conditional Probability
Bernoulli Trials

 

1

 

1, 2, 2a, 3

 

1

HW1, HW2

HW is normally due the following week!

1/9

Probability - Continued

 

 

 

HW3

1/16

Ch. 2 - Random Variables:  Distributions, Density, Gaussian, Other Distributions

2

4, 6, 7, 8, 9

2

HW4

1/23

Review for Exam 1
Ch. 2 - Moments/Conditional Probability


3


21, 23, 24


5

 

1/30

Exam 1 (ch. 1-2)
Ch. 3 - Multiple Random Variables 

 

4

 

5, 11, 14

 

3

 HW5 

2/6

Exam 1 Reprise

Ch. 3 - Functions of Random Variables:

 

 

17, 19

 

4

 

2/13

Ch. 3 - Functions continued , The Characteristic Function

 

 

 

HW6

2/20

Ch. 5 - Random Processes:

5

33

6

 

2/27

Review for Exam 2

Ch. 5 – Random Processes continued

 

 

 

 

3/5

Exam 2 (ch. 3, 5)

Ch. 6 - Correlation Functions

 

 

35

 

7

 

3/12

Exam 2 Reprise

Ch. 7 - Power Spectral Density

 

6

 

 

8

 

3/19

Course review
Ch. 8 - Linear Systems and Random Inputs

 

 

34, 36, 37

 

9

 

3/26

Final Exam (Comprehensive Ch. 1-3, 5-8)

 

 

 

 

Citations:

·       Dr. Bouzid Aliane, University of New Haven (PDF - need a password)

·       Dr. John Stensby, University of Alabama - Huntsville

·       Dr. John M. Shea, University of Florida