EE320 – Random Signal Analysis
Last Updated: May 28, 2009

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: jeffrey.denenberg@ieee.org

Web: doctord.webhop.net

Office Hrs: 12:30-1:30 pm, M-Th

Classroom: Buckman Hall - B232

 

Class Hrs: 10:50-12:05 pm Tues/Thurs

Textbook:      Roy D. Yates, David J Goodman, Probability and Stochastic Processes, Wiley, 2005, ISBN 0-471-27214-0.

References:    Textbook Cross References Table

  1. G. Cooper, C. McGillem, Probabilistic Methods of Signal and System Analysis, Oxford University Press, 1999, ISBN 0-19-512354-9.
  2. H. Hsu, Probability, Random Variables, and Random Processes, McGraw Hill, 1997
    (Schaum’s Outline Series – Strongly suggested)
  3. 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).
  4. Matlab Tutorial by B. Aliane – University of New Haven
  5. Grinstead/Snell, Introduction to Probability, Second Edition (A Free PDF Textbook)
  6. R. M. Gray, Introduction to Statistical Signal Processing – Stanford (A Free PDF Textbook)
  7. Random Processes by Nick Kingsbury – University of Cambridge

Homework:               As shown on the schedule, each assignment is due the following week. 
Late homework has reduced credit.

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

Tutorials on the web: Noise Tutorial – www.rfic.co.uk,

Results:                      As of 4/12/2009

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

1/27, 1/29

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

Discrete Probability:     Definitions - Relative Frequency, Axiomatic, Conditional Probability, Bernoulli Trials, Reliability, MatLab

 

1

 

1, 2, 2a, 3

 

1

HW1, HW2

HW is due the following week!

2/3, 2/5

Ch. 2 – Discrete Random Variables:  Distributions, Averages, Functions of a Random Variable, Expected Values, Variance/Standard Deviation, Conditional probability

 

 

 

HW3

2/10, 2/12

Ch. 3 – Continuous Random Variables:  Distributions, Density, Gaussian, Other Distributions, Delta Functions (Mixed Discrete/Continuous)

2

4, 6, 7, 8, 9

2

HW4

2/17
2/19

Ch. 4 – Pairs of Random Variables (Not in Exam 1)
Review for Exam 1


3


21, 23, 24


5

 

2/24

2/26

Exam 1 (Ch. 1, 2, 3)
Ch. 4 – Pairs of Random Variables (Continued)

 

4