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ECE 302 Probabilistic Methods in Electrical and Computer Engineering

Lecture Hours: 3. Credits: 3.

Normally Offered: Each Fall, Spring

Prerequisites: MA 262 or MA 266

Prerequisites by Topic: basic calculus skills; differential equations; familiarity with basic concepts of circuits and linear system analysis, such as convolution; familiarity with Fourier analysis and two-sided transforms used in solving linear systems and differential equations

Corequisites: ECE 301

Catalog Description: An introductory treatment of probability theory including distribution and density functions, moments and random variables. Applications of normal and exponential distributions. Estimation of means, variances. Correlation and spectral density functions. Random processes and response of linear systems to random inputs.

Course Objective(s): This course is intended to introduce the concepts of probability and random processes and to discuss their application to engineering problems. Particular emphasis is given to application of these methods to systems analysis. It is also intended that this course should be a suitable prerequisite for EE 600.

Required Text(s):

  1. Probability and Random Processes for Electrical Engineering, 3rd Edition, Alberto Leon-Garcia, Prentice-Hall, 1994, ISBN No. 0131471228.

Recommended Reference(s):

  1. MatLab: Student Version, Current Edition, The MathWorks, Inc..

Course Outcomes:

A student who successfully fulfills the course requirements will have demonstrated:

  1. an ability to solve simple probability problems in electrical and computer engineering applications. [1,2,4;a,b,e]
  2. an ability to model complex families of signals by means of random processes. [1,2,3,4;a,b,e,k]
  3. an ability to determine the random process model for the output of a linear system when the system and input random process models are known. [1,3,4;a,b,e,k]

Lecture Outline:

Week Topic
1 Introduction, Definitions; Set Operations; Probability Introduced
2 Probability Axioms; Math Model; Joint & Conditional Probability
3 Independence, Bernoulli Trials; Ran. Variables and Distribution Functions; Density Functions
4 Gaussian Random Variables; Other Density Functions; Conditional Probability
5 Expectation; Moments; Transformations of a Random Variables
6 Review; Test; Vector Random Variables
7 Joint Distribution & Density; Conditional Distributions, Independence; Sums of Random Variables
8 Random Processes; Correlation Functions
9 Process Measurements; Gaussian, Poisson Processes
10 Review; Test; Spectral Density
11 Relationship to Correlation Function; Some Noise Definitions; Linear System Fundamentals
12 Random Signals & Linear Systems; System Evaluation Using Random Noise; Spectral Character of System Response
13 Noise Bandwidth; Modeling Noise Sources; Matched Filters
14 Wiener Filters; Review; Test
15 Noise is AM; Noise is FM; Noise Feedback Systems
Final Exam