Course Syllabus

ECE 650 - Random Processes

Department: Electrical & Computer Engineering

Course Number: ECE 650

Course Title: Random Processes

Credit Units: 3

Course Description

Random vectors, sequences, and processes. Linear systems with random inputs. Second moment

theory and spectral analysis. Narrowband processes. Gaussian and Poisson processes.

Application to filtering, detection and estimation of signals in white and non-white noise.

Prerequisite by Topic

Students taking this course should know linear algebra, linear system theory (ECE 350/351) and

probability theory (ECE 450). In particular, from linear algebra they should be able to perform

basic operations on vectors and matrices. From linear system theory they should be able to

characterize linear systems using the impulse response, the transfer function, the differential (or

difference) equation, and the block diagram, and know the input/output relationships for linear

systems in both the time domain and the frequency domain. From probability theory, they should

be able to apply the basic rules of probability, and be able to use the probability density function

and the cumulative distribution function to compute probabilities. They should know what a

random variable is and be able to solve probability problems involving continuous and discrete

random variables. They should also be able to solve simple vector/matrix operations and

probability calculations in MATLAB.

Text, References & Software

Required Text:

Probability and Random Processes with Application to Signal Processing and Communications,

2nd ed., Scott L. Millers and Donald G. Childers, Elsevier Academic Press, 2012, ISBN:

9780123869814.

Software: MATLAB (available via: www.mathworks.com)

Course Objectives – After completing this course the students should be able to:

1. Solve basic probability problems requiring the use of random vectors and random sequences

2. Know definitions and apply concepts related to correlation and orthogonality

3. Apply the principles of probability to solve problems in estimation and detection

4. Use MATLAB to solve problems involving random variables and random vectors and to

simulate random experiments using Monte-Carlo techniques

5. Relate random processes to random sequences, random vectors, and random variables

6. Classify random processes as continuous or discrete, ergodic or non-ergodic, and stationary,

WSS, or non-stationary

7. Know the properties of a white process and of a Gaussian process

8. Obtain information from the autocorrelation function and the power spectral density of a WSS

random process.

9. Determine the autocorrelation function and the power spectral density for the output of an

LTI system with WSS input, given its autocorrelation function or its power spectral density

10. Apply basic signal processing techniques such as (coloring, whitening or filtering) to random

signals

Topics Covered/Course Outline

1. Brief Review of ECE 450: basic concepts of probability, random variables and random

vectors, to establish notation

2. Basics of Estimation (as an application of material covered in the review)

MMSE estimation (single & multiple observations); orthogonality principle;

3. Second moment theory of random vectors

whitening & coloring of random vectors (linear transformations to whiten colored noise

vectors, and to color white noise vectors so that they have a specified covariance matrix);

K-L Expansion

4. Random sequences; convergence theorems

5. Random processes

Basic Definitions: sample functions, ergodic processes, stationary processes, WSS

processes

Autocorrelation Functions (in general and for WSS processes) and Power Spectral

Densities (for WSS processes)

Random inputs to LTI systems

Other application of random processes (narrowband, Gaussian and Poisson

processes, application to filtering, detection and estimation of signals in white and non-

white noise, and, if time allows, simulation techniques in MATLAB)

Relationship to Program Outcomes

This course supports the achievement of the following outcomes:

a) Ability to apply knowledge of advanced principles to the analysis of electrical and

computer engineering problems.

b) Ability to apply knowledge of advanced techniques to the design of electrical and

computer engineering systems.

c) Ability to apply the appropriate industry practices, emerging technologies, state-of-

the-art design techniques, software tools, and research methods of solving electrical

and computer engineering problems.

f) Ability to maintain life-long learning and continue to be motivated to learn new

subjects.

g) Ability to learn new subjects that are required to solve problems in industry without

being dependent on a classroom environment.

h) Ability to be competitive in the engineering job market and/ or be admitted to an

excellent Ph.D. program.

Prepared and Revised by:

Debbie van Alphen

Revised: July, 2012