## ECE 5606 Stochastic Signals and Systems

#### Spring 2015 textbook list

The Spring 2015 ECE textbook list is available online for students.

#### Current Prerequisites & Course Offering

For current prerequisites for a particular course, and to view course offerings for a particular semester, see the Virginia Tech Course Timetables.

### ECE 5606 Stochastic Signals and Systems (3C)

Response of continuous and discrete time, linear and nonlinear systems to Gaussian and non-Gaussian random processes. Signal to noise power ratio computations (SNR) of systems. Introduction to signal detection theory. Optimal filtering (estimation) techniques of Wiener and Kalman to both open and closed loop systems.

What is the reason for this course?

The analysis of system response to stochastic signals and noise is fundamental for the understanding of advanced system analysis and synthesis.

Typically offered: Spring. Program Area: Communications.

Prerequisites: STAT 4714.

Why are these prerequisites or corequisites required?

A basic course in probability and statistics such as STAT 4714 provides the necessary background in probability theory and random variables that the beginning graduate student should have for ECPE 5605, which is an advanced treatment of probability and stochastic processes. ECPE 5606 is the second course in the sequence, which requires ECPE 5605 as prerequisite.

### Department Syllabus Information:

Major Measurable Learning Objectives:
• analyze the response of linear and nonlinear systems to both Gaussian and non-Gaussian random processes.
• design and evaluate the performance of both basic detection and optimal filtering systems.

Course Topics
Topic Percentage
Linear System transformations on multivariate Gaussian processes and Brownian motion 10%
Narrowband Gaussian and Gaussian-derived processes, e.g. processes with Rayleigh and Rician densities 10%
Response of open and closed loop systems to stochastic inputs 10%
Response of nonlinear systems to stationary stochastic process 10%
Filtering, smoothing and prediction of stationary stochastic processes; Wiener and matched filtering. 20%
Hypothesis testing, maximum likelihood ratio decisions; detection of known signals in a noisy environment. 20%
Introduction to state estimation theory in discrete time, linear, scalar systems. 20%