## ECE 5605 Stochastic Signals and Systems

#### Fall 2015 textbook list

The Fall 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 5605 Stochastic Signals and Systems (3C)

5605: Egnineering applications of probability theory, random variables and random processes. Topics include: Gaussian and non-Gaussian random variables, correlation and stationarity of random processes. Time and frequency response of linear systems to random inputs using both classical transform and modern state space techiques.

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: Fall. 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 systems to both deterministic and random input processes.
• design system structures to meet desired performance objectives for both continuous and discrete time applications.

Course Topics
Topic Percentage
Probability space, sigma fields; probability axioms, conditional probability, random variables 10%
Probability distributions and density functions; independent and conditional random variables 10%
Two or more random variables; functions of random variables expectations, moments; characteristic functions 10%
Correlation; covariance; parameter estimation; multivariate normal variables random sequences and stochastic convergence; Central Limit Theorem 10%
Stochastic processes; Gaussian, exponential, random phase sinusoids in continuous and discrete time 20%
Strict and wide-sense stationary processes; correlation functions and expected values 20%
Linear transformations on random variables; linear system response to stochastic processes; ergodicity; power spectral density. 20%