The BRADLEY DEPARTMENT of ELECTRICAL and COMPUTER ENGINEERING

# ECE 5605 Stochastic Signals and Systems | ECE | Virginia Tech

### Course Information

#### Description

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.

#### Why take this course?

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

#### Prerequisites

STAT 4714

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.

### 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

#### Percentage of Course

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%