ECE 3075: Random Signals Fall 2008

ECE 3075: Random Signals Fall 2008

ECE 3075: Random Signals<br /> Fall 2008

 

ECE 3075: Random Signals

Fall 2008

 

Instructor

Justin Romberg, email:

Office Hours: 4:30-6p at Starbucks on 5th street the day before homework is due,

                       by appointment in Centergy 5245 or Klaus 2125

Teaching Assistant

Kai Chu, email:   kai.chu@gatech.edu

Office Hours: Tuesday 9a-11a, Thursday 9a-10a in Van Leer 449

Description

ECE 3075 builds a solid mathematical foundation for understanding continuous and discrete random variables, random processes, and their interaction with linear systems.

Download a syllabus (pdf)

Outline (subject to change)

Review of basic probability

    set theory and axiomatic probability

    conditional probability and Bayes Theorem

    combinatorics

    Bernoulli trials

Review of basic random variables

    expectation and moments

    Gaussian random variables

    Rayleigh distribution

    conditional probability and exponential random variables

    joint distributions

    conditional likelihood

    statistical independence and correlation

    the moment generating function; adding two independent random variables

    functions of two random variables

Introduction to estimation

    estimating the mean and variance

    the maximum likelihood estimator (MLE) and maximum a posterior estimator (MAP)

    hypothesis testing

Gaussian random vectors

    jointly Gaussian random vectors (GRVs)

    conditional pdfs for GRVs

    minimum mean-square error (MMSE) prediction

    the non-Gaussian case: optimal linear estimators

Random Processes

    stationary, wide-sense stationary, and ergodic process

    the autocorrelation function

    review of linear time-invariant systems (LTI systems)

    wide-sense stationary processes and LTI systems

    power-spectral density

    filtering out noise

    basic linear prediction

    introduction to spectral estimation

    Poisson and point processes