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