Discrete-Time Random Signals

Course #EC3410

Est.imated Completion Time: 3 months

Overview

Fundamentals of random processes are developed with an emphasis on discrete time for digital signal processing, control, and communications. Parameter estimation concepts are introduced, and impact of uncertainty in parameter evaluation (estimated moments and confidence intervals) are presented. Random processes are introduced. DKLT and applications to image processing and classification problems are considered. Impact of linear transformations to linear systems is discussed. FIR Wiener, and matched filters are introduced. IIR Wiener filter introduced, time permitting. Applications to signal and system characterization in areas such as system identification, forecasting, and equalizations are considered to illustrate concepts discussed during the course.

Included in degrees & certificates

290

Prerequisites

EC2410
EC2010

Learning Outcomes

· Develop the ability to characterize, analyze and extract information from random signals.

· Learn to be able to characterize stationary random processes from a second moment viewpoint in the time domain and frequency domains as they are processed through linear systems. Develop an understanding for Gaussian white noise for 1- and N-dimensional random vectors.

· Learn to characterize random signals from a second moment viewpoint as they are processed through discrete linear systems.

· Learn how to evaluate the behavior of signals and how multiple signals are related to each other using (cross) correlation and (cross) covariance information.

· Learn how to deal with uncertainty in estimated parameters via confidence intervals.

· Understand the principle of orthogonality and learn to apply it to problems involving linear mean-square estimation.

· Learn the principles of Wiener optimal filtering and be able to design FIR and/or IIR Wiener filters in applications such as estimation, prediction, channel equalization, or system identification.

· Learn the principles of matched filter and be able to design a matched filter for a communication and/or radar signal detection application.

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