EE562a_Lecture_Part_1 - EE 562a Lecture Notes Christopher...

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Unformatted text preview: EE 562a Lecture Notes Christopher Wayne Walker, Ph.D. 1 1.0 Introduction to Random Processes In this class we will study the theory of random or stochastic processes. Some applications in detection and estimation theory will be provided. The theory we learn in this course has applications in communications, signal and image processing, control theory and other areas. Several distinct mathematical concepts will be covered. A random process is a finite or possibly infinite collection of random variables. A random process X(u, t) assigns a function X(u0 , t) to each outcome u0 ∈ U. Here U is a sample space and t ∈ T (an index set). For fixed t0 ∈ T , X(u, t0 ) is a random variable. For fixed outcome u0 ∈ U, X(u0, t) is a sample function. X(u0 , t0 ) is a scalar. We will revisit this more formally later. 2 ...
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This note was uploaded on 05/25/2009 for the course EE 562a taught by Professor Toddbrun during the Spring '07 term at USC.

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