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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.
- Spring '07