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lecture15 - ECE 5510 Random Processes Lecture Notes Fall...

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Unformatted text preview: ECE 5510: Random Processes Lecture Notes Fall 2008 Lecture 15 Today: (1) Random Process Intro • HW 7 due Thu at 5pm. OH today after class until 1:15; Thu 1-3. • Exam 2 is Tue. Nov. 11, two weeks from today. This week’s material concludes the material covered in Exam 2. Next Tue (Nov. 4) is a review class; Thu (Nov 6) I will be out of town, Piyush Agrawal will cover a new topic, “Expectation and Sta- tionarity of Random Processes”. This topic is important for Appl. Assignment 5. • AA #4 now due 5pm Wed. Nov. 5th (I don’t want to compete with election day); AA #5 now due Tue. Nov. 18. • Still waiting for the report from CTLE, so we’ll discuss on Thu. 1 Random Processes This starts into Chapter 10, ‘Stochastic’ Processes. As Y&G says, ”The word stochastic means random.” So I prefer ‘Random Pro- cesses’. What’s new? • We’re watching a random variable change over time, or over space, (or sometimes both). • Before we had a few random variables, X 1 ,X 2 ,X 3 . Now we have possibly infinitely many: X 1 ,X 2 ,... . • In addition, we may not be taking samples - we may have a continuously changing random variable, indexed by time t . We’ll denote this as X ( t ). Def’n: Random Process A random process X ( t ) consists of an experiment with a probability measure P [ · ], a sample space S , and a function that assigns a time (or space) function x ( t,s ) to each outcome s in the sample space. Recall that we used S to denote the event space, and every s ∈ S is a possible ‘way’ that the outcome could occur. ECE 5510 Fall 2008 2 1.1 Continuous and Discrete-Time Types of Random Processes: A random process (R.P.) can be either 1. Discrete-time : Samples are taken at particular time in- stants, for example, t n = nT where n is an integer and T is the sampling period. In this case, rather than referring to X ( t n ), we abbreviate it as X n . (This matches exactly our previous notation.) In this case, we also call it a random se- quence ....
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lecture15 - ECE 5510 Random Processes Lecture Notes Fall...

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