100209-lecture3 - EE522 Communications Theory 2010. 02. 09...

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1 EE522 Communications Theory 2010. 02. 09 Instructor: Hwang Soo Lee Lecture #3 – Random Processes and Quantization
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2 Announcements ± Handout: Lecture #3 Notes ± Homework #1 is due Thursday 02/11.
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3 Random Processes ± A random variable has a single value. However, actual signals change with time. ± Random variables model unknown events. ± Random processes model unknown signals. ± A random process is just a collection of random variables. ± If X(t) is a random process then X(1), X(1.5), and X(37.5) are all random variables for any specific time t.
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4 Terminology Describing Random Processes ± A stationary random process has statistical properties which do not change at all with time (i.e., all joint pdfs do not change). ± A wide sense stationary (WSS) process has a mean and autocorrelation function which do not change with time (this is usually sufficient). ± A random process is ergodic if the time average always converges to the statistical average. ± Unless specified, we will assume that all random processes are WSS and ergodic.
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5 Description of Random Processes ± Knowing the pdf of individual samples of the random process is not sufficient. We also need to know how individual samples are related to each other. ± Two tools are available to describe this relationship: ² Autocorrelation function ² Power spectral density function
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6 Autocorrelation ± Autocorrelation measures how a random process changes with time. ± Intuitively, X(1) and X(1.1) will be more strongly
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This note was uploaded on 11/23/2010 for the course EE EE522 taught by Professor Eeehwangsoo during the Spring '10 term at Korea Advanced Institute of Science and Technology.

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100209-lecture3 - EE522 Communications Theory 2010. 02. 09...

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