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Unformatted text preview: ECE 5510: Random Processes Lecture Notes Fall 2008 Lecture 22 Today: DiscreteTime (1) DTFT (2) Power Spectral Density (3) Examples HW 10 due Tue Dec 9 at 5pm. Application Assignment 6 due Thu Dec 11 at 5pm. Discussion items? 0.1 Ctstime WSS Process/LTI Filtering Examples 1. (From Miller & Childers, p448) The input to a linear filter is a random process with the following autocorrelation function: R X ( ) = A sin( ) . The filter impulse response is of the same form and is h ( t ) = 1 sin( 1 ) 1 . Determine the autocorrelation function of the filter output for 1 and for < 1 . 2. (from A. Yagle) A WSS r.p. X ( t ) with PSD S X ( f ) = 6 (2 f ) 2 +16 is input into a LTI system with impulse response h ( t ) = ( t ) + e 3 t u ( t ) where ( t ) is an impulse function and u ( t ) is a unit step function. Compute the PSD S Y ( f ) and variance Var Y [ Y ( t )] of the output Y ( t ) 1 DiscreteTime R.P. Spectral Analysis Traditionally, the discrete time case is not taught in a random pro cess course. But real digital signals are everywhere, and so I imagine that most of the time that this analysis is necessary is with discrete time random processes. For example, image processing, audio pro cessing, video processing, all are mostly digital. Traditionally, comcessing, video processing, all are mostly digital....
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 Fall '08
 Chen,R

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