# hw9 - Virginia Tech The Bradley Department of Electrical...

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Virginia Tech The Bradley Department of Electrical and Computer Engineering ECE 5605 – Stochastic Signals and Systems – Fall 08 Problem Set 9 Problem 1. Let X ( t ) and Y ( t ) be independent, WSS random processes with zero means and the same covariance function C ( τ ). Let Z ( t ) be deﬁned by Z ( t ) = aX ( t ) + bY ( t ) . a. Determine whether Z ( t ) is also WSS. b. Determine the pdf of Z ( t ) if X ( t ) and Y ( t ) are also jointly Gaussian random processes. Problem 2. Let X ( t ) be a zero-mean wide-sense stationary random process with autocovariance function given by C X ( τ ). The output of a “square-law detector” is Y ( t ) = X 2 ( t ) . a. Determine whether Y ( t ) is also a wide-sense stationary random process. b. Determine whether Y ( t ) is also a wide-sense stationary random process if X ( t ) is a Gaussian random process. Problem 3. Let the random variables A and B be independent and identically distributed with common density f ( x ) = 1 2 e -| x | . Show that the process

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## This note was uploaded on 05/05/2010 for the course ECECS 5605 taught by Professor Dasilver during the Fall '08 term at Virginia Tech.

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hw9 - Virginia Tech The Bradley Department of Electrical...

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