This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Virginia Tech The Bradley Department of Electrical and Computer Engineering ECE 5605 Stochastic Signals and Systems Fall 08 Problem Set 7 Problem 1. Let be a random variable uniformly distributed on [0 , 2 ). Consider the process X ( t ) = cos 2 ( t + ) . Find the mean value of X ( t ). Problem 2. Let Y ( t ) = X ( t ) aX ( t + d ), where X ( t ) is a Gaussian random process. a. Find the mean and autocovariance of Y ( t ). b. Find the pdf of Y ( t ). c. Find the joint pdf of Y ( t 1 ) and Y ( t 2 ). Problem 3. Let X ( t ) be a zeromean Gaussian random process with autocovariance function given by C X ( t 1 ,t 2 ). If X ( t ) is the input to a square law detector, then the output is Y ( t ) = X ( t ) 2 . Find the mean and autocovariance of the output Y ( t ). Hint : If X 1 ,X 2 ,X 3 ,X 4 are zeromean jointly Gaussian random variables, E [ X 1 X 2 X 3 X 4 ] = E [ X 1 X 2 ] E [ X 3 X 4 ] + E [ X 1 X 3 ] E [ X 2 X 4 ] + E [ X 1 X 4 ] E [ X 2 X 3 ] ....
View Full
Document
 Fall '08
 DASILVER

Click to edit the document details