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# HW2 - EE 7615 Problem Set 2 Due 9,22,10 1 Please attempt...

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Unformatted text preview: EE 7615 Problem Set # 2 Due: 9,22,10 1) Please attempt each problem on a new page. 2) Show all your work clearly. 1. { X ( t ) } is a zero mean wide sense stationary Gaussian random process whose power spectral density is given by S X ( f ) = ( 1 | f | < 1 0 otherwise. { X ( t ) } is the input into a square law device whose output process { Y ( t ) } is given by Y ( t ) = [ X ( t )] 2 . { Y ( t ) } is then the input into a linear time-invariant system with frequency response given below. H ( f ) = ( 1 1 < | f | < 3 0 otherwise. Let the output of the filter be denoted as { Z ( t ) } . (a) Calculate the mean of the processes { Y ( t ) } and { Z ( t ) } . (b) Calculate the autocorrelation function of { Y ( t ) } in terms of that of { X ( t ) } . Is { Y ( t ) } a wide sense stationary process? If yes, find its power spectral density. (c) Is { Z ( t ) } a wide sense stationary process? If yes, evaluate its power spectral density....
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HW2 - EE 7615 Problem Set 2 Due 9,22,10 1 Please attempt...

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