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Screen Shot 2018-06-15 at 10.39.29 pm.png - Question 2...

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Unformatted text preview: Question 2: Random Processes ( 12 marks\ 2. 1 . Assume*" and I" are Ing uncorrelated Gaussian random variables , each with mean O' and` wiringce o' . It won' random variable } is formed by the following equation* 2 = pi + ( V1 - 1^ ^` where the parameter lol = 1 . Show that the correlation carlliciout of the random variables_{ and } is p . \$ marks 2.6 . Given it fandom process I ( 11 ) ( i ) When is the random process I ( 1 ) said to be* I mark . Wide- sense stationary . Autocorrelation ergarlic* ( in ) If I ( 1 ) = \$1 can ( 140 ) + 1} sin (`` ) , where A and B are uncorrelated zero mean random variables with miriance "`. Show that I ( " ) is a wide- scuse stationary random process` Show your step" clearly .* \$ marks 2. C. "The power Spectrum of a wide- scale stationary process = ( " ) is given by* ( i ) Write spectral factorization of ! = ( = ) in terms of \$1 ( = ) ( " minimum phase filter ; and 1/1 = - " ) ( a maximum place` filter ) . \$ marks 1 / 11 ) I' ( 1 ) P` 1 = ) = on ` ( 10 ) #` \$1( = ) P} 1 = ) = will ( = \ #`' (1 1 : " ) ( in ) Find the autocorrelation sequence of ;I ( 71) . 2 marks...
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• Spring '18
• Variance, Probability theory, Stochastic process, Stationary process, power spectrum

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