**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