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Question 52 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper.
Q2. The power spectral density of a real process})
for positive frequencies is shown below. The values of \]})
and \]\|})
, respectively are
(A) 
(B) 
(C) })
(D) })
Solution
For a wide sense stationary function, the auto-correlation with delay is defined as,
From the Weiner-Kinchin theorem, the auto-correlation function and power spectral density
are Fourier Transform pairs, i.e.
Expressing in terms of , where
.
When the delay , the above equations simplifies to
.
Applying this to the problem at hand,
.
Further, since the power spectral density does not have any dc component, the mean of the signal
Based on the above, the right choice is (B)
References
[1] GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf
[3] Wide sense stationary function
[4] Auto-correlation
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