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GATE-2012 ECE Q2 (communication)

by Krishna Sankar on December 15, 2012

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

power_spectral_density

(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

[2] Weiner-Kinchin theorem

[3] Wide sense stationary function

[4] Auto-correlation

 

 

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