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GATE-2012 ECE Q2 (communication)

Posted By Krishna Sankar On December 15, 2012 @ 6:17 pm In GATE | No Comments

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 [1], the auto-correlation [2] with delay  is defined as,

From the Weiner-Kinchin theorem [3], 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 [4]

[2] Weiner-Kinchin theorem [3]

[3] Wide sense stationary function [1]

[4] Auto-correlation [2]

 

 


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URLs in this post:

[1] wide sense stationary function: http://en.wikipedia.org/wiki/Stationary_process#Weak_or_wide-sense_stationarity

[2] auto-correlation: http://en.wikipedia.org/wiki/Autocorrelation_function#Properties

[3] Weiner-Kinchin theorem: http://en.wikipedia.org/wiki/Wiener%E2%80%93Khinchin_theorem

[4] http://gate.iitm.ac.in/gateqps/2012/ec.pdf: http://gate.iitm.ac.in/gateqps/2012/ec.pdf

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