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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.

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) **

[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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