- DSP log - http://www.dsplog.com -

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 (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

 GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf 

 Weiner-Kinchin theorem 

 Auto-correlation 

URL to article: http://www.dsplog.com/2012/12/15/gate-2012-ece-q2-communication/

URLs in this post:

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

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

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

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