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GATE-2012 ECE Q11 (signals)

Posted By Krishna Sankar On December 27, 2012 @ 6:06 am In GATE | 1 Comment

Question 11 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper.

(D) Solution

From the definition of Laplace transform  for a function defined for all real numbers  is,

, where

with real numbers  and .

To find the Laplace transform of , let us differentiate the above equation by on both sides,

.

Rearranging,

.

Further using the reciprocal rule  from calculus, the derivative of  is given by,

where.

Applying these two aspects to the problem,

.

Based on the above, the right choice is (D) .

Comment : What does the term ‘unilateral’ stand for in the statement unilateral Laplace transform ?

References

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

 Laplace transform 

 Reciprocal rule 

URL to article: http://www.dsplog.com/2012/12/27/gate-2012-ece-q11-signals/

URLs in this post:

 Laplace transform: http://en.wikipedia.org/wiki/Laplace_transform

 reciprocal rule: http://en.wikipedia.org/wiki/Reciprocal_rule

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