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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.

Q11. The unilateral Laplace transform of is . The unilateral Laplace transform ofis

(A) 

(B) 

(C) 

(D) 

Solution

From the definition of Laplace transform [1] 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 [2] 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

[1] GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf [3]

[2] Laplace transform [1]

[3] Reciprocal rule [2]

 

 


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URLs in this post:

[1] Laplace transform: http://en.wikipedia.org/wiki/Laplace_transform

[2] reciprocal rule: http://en.wikipedia.org/wiki/Reciprocal_rule

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

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