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GATE-2012 ECE Q11 (signals)

by Krishna Sankar on December 27, 2012

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 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

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

[2] Laplace transform

[3] Reciprocal rule

 

 

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