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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.

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 ?

[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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