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

[3] Reciprocal rule

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