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Signals and Systems
Laplace Transform

Practice questions from Laplace Transform.

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Q#1 Laplace Transform GATE EE 2024 (Set 1) MCQ +1 mark -0.33 marks

If  is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal  is

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Q#2 Laplace Transform GATE EE 2020 (Set 1) MCQ +1 mark -0.33 marks

Which of the following statements is true about the two sided Laplace transform?

It exists for every signal that may or may not have a Fourier transform.

It has no poles for any bounded signal that is non-zero only inside a finite time interval.

The number of finite poles and finite zeroes must be equal.

If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.

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Q#3 Laplace Transform GATE EE 2019 (Set 1) MCQ +1 mark -0.33 marks

A system transfer function is  . If  , and all other coefficients are positive, the transfer function represents a

Band pass filter

High pass filter

Notch filter

Low pass filter

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Q#4 Laplace Transform GATE EE 2019 (Set 1) MCQ +1 mark -0.33 marks

The inverse Laplace transform of  

 is        

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Q#5 Laplace Transform GATE EE 2016 (Set 1) MCQ +1 mark -0.33 marks

The Laplace Transform of  is

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Q#6 Laplace Transform GATE EE 2016 (Set 2) MCQ +1 mark -0.33 marks

Consider a causal LTI system characterized by differential equation . The response of the system to the input , where u(t) denotes the unit step function, is

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Q#7 Laplace Transform GATE EE 2015 (Set 2) MCQ +1 mark -0.33 marks

The Laplace transform of  is . The Laplace transform of  is

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Q#8 Laplace Transform GATE EE 2014 (Set 1) MCQ +1 mark -0.33 marks

Let  be the Laplace transform of a signal x(t). Then,  is

0

3

5

21

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Q#9 Laplace Transform GATE EE 2014 (Set 2) MCQ +1 mark -0.33 marks

Consider an LTI system with impulse response. If the output of the system is  then the input, x(t), is given by

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Q#10 Laplace Transform GATE EE 2013 (Set 1) MCQ +1 mark -0.33 marks

The impulse response of a system is h(t)=t u(t) . for an input u(t-1), the output is

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Q#11 Laplace Transform GATE EE 2013 (Set 1) MCQ +1 mark -0.33 marks

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?        

All the poles of the system must lie on the left side of the  axis.

Zeros of the system can lie anywhere in the s-plane.

All the poles must lie within |s|=1.

All the roots of the characteristic equation must be located on the left side of the jw axis.

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Q#12 Laplace Transform GATE EE 2012 (Set 1) MCQ +1 mark -0.33 marks

The unilateral Laplace transform of f(t) is . The unilateral Laplace transform of t f(t) is

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Q#13 Laplace Transform GATE EE 2011 (Set 1) MCQ +1 mark -0.33 marks

Given two continuous time signals  and  which exist for t > 0, the convolution  is

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Q#14 Laplace Transform GATE EE 2011 (Set 1) MCQ +2 marks -0.66 marks

Let the Laplace transform of a function f(t) which exists for t > 0 be  and the Laplace transform of its delayed version  be  . Let  be the complex conjugate of  with the Laplace variable set as .If  , then the inverse Laplace transform of G(s) is        

An ideal impulse

An ideal delayed impulse

An ideal step function u(t)

An ideal delayed step function

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Q#15 Laplace Transform GATE EE 2010 (Set 1) MCQ +2 marks -0.66 marks

Given f(t) and g(t) as shown below:        

g(t) can be expressed as        

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Q#16 Laplace Transform GATE EE 2010 (Set 1) MCQ +2 marks -0.66 marks

Given f(t) and g(t) as shown below:        

The Laplace transform of g(t) is        

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Q#17 Laplace Transform GATE EE 2007 (Set 1) MCQ +2 marks -0.66 marks

If u(t), r(t) denote the unit step and unit ramp functions respectively and u(t)*r(t) their convolution. Then the function u(t+1)*r(t−2) is given by

None of the above.

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Q#18 Laplace Transform GATE EE 2006 (Set 1) MCQ +2 marks -0.66 marks

The running integrator, given by

Has no finite singularities in its double sided Laplace Transform Y(s)

Produces a bounded output for every causal bounded input

Produces a bounded output for every anti casual bounded input

Has no finite zeros in its double sided Laplace Transform Y(s)

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Q#19 Laplace Transform GATE EE 2005 (Set 1) MCQ +2 marks -0.66 marks

The Laplace transform of a function f(t) is .  As t →∞, f(t) approaches

3

5

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Q#20 Laplace Transform GATE EE 2002 (Set 1) MCQ +1 mark -0.33 marks

Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is

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Q#21 Laplace Transform GATE EE 1999 (Set 1) MCQ +2 marks -0.66 marks

A rectangular current pulse of duration T and magnitude I has the Laplace transform

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Q#22 Laplace Transform GATE EE 1995 (Set 1) MCQ +1 mark -0.33 marks

The convolution of the functions  and   is equal to _________.

None of these

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