GATE ECE

Continuous Time Signal Laplace Transform

Signals and Systems

(Past Years Questions)

Marks 1

More
The bilateral Laplace transform of a function $$f\left( t \right) = \left\{ {\matrix{ {1\,if\,a \le t \le b} \cr ...
GATE ECE 2015 Set 2
The input $$ - 3{e^{2t}}\,\,u\left( t \right)$$, where u(t) is the unit step function$$\, {{s - 2} \over {s + 3}}$$. If ...
GATE ECE 2014 Set 3
A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\...
GATE ECE 2014 Set 1
If the Laplace transform of a signal y(t) is $$Y\left( s \right) = {1 \over {s\left( {s - 1} \right)}},$$ then its final...
GATE ECE 2007
The Laplace transform of i(t) tends to $$I\left( s \right)\,\, = \,{2 \over {s\left( {1 + s} \right)}}$$ As $$t \to \i...
GATE ECE 2003
Given that $$L\left[ {f\left( t \right)} \right]\, = \,$$ $${{s + 2} \over {{s^2} + 1}},$$ $$$L\left[ {g\left( t \right...
GATE ECE 2000
$$If\,\,L\left[ {f\left( t \right)} \right]\, = \,F\left( s \right),$$ then $$L\left[ {f\left( {t - T} \right)} \right]$...
GATE ECE 1999
If L$$\left[ {f\left( t \right)} \right]$$ = $$\omega /\left( {{s^2} + {\omega ^2}} \right),$$ then the value of $$\matr...
GATE ECE 1998
The Laplace Transform of eat .cos$$\left( {\alpha t} \right).u\left( t \right)$$ is equal to
GATE ECE 1997
If L$$\left[ {f\left( t \right)} \right]$$ = $${{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}}$$, then $$f\left( {0 +...
GATE ECE 1995
The final value theorem is used to find the
GATE ECE 1995
The laplace transform of a unit ramp function starting at t=a, is
GATE ECE 1994

Marks 2

More
The Laplace transform of the casual periodic square wave of period T shown in the figure below is ...
GATE ECE 2016 Set 1
Let x(t) = a s(t) +s(-t) with s(t) = $$\beta {e^{ - 4t}}u\left( t \right)$$, where u(t) is unit step function. If the bi...
GATE ECE 2015 Set 2
The solution of the differential equation $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}\,\,\,\,\,{{{d^2}y} \ov...
GATE ECE 2015 Set 1
The unilateral Laplace transform of F(t) is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral ...
GATE ECE 2014 Set 4
A stable linear time invariant (LTI) system has a transfer function H(s) = $${1 \over {{s^2} + s - 6}}$$. To make this s...
GATE ECE 2014 Set 4
A casual LTI system has zero initial conditions and impulse response h(t). Its input x(t) and output y(t) are related th...
GATE ECE 2014 Set 4
Let h(t) denote the impulse response of a casual system with transfer function $${1 \over {s + 1}}$$. Consider the follo...
GATE ECE 2014 Set 3
A system is described by the following differential equation, where u(t) is the input to the system and y(t) is output o...
GATE ECE 2014 Set 1
A system is described by the differential equation $$${{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y\left( t \right...
GATE ECE 2013
If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then...
GATE ECE 2011
Given f(t) = $${L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {K - 3} \right)s}}} \right].$$ If $$\matrix{ ...
GATE ECE 2010
Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \r...
GATE ECE 2009
Consider the function f(t) having Laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}...
GATE ECE 2006
In what range should Re(s) remain so that the Laplace transform of the function e(a+2)t+5 exists?
GATE ECE 2005
The Laplace transform of a continuous - time signal x(t) is $$X\left( s \right) = {{5 - s} \over {{s^2} - s - 2}}$$. If ...
GATE ECE 2002
The inverse Laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is
GATE ECE 1996
The Laplace transform of the periodioc function f(t) describe4d by the curve below, i.e., $$f\left( t \right) = \left\{ ...
GATE ECE 1993
If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {K \over {\left( {s + 1} \right)\,\left( {{s^2} + ...
GATE ECE 1993
The Laplace transform of a function f(t)u(t), where f(t) is periodic with period T, is A(s) times the Laplace transform ...
GATE ECE 1988
Laplace transform of the functions t u(t) and u(t) sin(t) are respectively:
GATE ECE 1987

Marks 5

More
A sinsoidal signal, v(t) = A sin(t), is applied to an ideal full-wave rectifier. Show that the Laplace Transform of the...
GATE ECE 1995
Find the Laplace transform of the waveform x(t) shown in Fig.1. ...
GATE ECE 1991

EXAM MAP

Graduate Aptitude Test in Engineering

GATE ECE GATE CSE GATE CE GATE EE GATE ME GATE PI GATE IN

Joint Entrance Examination

JEE Main JEE Advanced