# Continuous Time Signal Laplace Transform · Signals and Systems · GATE ECE

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## Marks 1

GATE ECE 2015 Set 2
The bilateral Laplace transform of a function $$f\left( t \right) = \left\{ {\matrix{ {1\,if\,a \le t \le b} \cr {0\,otherwise} \cr } } \r... GATE ECE 2014 Set 3 The input$$ - 3{e^{2t}}\,\,u\left( t \right)$$, where u(t) is the unit step function$$\, {{s - 2} \over {s + 3}}$$. If the initial value of the outpu... GATE ECE 2014 Set 1 A continuous, linear time - invariant fiilter has an impulse response h(t) described by$$h\left( t \right) = \left\{ {\matrix{ {3\,for\,0 \le t \l...
GATE ECE 2007
If the Laplace transform of a signal y(t) is $$Y\left( s \right) = {1 \over {s\left( {s - 1} \right)}},$$ then its final value is
GATE ECE 2003
The Laplace transform of i(t) tends to $$I\left( s \right)\,\, = \,{2 \over {s\left( {1 + s} \right)}}$$ As $$t \to \infty$$ , the value of i(t) te...
GATE ECE 2000
Given that $$L\left[ {f\left( t \right)} \right]\, = \,$$ $${{s + 2} \over {{s^2} + 1}},$$ $$L\left[ {g\left( t \right)} \right] = {{{s^2} + 1} \ove... GATE ECE 1999$$If\,\,L\left[ {f\left( t \right)} \right]\, = \,F\left( s \right),$$then$$L\left[ {f\left( {t - T} \right)} \right]$$is equal to GATE ECE 1998 If L$$\left[ {f\left( t \right)} \right]$$=$$\omega /\left( {{s^2} + {\omega ^2}} \right),$$then the value of$$\matrix{ {Lim\,f\,\left( t \righ...
GATE ECE 1997
The Laplace Transform of eat .cos$$\left( {\alpha t} \right).u\left( t \right)$$ is equal to
GATE ECE 1995
The final value theorem is used to find the
GATE ECE 1995
If L$$\left[ {f\left( t \right)} \right]$$ = $${{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}}$$, then $$f\left( {0 + } \right)\,$$ and $$f\left( \... GATE ECE 1994 The laplace transform of a unit ramp function starting at t=a, is ## Marks 2 GATE ECE 2016 Set 1 The Laplace transform of the casual periodic square wave of period T shown in the figure below is ... GATE ECE 2015 Set 2 Let x(t) = a s(t) +s(-t) with s(t) =$$\beta {e^{ - 4t}}u\left( t \right)$$, where u(t) is unit step function. If the bilateral Laplace transform of x... GATE ECE 2015 Set 1 The solution of the differential equation$${{h\left( {t + 1} \right)} \over {h\left( t \right)}}\,\,\,\,\,{{{d^2}y} \over {d{t^{ \to 2}}}} + {{2\,dy}...
GATE ECE 2014 Set 4
The unilateral Laplace transform of F(t) is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of g(t) = $... 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 system casual it needs to be ca... 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 through the linear constant - co... GATE ECE 2014 Set 3 Let h(t) denote the impulse response of a casual system with transfer function $${1 \over {s + 1}}$$. Consider the following three statements. S1: Th... GATE ECE 2014 Set 1 A system is described by the following differential equation, where u(t) is the input to the system and y(t) is output of the system $$\mathop y\limit... GATE ECE 2013 A system is described by the differential equation$$${{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y\left( t \right) = x\left( t \right)$$Let x... GATE ECE 2011 If$$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$then the initial and final values ... GATE ECE 2010 Given f(t) =$${L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {K - 3} \right)s}}} \right].$$If$$\matrix{ {Lim\,f\,\left( t \right) =...
GATE ECE 2009
Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)\,d\tau }$$ is
GATE ECE 2006
Consider the function f(t) having Laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}\,\,\,\,\,\,{\mathop{\rm Re}\n... GATE ECE 2005 In what range should Re(s) remain so that the Laplace transform of the function e(a+2)t+5 exists? GATE ECE 2002 The Laplace transform of a continuous - time signal x(t) is$$X\left( s \right) = {{5 - s} \over {{s^2} - s - 2}}$$. If the Fourier transform of tyhis... GATE ECE 1996 The inverse Laplace transform of the function$${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$is GATE ECE 1993 If$$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {K \over {\left( {s + 1} \right)\,\left( {{s^2} + 4} \right)}}$$then$$\mat...
GATE ECE 1993
The Laplace transform of the periodioc function f(t) describe4d by the curve below, i.e., f\left( t \right) = \left\{ {\matrix{ {\sin \,t\,\,\,if...
GATE ECE 1988
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 of its first period. Then
GATE ECE 1987
Laplace transform of the functions t u(t) and u(t) sin(t) are respectively:

## Marks 5

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