GATE ECE

Continuous Time Linear Invariant System

Signals and Systems

(Past Years Questions)

Marks 1

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The input x(t) and the output y(t) of a continuous time system are related as $$y\left( t \right) = \int\limits_{t - T}...
GATE ECE 2017 Set 2
Consider the following statements for continuous-time linear time invariant (LTI) system. I. There is no bounded input ...
GATE ECE 2017 Set 1
The impulse response of an LTI system can be obtained by
GATE ECE 2015 Set 3
The result of the convolution $$x\left( { - t} \right) * \delta \left( { - t - {t_0}} \right)$$ is
GATE ECE 2015 Set 1
Two system with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cas...
GATE ECE 2013
The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is
GATE ECE 2013
The differential equation $$100{{{d^2}y} \over {dt}} - 20{{dy} \over {dt}} + y = x\left( t \right)$$ describes a system ...
GATE ECE 2011
The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptio...
GATE ECE 2008
The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\e...
GATE ECE 2008
Which of the following can be impulse response of a causal system?
GATE ECE 2005
Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of t...
GATE ECE 2003
Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to
GATE ECE 2002
The transfer function of a system is given by $$H\left( s \right) = {1 \over {{s^2}\left( {s - 2} \right)}}$$. The impul...
GATE ECE 2001
A system with an input x(t) and an output y(t) is described by the relation: y(t) = t x(t). This system is
GATE ECE 2000
The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the...
GATE ECE 1998
The transfer function of a zero - order - hold system is
GATE ECE 1998
The transfer function of a linear system is the
GATE ECE 1995
Non - minimum phase transfer function is defined as the transfer function
GATE ECE 1995
Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) i...
GATE ECE 1995
Indicate whether the following statement is TRUE/FALSE: Give reason for your answer. If G(s) is a stable transfer func...
GATE ECE 1994

Marks 2

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The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = $$\left[ {\sin (t)/\pi ...
GATE ECE 2017 Set 2
Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are $...
GATE ECE 2017 Set 2
Consider an LTI system with magnitude response $$$\left| {H(f)} \right| = \left\{ {\matrix{ {1 - \,{{\left| f \right|...
GATE ECE 2017 Set 2
A continuous time signal x(t) = $$4\cos (200\pi t)$$ + $$8\cos(400\pi t)$$, where t is in seconds, is the input to a lin...
GATE ECE 2017 Set 1
The output of a standrad second-order system for a unit step input is given as $$y(t) = 1 - {2 \over {\sqrt 3 }}{e^{ - t...
GATE ECE 2015 Set 2
Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If t...
GATE ECE 2015 Set 2
The impulse response of a continuous time system is given by $$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of th...
GATE ECE 2013
The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\ta...
GATE ECE 2012
An input x(t) = exp( -2t) u(t) + $$\delta $$(t-6) is applied to an LTI system with impulse response h(t) = u(t). The out...
GATE ECE 2011
A continuous time LTI system is described by $${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)...
GATE ECE 2010
Consider a system whose input x and output y are related by the equation $$$y(t) = \int\limits_{ - \infty }^\infty {x(...
GATE ECE 2009
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 an...
GATE ECE 2008
Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with...
GATE ECE 2008
The frequency response of a linear, time-invariant system is given by H(f) = $${5 \over {1 + j10\pi f}}$$. The step resp...
GATE ECE 2007
Let g(t) = p(t) * p(t), where * denotes convolution and p(t) = u(t) - (t-1) with u(t) being the unit step function. The ...
GATE ECE 2006
The output y(t) of a linear time invariant system is related to its input x(t) by the following equation: y(t) = 0.5 x ...
GATE ECE 2005
A system described by the differential equation: $${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dt}} + 2y = x(t)$$ is initi...
GATE ECE 2004
A rectangular pulse train s(t) as shown in Fig.1 is convolved with the signal $${\cos ^2}$$ ($$4\pi \,{10^{3\,}}$$t). Th...
GATE ECE 2004
A causal system having the transfer function H(s) = $${1 \over {s + 2}}$$, is excited with 10 u(t). The time at which th...
GATE ECE 2004
The impulse response function of four linear system S1, S2, S3, S4 are given respectively by $${h_1}$$(t), = 1; $${h...
GATE ECE 2001
A linear time invariant system has an impulse response $${e^{2t}},\,\,t\, > \,0.$$ If the initial conditions are zero an...
GATE ECE 2000
Let u(t) be the unit step function. Which of the waveforms in Fig.(a) -(d) corresponds to the convolution of $$\left[ {u...
GATE ECE 2000
Match each of the items 1, 2 on the left with the most appropriate item A, B, C or D on the right. In the case of a lin...
GATE ECE 1997
Match each of the items A, B and C with an appropriate item from 1, 2, 3, 4 and 5. List - 1 (A) $${a_1}{{{d^{2y}}} \ove...
GATE ECE 1994
An excitation is applied to a system at $$t = T$$ and its response is zero for $$ - \infty ...
GATE ECE 1991
The voltage across an impedance in a network is V(s) = Z(s) I(s), where V(s), Z(s) and $${\rm I}$$(s) are the Laplace Tr...
GATE ECE 1991
The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{...
GATE ECE 1990
The impulse response and the excitation function of a linear time invariant casual system are shown in Fig. a and b resp...
GATE ECE 1990
The transfer function of a zero-order hold is
GATE ECE 1988

Marks 5

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A deterministic signal x(t) = $$\cos (2\pi t)$$ is passed through a differentiator as shown in Figure. (a) Determine th...
GATE ECE 2002
For the linear, time-invariant system whose block diagram is shown in Fig.(a), with input x(t) and output y(t). (a) Find...
GATE ECE 2000
Fig.1, shows the block diagram representation of a control system. The system in block A has an impulse response $${h_A}...
GATE ECE 1997
Consider the following interconnection of the three LTI systems (Fig.1). $${h_1}(t)$$ , $${h_2}(t)$$ and $${h_3}(t)$$ ar...
GATE ECE 1993

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