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Signals and Systems
Representation of Continuous Time Signal Fourier Series
Discrete Time Signal Fourier Series Fourier Transform
Discrete Time Signal Z Transform
Continuous Time Linear Invariant System
Transmission of Signal Through Continuous Time LTI Systems
Discrete Time Linear Time Invariant Systems
Sampling
Continuous Time Signal Laplace Transform
Discrete Fourier Transform and Fast Fourier Transform
Transmission of Signal Through Discrete Time Lti Systems
Miscellaneous
Fourier Transform
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GATE ECE
Continuous Time Linear Invariant System
Signals and Systems
Previous Years Questions
START HERE
Marks 1
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The input x(t) and the output y(t) of a continuous time system are related as $$y\left( t \right) = \int\limits_{t - T}...
GATE ECE 2017 Set 2
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Consider the following statements for continuous-time linear time invariant (LTI) system. I. There is no bounded input ...
GATE ECE 2017 Set 1
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The impulse response of an LTI system can be obtained by
GATE ECE 2015 Set 3
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The result of the convolution $$x\left( { - t} \right) * \delta \left( { - t - {t_0}} \right)$$ is
GATE ECE 2015 Set 1
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The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is
GATE ECE 2013
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Two system with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cas...
GATE ECE 2013
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The differential equation $$100{{{d^2}y} \over {dt}} - 20{{dy} \over {dt}} + y = x\left( t \right)$$ describes a system ...
GATE ECE 2011
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The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\e...
GATE ECE 2008
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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
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Which of the following can be impulse response of a causal system?
GATE ECE 2005
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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
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Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to
GATE ECE 2002
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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
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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
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The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of ...
GATE ECE 1998
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The transfer function of a zero - order - hold system is
GATE ECE 1998
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Non - minimum phase transfer function is defined as the transfer function
GATE ECE 1995
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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
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The transfer function of a linear system is the
GATE ECE 1995
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Indicate whether the following statement is TRUE/FALSE: Give reason for your answer. If G(s) is a stable transfer func...
GATE ECE 1994
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Marks 2
More
Consider an LTI system with magnitude response $$$\left| {H(f)} \right| = \left\{ {\matrix{ {1 - \,{{\left| f \right|...
GATE ECE 2017 Set 2
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Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are $...
GATE ECE 2017 Set 2
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A continuous time signal x(t) = $$4\cos (200\pi t)$$ + $$8\cos(400\pi t)$$, where t is in seconds, is the input to a lin...
GATE ECE 2017 Set 1
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The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = $$\left[ {\sin (t)/\pi ...
GATE ECE 2017 Set 2
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The output of a standrad second-order system for a unit step input is given as $$y(t) = 1 - {2 \over {\sqrt 3 }}{e^{ - t...
GATE ECE 2015 Set 2
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Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If t...
GATE ECE 2015 Set 2
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The impulse response of a continuous time system is given by $$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of th...
GATE ECE 2013
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The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\ta...
GATE ECE 2012
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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
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A continuous time LTI system is described by $${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)...
GATE ECE 2010
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Consider a system whose input x and output y are related by the equation $$$y(t) = \int\limits_{ - \infty }^\infty {x(...
GATE ECE 2009
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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
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A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 an...
GATE ECE 2008
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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
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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
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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
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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
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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
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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
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The impulse response function of four linear system S1, S2, S3, S4 are given respectively by $${h_1}$$(t), = 1; $${h...
GATE ECE 2001
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Let u(t) be the unit step function. Which of the waveforms in Fig.(a) -(d) corresponds to the convolution of $$\left[ {u...
GATE ECE 2000
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A linear time invariant system has an impulse response $${e^{2t}},\,\,t\, > \,0.$$ If the initial conditions are zero...
GATE ECE 2000
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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
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Match each of the items A, B and C with an appropriate item from 1, 2, 3, 4 and 5. List - 1 (A) $${a_1}{{{d^{2y}}} \ove...
GATE ECE 1994
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An excitation is applied to a system at $$t = T$$ and its response is zero for $$ - \infty < t < T$$. Such a sys...
GATE ECE 1991
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The voltage across an impedance in a network is V(s) = Z(s) I(s), where V(s), Z(s) and $${\rm I}$$(s) are the Laplace Tr...
GATE ECE 1991
GO TO QUESTION
The impulse response and the excitation function of a linear time invariant casual system are shown in Fig. a and b resp...
GATE ECE 1990
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The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{...
GATE ECE 1990
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The transfer function of a zero-order hold is
GATE ECE 1988
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Marks 5
More
A deterministic signal x(t) = $$\cos (2\pi t)$$ is passed through a differentiator as shown in Figure. (a) Determine th...
GATE ECE 2002
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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
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Fig.1, shows the block diagram representation of a control system. The system in block A has an impulse response $${h_A}...
GATE ECE 1997
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Consider the following interconnection of the three LTI systems (Fig.1). $${h_1}(t)$$ , $${h_2}(t)$$ and $${h_3}(t)$$ ar...
GATE ECE 1993
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