GATE EE

Linear Time Invariant Systems

Signals and Systems

(Past Years Questions)

Marks 1

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Consider a continuous-time system with input x(t) and output y(t) given by $$y\left(t\right)=x\left(t\right)\cos\left(t\...
GATE EE 2016 Set 1
The impulse response g(t) of a system G, is as shown in Figure (a). What is the maximum value attained by the impulse re...
GATE EE 2015 Set 1
Consider an LTI system with transfer function $$H\left(s\right)=\frac1{s\left(s+4\right)}$$.If the input to the system i...
GATE EE 2014 Set 2
Consider an LTI system with impulse response $$h\left(t\right)=e^{-5t}u\left(t\right)$$ . If the output of the system is...
GATE EE 2014 Set 2
x(t) is nonzero only for $$T_x\;...
GATE EE 2014 Set 1
Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the ca...
GATE EE 2013
The impulse response of a system is h(t) = tu(t). For an input u(t − 1), the output is
GATE EE 2013
Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is ...
GATE EE 2013
Given two continuous time signals $$x\left(t\right)=e^{-t}$$ and $$y\left(t\right)=e^{-2t}$$ which exist for t > 0, the ...
GATE EE 2011
A low–pass filter with a cut-off frequency of 30 Hz is cascaded with a high-pass filter with a cut-off frequency of 20 H...
GATE EE 2011
For the system $$\frac2{\left(s+1\right)}$$, the approximate time taken for a step response to reach 98% of its final va...
GATE EE 2010
The system represented by the input-output relationship $$y\left(t\right)=\int_{-\infty}^{5t}x\left(\tau\right)d\tau$$, ...
GATE EE 2010
A linear Time Invariant system with an impulse response $$h(t)$$ produces output $$y(t)$$ when input $$x(t)$$ is applied...
GATE EE 2009
A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Give...
GATE EE 2008
A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Give...
GATE EE 2008
The impulse response of a causal linear time-invariant system is given as $$h(t)$$. Now consider the following two state...
GATE EE 2008
Let a signal $${a_1}\,\sin \left( {{\omega _1}t + {\phi _1}} \right)$$ be applied to a stable linear time-invariant sys...
GATE EE 2007
$$s(t)$$ is step response and $$h(t)$$ is impulse response of a system. Its response $$y(t)$$ for any input $$u(t)$$ is ...
GATE EE 2002
If $$f(t)$$ is the step-response of a linear time-invariant system, then its impulse response is given by ___________
GATE EE 1994
$$s(t)$$ is step response and $$h(t)$$ is impulse response of a system. Its response $$y(t)$$ for any input $$u(t)$$ is ...
GATE EE 1993

Marks 2

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For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE?
GATE EE 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 ...
GATE EE 2013
L et y[n] denote the convolution of h[n] and g[n], where $$h\left[n\right]=\left(1/2\right)^nu\left[n\right]$$ and g[n] ...
GATE EE 2012
The input x(t) and output y(t) of a system are related as $$\int_{-\infty}^tx\left(\tau\right)\cos\left(3\tau\right)d\ta...
GATE EE 2012
The response h(t) of a linear time invariant system to an impulse $$\delta\left(t\right)$$, under initially relaxed cond...
GATE EE 2011
Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the ...
GATE EE 2010
A cascade of 3 Linear Time Invariant systems is casual and unstable. From this, we conclude that
GATE EE 2009
The $$z$$$$-$$ transform of a signal $$x\left[ n \right]$$ is given by $$4{z^{ - 3}} + 3{z^{ - 1}} + 2 - 6{z^2} + 2{z^3}...
GATE EE 2009
A system with input $$x(t)$$ and output $$y(t)$$ is defined by the input $$-$$ output relation: $$y\left( t \right) = \...
GATE EE 2008
A signal $$x\left( t \right) = \sin c\left( {\alpha t} \right)$$ where $$\alpha $$ is a real constant $$\left( {\sin \,c...
GATE EE 2008
The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}.$$ ...
GATE EE 2008
$$X\left( z \right) = 1 - 3\,\,{z^{ - 1}},\,\,Y\left( z \right) = 1 + 2\,\,{z^{ - 2}}$$ are $$Z$$-transforms of two sign...
GATE EE 2007
Consider the discrete-time system shown in the figure where the impulse response of $$G\left( z \right)$$ is $$g\left( ...
GATE EE 2007
A signal is processed by a causal filter with transfer function $$G(s).$$ For a distortion free output signal waveform, ...
GATE EE 2007
A signal is processed by a causal filter with transfer function $$G(s).$$ For a distortion free output signal waveform, ...
GATE EE 2007
A discrete real all pass system has a pole at $$z = 2\angle {30^ \circ };\,$$ it, therefore,
GATE EE 2006
$$x\left[ n \right] = 0;\,n 0,\,x\left[ { - 1} \right] = - 1,\,x\left[ 0 \right]$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\...
GATE EE 2006
A continuous-time system is described by $$y\left( t \right) = {e^{ - |x\left( t \right)|}},$$ where $$y(t)$$ is the out...
GATE EE 2006
$$y\left[ n \right]$$ denotes the output and $$x\left[ n \right]$$ denotes the input of a discrete-time system given by ...
GATE EE 2006
In the system shown in Fig. the input $$x\left( t \right) = \sin t.$$ In the steady-state, the response $$y(t)$$ will be...
GATE EE 2004
Given the relationship between the input $$u(t)$$ and the output $$y(t)$$ to be $$y\left( t \right) = \int\limits_0^t {\...
GATE EE 2001

Marks 4

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Match the following transfer functions and impulse responses Transfer functions $$\eqalign{ & \left( a \right)\,\,\,\,...
GATE EE 1992

Marks 5

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A single input single output system with $$y$$ as output and $$u$$ as input, is described by $$${{{d^2}y} \over {d{t^2}...
GATE EE 2002
A first order system is initially at rest and excited by a step input at time $$t=0.$$ Its output becomes $$1.1$$ $$V$$ ...
GATE EE 1997
The impulse response of a network is $$h\left( t \right) = 1$$ for $$0 \le t ...
GATE EE 1992

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