# Continuous Time Linear Invariant System · Signals and Systems · GATE ECE

Start Practice## Marks 1

GATE ECE 2017 Set 1

Consider the following statements for continuous-time linear time invariant (LTI) system.
I. There is no bounded input bounded output (BIBO) stable s...

GATE ECE 2017 Set 2

The input x(t) and the output y(t) of a continuous time system are related as
$$y\left( t \right) = \int\limits_{t - T}^t {x\left( u \right)du.} $$. ...

GATE ECE 2015 Set 3

The impulse response of an LTI system can be obtained by

GATE ECE 2015 Set 1

The result of the convolution $$x\left( { - t} \right) * \delta \left( { - t - {t_0}} \right)$$ is

GATE ECE 2013

Two system with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by...

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 2011

The differential equation $$100{{{d^2}y} \over {dt}} - 20{{dy} \over {dt}} + y = x\left( t \right)$$ describes a system with an input x(t) and output ...

GATE ECE 2008

The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal sys...

GATE ECE 2008

The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\exp \left( {\alpha t} \right)u\...

GATE ECE 2005

Which of the following can be impulse response of a causal system?

GATE ECE 2003

Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of the system should be

GATE ECE 2002

Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to

GATE ECE 2001

The transfer function of a system is given by $$H\left( s \right) = {1 \over {{s^2}\left( {s - 2} \right)}}$$. The impulse response of the system is

GATE ECE 2000

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 1998

The transfer function of a zero - order - hold system is

GATE ECE 1998

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e-...

GATE ECE 1995

The transfer function of a linear system is the

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) is

GATE ECE 1995

Non - minimum phase transfer function is defined as the transfer function

GATE ECE 1994

Indicate whether the following statement is TRUE/FALSE: Give reason for your answer.
If G(s) is a stable transfer function, then $$F\left( s \right)...

## Marks 2

GATE ECE 2017 Set 1

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 linear time invariant (LTI) filte...

GATE ECE 2017 Set 2

The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = $$\left[ {\sin (t)/\pi t} \right]u(t);$$ where u(t) i...

GATE ECE 2017 Set 2

Consider the parallel combination of two LTI systems shown in the figure.
The impulse responses of the systems are
$${h_1}(t) = 2\delta (t + 2)\, ...

GATE ECE 2017 Set 2

Consider an LTI system with magnitude response $$$\left| {H(f)} \right| = \left\{ {\matrix{
{1 - \,{{\left| f \right|} \over {20}},} & {\left| ...

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 the system is neither causal no...

GATE ECE 2015 Set 2

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}}\cos \left( {\sqrt 3 t - {\p...

GATE ECE 2013

The impulse response of a continuous time system is given by $$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of the step response at t = 2 is

GATE ECE 2012

The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\tau $$.
The system is

GATE ECE 2011

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 output is

GATE ECE 2010

A continuous time LTI system is described by $${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)} \over {dt}} + 4x(t)$$.
Assu...

GATE ECE 2009

Consider a system whose input x and output y are related by the equation
$$$y(t) = \int\limits_{ - \infty }^\infty {x(t - \tau )\,h(2\tau )\,d\tau }...

GATE ECE 2008

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 and s = - 4, and one simple zero...

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 system relations R1, R2, R3, ...

GATE ECE 2007

The frequency response of a linear, time-invariant system is given by H(f) = $${5 \over {1 + j10\pi f}}$$. The step response of the system is

GATE ECE 2006

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 impulse response of filter mat...

GATE ECE 2005

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 $$(t - {t_d} + T) + \,x\,(t - ...

GATE ECE 2004

A system described by the differential equation: $${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dt}} + 2y = x(t)$$ is initially at rest. For input x(t) =...

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). The convolved signal will be a
...

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 the output reaches 99% of its st...

GATE ECE 2001

The impulse response function of four linear system S1, S2, S3, S4 are given respectively by
$${h_1}$$(t), = 1;
$${h_2}$$(t), = U(t);
$${h_3}(t...

GATE ECE 2000

A linear time invariant system has an impulse response $${e^{2t}},\,\,t\, > \,0.$$ If the initial conditions are zero and the input is $${e^{3t}}$$...

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\left( t \right)\, - \,u\left(...

GATE ECE 1997

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 linear time invariant system
Li...

GATE ECE 1994

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}}} \over {d{x^2}}} + {a_2}y{{dy} \ove...

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 Transforms of the corresponding ...

GATE ECE 1991

An excitation is applied to a system at $$t = T$$ and its response is zero for $$ - \infty < t < T$$.
Such a system is a

GATE ECE 1990

The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{ - 2t}}u\left( t \right).$$ Th...

GATE ECE 1990

The impulse response and the excitation function of a linear time invariant casual system are shown in Fig. a and b respectively. The output of the sy...

GATE ECE 1988

The transfer function of a zero-order hold is

## Marks 5

GATE ECE 2002

A deterministic signal x(t) = $$\cos (2\pi t)$$ is passed through a differentiator as shown in
Figure.
(a) Determine the autocorrelation Rxx ($$\tau ...

GATE ECE 2000

For the linear, time-invariant system whose block diagram is shown in Fig.(a),
with input x(t) and output y(t).
(a) Find the transfer function.
(b) Fo...

GATE ECE 1997

Fig.1, shows the block diagram representation of a control system. The system in block A has an impulse response $${h_A}(t) = {e^{ - t}}\,u(t)$$. The ...

GATE ECE 1993

Consider the following interconnection of the three LTI systems (Fig.1). $${h_1}(t)$$ , $${h_2}(t)$$ and $${h_3}(t)$$ are the impulse responses of the...