GATE ECE
Signals and Systems
Continuous Time Linear Invariant System
Previous Years Questions

## Marks 1

Consider the following statements for continuous-time linear time invariant (LTI) system. I. There is no bounded input bounded output (BIBO) stable s...
The input x(t) and the output y(t) of a continuous time system are related as $$y\left( t \right) = \int\limits_{t - T}^t {x\left( u \right)du.}$$. ...
The impulse response of an LTI system can be obtained by
The result of the convolution $$x\left( { - t} \right) * \delta \left( { - t - {t_0}} \right)$$ is
The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is
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...
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 ...
The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\exp \left( {\alpha t} \right)u\... The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal sys... Which of the following can be impulse response of a causal system? Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of the system should be Convolution of x(t + 5) with impulse function$$\delta \left( {t\, - \,7} \right)$$is equal to The transfer function of a system is given by$$H\left( s \right) = {1 \over {{s^2}\left( {s - 2} \right)}}$$. The impulse response of the system is A system with an input x(t) and an output y(t) is described by the relation: y(t) = t x(t). This system is The transfer function of a zero - order - hold system is The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e-... The transfer function of a linear system is the Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is Non - minimum phase transfer function is defined as the transfer function Indicate whether the following statement is TRUE/FALSE: Give reason for your answer. If G(s) is a stable transfer function, then$$F\left( s \right)...

## Marks 2

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...
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...
Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are $${h_1}(t) = 2\delta (t + 2)\, ... Consider an LTI system with magnitude response$$$\left| {H(f)} \right| = \left\{ {\matrix{ {1 - \,{{\left| f \right|} \over {20}},} & {\left| ... The output of a standrad second-order system for a unit step input is given as $$y(t) = 1 - {2 \over {\sqrt 3 }}{e^{ - t}}\cos \left( {\sqrt 3 t - {\p... Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If the system is neither causal no... The impulse response of a continuous time system is given by$$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of the step response at t = 2 is The input x(t) and output y(t) of a system are related as y(t) =$$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\tau $$. The system is An input x(t) = exp( -2t) u(t) +$$\delta $$(t-6) is applied to an LTI system with impulse response h(t) = u(t). The output is A continuous time LTI system is described by$${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)} \over {dt}} + 4x(t)$$. Assu... Consider a system whose input x and output y are related by the equation$$$y(t) = \int\limits_{ - \infty }^\infty {x(t - \tau )\,h(2\tau )\,d\tau }...
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...
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, ...
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
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...
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 $$(t - {t_d} + T) + \,x\,(t - ... A system described by the differential equation:$${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dt}} + 2y = x(t)$$is initially at rest. For input x(t) =... A rectangular pulse train s(t) as shown in Fig.1 is convolved with the signal$${\cos ^2}$$($$4\pi \,{10^{3\,}}$$t). The convolved signal will be a ... A causal system having the transfer function H(s) =$${1 \over {s + 2}}$$, is excited with 10 u(t). The time at which the output reaches 99% of its st... The impulse response function of four linear system S1, S2, S3, S4 are given respectively by$${h_1}$$(t), = 1;$${h_2}$$(t), = U(t);$${h_3}(t...
A linear time invariant system has an impulse response $${e^{2t}},\,\,t\, > \,0.$$ If the initial conditions are zero and the input is $${e^{3t}}$$...
Let u(t) be the unit step function. Which of the waveforms in Fig.(a) -(d) corresponds to the convolution of $$\left[ {u\left( t \right)\, - \,u\left(... Match each of the items 1, 2 on the left with the most appropriate item A, B, C or D on the right. In the case of a linear time invariant system Li... Match each of the items A, B and C with an appropriate item from 1, 2, 3, 4 and 5. List - 1 (A)$${a_1}{{{d^{2y}}} \over {d{x^2}}} + {a_2}y{{dy} \ove...
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 ...
An excitation is applied to a system at $$t = T$$ and its response is zero for $$- \infty < t < T$$. Such a system is a
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...
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...
The transfer function of a zero-order hold is

## Marks 5

A deterministic signal x(t) = $$\cos (2\pi t)$$ is passed through a differentiator as shown in Figure. (a) Determine the autocorrelation Rxx ($$\tau ... For the linear, time-invariant system whose block diagram is shown in Fig.(a), with input x(t) and output y(t). (a) Find the transfer function. (b) Fo... Fig.1, shows the block diagram representation of a control system. The system in block A has an impulse response$${h_A}(t) = {e^{ - t}}\,u(t)$$. The ... Consider the following interconnection of the three LTI systems (Fig.1).$${h_1}(t)$$,$${h_2}(t)$$and$${h_3}(t) are the impulse responses of the...
EXAM MAP
Joint Entrance Examination