1
GATE ECE 2017 Set 2
Numerical
+2
-0
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) is a unit step function. The system output y(t) as $$t \to \infty$$ is _____________________.
2
GATE ECE 2017 Set 2
Numerical
+2
-0
Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are

$${h_1}(t) = 2\delta (t + 2)\, - 3\delta (t + 1)$$
$${h_2}(t) = \delta (t - 2)$$
If the input x(t) is a unit step signal, then the energy of y(t) is__________________.
3
GATE ECE 2017 Set 2
Numerical
+2
-0
Consider an LTI system with magnitude response $$\left| {H(f)} \right| = \left\{ {\matrix{ {1 - \,{{\left| f \right|} \over {20}},} & {\left| f \right| \le 20} \cr {0,} & {\left| f \right| > 20} \cr } } \right.$$\$ and phase response Arg[H(f)]= - 2f.
If the input to the system is $$x(t) = 8\cos \left( {20\pi t + \,{\pi \over 4}} \right) + \,16\sin \left( {40\pi t + {\pi \over 8}} \right) + 24\,\cos \left( {80\pi t + {\pi \over {16}}} \right)$$
Then the average power of the output signal y(t) is_____________.
4
GATE ECE 2015 Set 2
+2
-0.6
The output of a standrad second-order system for a unit step input is given as $$y(t) = 1 - {2 \over {\sqrt 3 }}{e^{ - t}}\cos \left( {\sqrt 3 t - {\pi \over 6}} \right)$$.

The transfer function of the system is

A
$${2 \over {(s + 2)(s + \sqrt 3) }}$$
B
$${1 \over {{s^2} + 2s + 1}}$$
C
$${3 \over {{s^2} + 2s + 3}}$$
D
$${3 \over {{s^2} + 2s + 4}}$$
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Communications
Electromagnetics
General Aptitude
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