1
GATE ECE 2013
+1
-0.3
Assuming zero initial condition, the response y (t) of the system given below to a unit step input u(t) is
A
u (t)
B
tu (t)
C
$${{{t^2}} \over 2}(t)$$
D
$${e^{ - t}}u(t)$$
2
GATE ECE 2013
+1
-0.3
Let g(t) = $${e^{ - \pi {t^2}}}$$, and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the output is
A
$${e^{ - \pi {f^2}}}\,$$
B
$${e^{ - \pi {f^2}/2}}\,$$
C
$${e^{ - \pi \left| f \right|}}$$
D
$${e^{ - 2\pi {f^2}}}$$
3
GATE ECE 2010
+1
-0.3
Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is
A
B
C
D
4
GATE ECE 2010
+1
-0.3
A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}}\,\,$$ has an output
$$y(t) = \cos \left( {2t - {\pi \over 3}} \right)\,$$ for the input signal
$$x(t) = p\cos \left( {2t - {\pi \over 2}} \right)$$. Then, the system parameter 'p' is
A
$$\sqrt 3$$
B
$$\,{2 \over {\sqrt 3 \,}}$$
C
1
D
$${{\sqrt 3 \,} \over 2}$$
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