1
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
$${e^{ - 2\pi {f^2}}}$$
2
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
3
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
$${{\sqrt 3 \,} \over 2}$$
4
GATE ECE 2006
+1
-0.3
In the system shown below,
x(t) = (sint)u(t). In steady-state, the response y(t) will be
A
$${1 \over {\sqrt 2 }}\sin \left( {t - {\pi \over 4}} \right)$$
B
$${1 \over {\sqrt 2 }}\sin \left( {t + {\pi \over 4}} \right)$$
C
$${1 \over {\sqrt 2 }}{e^{ - t}}\sin (t)$$
D
$$\sin (t) - \cos (t)$$
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