1
GATE ECE 2002
+2
-0.6
In Fig. m(t) = $$= {{2\sin 2\pi t} \over t}$$, $$s(t) = \cos \,200\pi t\,\,andn(t) = {{\sin 199\pi t} \over t}$$.

The output y(t) will be

A
$${{\sin 2\pi \,t} \over t}$$
B
$${{\sin 2\pi \,t} \over t}\, + {{\sin \pi \,t} \over t}\cos \,3\pi t$$
C
$${{\sin 2\pi \,t} \over t}\, + {{\sin 0.5\,\pi \,t} \over t}\cos \,1.5\pi t$$
D
$${{\sin 2\pi \,t} \over t}\, + {{\sin \pi \,t} \over t}\,\cos \,0.75\pi t\,\,$$
2
GATE ECE 2000
+2
-0.6
A system has a phase response given by $$\phi \,(\omega )$$ where $$\omega$$ is the angular frequency. The phase delay and group delay at $$\omega$$ = $${\omega _0}$$ are respectively given by
A
$$- {{\phi ({\omega _0})} \over {{\omega _0}}}, - {{d\phi (\omega )} \over {d\omega }}\left| {\omega = {\omega _0}} \right.$$
B
$$\phi ({\omega _0}), - {{{d^2}\phi (\omega )} \over {d{\omega ^2}}}\left| {\omega = {\omega _0}} \right.$$
C
$${{{\omega _0}} \over {\phi ({\omega _0})}}, - {{d\phi (\omega )} \over {d\omega }}\left| {\omega = {\omega _0}} \right.$$
D
$${\omega _0}\,\phi \,({\omega _0})\,,\,\int_{ - \infty }^{{\omega _0}} \phi (\lambda )\,d\,\lambda$$
3
GATE ECE 1999
+2
-0.6
The input to a matched filter is given by $$s(t) = \left\{ {\matrix{ {10\sin (2\pi \times {{10}^6}t),} & {0 < \left| t \right| < {{10}^{ - 4}}\sec } \cr 0 & {Otherwise} \cr } } \right.$$

The peak amplitude of the filter output is

A
10 Volts
B
5 Volts
C
10 millivolts
D
5 millivolts
4
GATE ECE 1993
Subjective
+2
-0
Sketch the waveform (with properly marked axes) at the output of a matched filter matched for a signal s(t), of duration T, given by $$s(t) = \left\{ {\matrix{ {A\,\,\,\,for} & {0 \le t < {2 \over 3}T} \cr {0\,\,\,\,\,\,for} & {{2 \over 3}T \le t < T} \cr } } \right.$$
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