1
GATE ECE 2003
+2
-0.6
The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0 $$k\Omega$$ and C = 1.0 $$\mu F$$.

Let H(t) denote the frequency response of the RC-LPF. Let $${f_1}$$ be the highest frequency such that $$0 \le \left| f \right| \le {f_1},{{\left| {H({f_1})} \right|} \over {H(0)}} \ge 0.95$$. Then $${f_1}$$ (in Hz) is

A
327.8
B
163.9
C
52.2
D
104.4
2
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
$${{\sin 2\pi \,t} \over t}\, + {{\sin \pi \,t} \over t}\,\cos \,0.75\pi t\,\,$$
3
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
$${\omega _0}\,\phi \,({\omega _0})\,,\,\int_{ - \infty }^{{\omega _0}} \phi (\lambda )\,d\,\lambda$$
4
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
EXAM MAP
Medical
NEET