1
GATE ECE 2007
+2
-0.6
The 3 - dB bandwidth of the low - pass signal $${e^{ - 1}}$$ u(t), where u(t) is the unit step function, is given by
A
$${1 \over {2\pi }}Hz$$
B
$${1 \over {2\pi }}\sqrt {\sqrt 2 - 1\,} Hz$$
C
$$\infty$$
D
1 Hz
2
GATE ECE 2004
+2
-0.6
A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is
A
$$- {90^ \circ }$$
B
$${0^ \circ }$$
C
$${90^ \circ }$$
D
$$- {180^ \circ }$$
3
GATE ECE 2004
+2
-0.6
Consider the signal x(t) shown in Fig. Let h(t) denote the impulse response of the filter matched to x(t), with h(t) being non-zero only in the interval 0 to 4 sec. The slope of h(t) in the interval 3 < t < 4 sec is
A
$$1/2\,{\sec ^{ - 1}}$$
B
$$-1\,{\sec ^{ - 1}}$$
C
$$-1/2\,{\sec ^{ - 1}}$$
D
$$1\,{\sec ^{ - 1}}$$
4
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 $${t_g}$$ (f) be the group delay function of the given RC-LPF and $${f_2}$$ = 100 Hz. Then $${t_g}$$$${(f_2)}$$ in ms, is

A
0.717
B
7.17
C
71.7
D
4.505
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