1
GATE ECE 2004
+2
-0.6
A rectangular pulse train s(t) as shown in Fig.1 is convolved with the signal $${\cos ^2}$$ ($$4\pi \,{10^{3\,}}$$t). The convolved signal will be a
A
DC
B
12 kHz sinusoid
C
8 kHz sinusoid
D
14 kHz sinusoid
2
GATE ECE 2004
+2
-0.6
A causal system having the transfer function H(s) = $${1 \over {s + 2}}$$, is excited with 10 u(t). The time at which the output reaches 99% of its steady state value is
A
2.7 sec
B
2.5 sec
C
2.3 sec
D
2.1 sec
3
GATE ECE 2001
+2
-0.6
The impulse response function of four linear system S1, S2, S3, S4 are given respectively by

$${h_1}$$(t), = 1;

$${h_2}$$(t), = U(t);

$${h_3}(t)\, = \,{{U(t)} \over {t + 1}}$$;

$${h_4}(t)\, = {e^{ - 3t}}U(t)$$ ,

where U (t) is the unit step function. Which of these system is time invariant, causal, and stable?

A
SI
B
S2
C
S3
D
S4
4
GATE ECE 2000
+2
-0.6
A linear time invariant system has an impulse response $${e^{2t}},\,\,t\, > \,0.$$ If the initial conditions are zero and the input is $${e^{3t}}$$, the output for $$t\, > \,0$$ is
A
$${e^{3t}} - {e^{2t}}$$
B
$${e^{5t}}$$
C
$${e^{3t}} + {e^{2t}}$$
D
None of the above
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