1
GATE ECE 1998
+1
-0.3
The transfer function of a zero - order - hold system is
A
$$\left( {1/s} \right)\left( {1 + {e^{ - sT}}} \right)$$v
B
$$\left( {1/s} \right)\left( {1 - {e^{ - sT}}} \right)$$
C
$$1 - \left( {1/s} \right){e^{ - sT}}$$
D
$$1 + \left( {1/s} \right){e^{ - sT}}$$
2
GATE ECE 1998
+1
-0.3
The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e-at u(t), a>0 will be
A
a e-at
B
(1/a) (1 - e-at)
C
a(1 - e-at)
D
1 - e-at)
3
GATE ECE 1995
+1
-0.3
The transfer function of a linear system is the
A
ratio of the output, v0(t), and input, vi(t).
B
ratio of the derivatives of the output and the input.
C
ratio of the Laplace transform of the output and that of the input with all initial conditions zeros.
D
none of these.
4
GATE ECE 1995
+1
-0.3
Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is
A
$$\int\limits_0^t {h\left( \tau \right)} u\left( {t - \tau } \right)d\tau \,\,\,\,\,\,$$
B
$${d \over {dt}}\int\limits_0^t {h\left( \tau \right)u\left( {t - \tau } \right)d\tau \,\,\,\,\,}$$
C
$${\int\limits_0^t {\left[ {\int\limits_0^t {h\left( \tau \right)u\left( {t - \tau } \right)d\tau } } \right]dt\,\,\,\,\,\,} }$$
D
$${\int\limits_0^t {{h^2}\left( \tau \right)u\left( {t - \tau } \right)d\tau } }$$
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