1
GATE ECE 2003
+1
-0.3
Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of the system should be
A
$$4\,{e^{j4\pi f}}$$
B
$$2\,{e^{ - j8\pi f}}$$ v
C
$$4\,{e^{ - j4\pi f}}$$
D
$$2\,{e^{j8\pi f}}$$
2
GATE ECE 2002
+1
-0.3
Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to
A
$$X\left( {t - 12} \right)$$
B
$$X\left( {t + 12} \right)$$
C
$$X\left( {t - 2} \right)$$
D
$$X\left( {t + 2} \right)$$
3
GATE ECE 2001
+1
-0.3
The transfer function of a system is given by $$H\left( s \right) = {1 \over {{s^2}\left( {s - 2} \right)}}$$. The impulse response of the system is
A
$$\left( {{t^2} * {e^{ - 2t}}} \right)U\left( t \right)$$
B
$$\left( {t * {e^{2t}}} \right)U\left( t \right)$$
C
$$\left( {{t^2}{e^{ - 2t}}} \right)U\left( t \right)$$
D
$$\left( {t{e^{ - 2t}}} \right)U\left( t \right)$$
4
GATE ECE 2000
+1
-0.3
A system with an input x(t) and an output y(t) is described by the relation: y(t) = t x(t). This system is
A
linear and time-invariant.
B
linear and time-varying.
C
non-linear and time-invariant.
D
non-linear and time-varying.
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