1
GATE ECE 2008
+1
-0.3
The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\exp \left( {\alpha t} \right)u\left( t \right)\,\,\, + \,\,\exp \left( {\beta t} \right)u\left( { - t} \right),$$ where u(t) denotes the unit step function, and $$\alpha$$ and $$\beta$$ are real constants. This system is stable if
A
$$\alpha$$ is positive and $$\beta$$ is positive
B
$$\alpha$$ is negative and $$\beta$$ is negative
C
$$\alpha$$ is positive and $$\beta$$ is negative
D
$$\alpha$$ is negative and $$\beta$$ is positive
2
GATE ECE 2008
+1
-0.3
The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system?
A
$$y\left( t \right) = x\left( {t - 2} \right) + x\left( {t + 4} \right)$$
B
$$y\left( t \right) = \left( {t - 4} \right)x\left( {t + 1} \right)$$
C
$$y\left( t \right) = \left( {t + 4} \right)x\left( {t - 1} \right)$$
D
$$y\left( t \right) = \left( {t + 5} \right)x\left( {t + 5} \right)$$
3
GATE ECE 2005
+1
-0.3
Which of the following can be impulse response of a causal system?
A
B
C
D
4
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
$$2\,{e^{j8\pi f}}$$
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