1
GATE EE 2008
+1
-0.3
A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Given $$K$$ and $$\phi$$ are constants, the output of the system will be of the form $$K{e^{ - \beta t}}\,\sin \,\left( {\upsilon t + \phi } \right)$$ where
A
$$\beta$$ need not be equal to $$\alpha$$ but $$\upsilon$$ equal to
B
$$\upsilon$$ need not be equal to $$\omega$$ but $$\beta$$ equal to $$\alpha$$
C
$$\beta$$ equal to $$\alpha$$ and $$\upsilon$$ equal to $$\omega$$
D
$$\beta$$ need not be equal to $$\alpha$$ and $$\upsilon$$ need not be equal to $$\omega$$
2
GATE EE 2008
+1
-0.3
A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Given $$K$$ and $$\phi$$ are constants, the output of the system will be of the form $$K{e^{ - \beta t}}\,\sin \,\left( {\upsilon t + \phi } \right)$$ where
A
$$\beta$$ need not be equal to $$\alpha$$ but $$\upsilon$$ equal to
B
$$\upsilon$$ need not be equal to $$\omega$$ but $$\beta$$ equal to $$\alpha$$
C
$$\beta$$ equal to $$\alpha$$ and $$\upsilon$$ equal to $$\omega$$
D
$$\beta$$ need not be equal to $$\alpha$$ and $$\upsilon$$ need not be equal to $$\omega$$
3
GATE EE 2008
+1
-0.3
The impulse response of a causal linear time-invariant system is given as $$h(t)$$. Now consider the following two statements:

Statement-$$\left( {\rm I} \right)$$: Principle of superposition holds
Statement-$$\left( {\rm II} \right)$$: $$h\left( t \right) = 0$$ for $$t < 0$$

Which one of the following statements is correct?

A
Statement $$\left( {\rm I} \right)$$ is correct and Statement $$\left( {\rm II} \right)$$ is wrong
B
Statement $$\left( {\rm II} \right)$$ is correct and Statement $$\left( {\rm I} \right)$$ is wrong
C
Both Statement $$\left( {\rm I} \right)$$ and Statement $$\left( {\rm II} \right)$$ are wrong
D
Both Statement $$\left( {\rm I} \right)$$ and Statement $$\left( {\rm II} \right)$$ are correct
4
GATE EE 2008
+2
-0.6
A signal $$x\left( t \right) = \sin c\left( {\alpha t} \right)$$ where $$\alpha$$ is a real constant $$\left( {\sin \,c\left( x \right) = {{\sin \left( {\pi x} \right)} \over {\pi x}}} \right)$$ is the input to a linear Time invariant system whose impulse response $$h\left( t \right) = \sin c\left( {\beta t} \right)$$ where $$\beta$$ is a real constant. If $$\min \left( {\alpha ,\,\,\beta } \right)$$ denotes the minimum of $$\alpha$$ and $$\beta$$, and similarly $$\max \left( {\alpha ,\,\,\beta } \right)$$ denotes the maximum of $$\alpha$$ and $$\beta$$, and $$K$$ is a constant, which one of the following statements is true about the output of the system?
A
It will be of the form $$K$$ $$sinc$$$$\left( {\gamma t} \right)$$ where $$\gamma = \,\min \left( {\alpha ,\,\,\beta } \right)$$
B
It will be of the form $$K$$ $$sinc$$$$\left( {\gamma t} \right)$$ where $$\gamma = \,\max \left( {\alpha ,\,\,\beta } \right)$$
C
It will be of the form $$K$$ $$\sin c\left( {\alpha t} \right)$$
D
It cannot be a $$sinc$$ type of signal
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