1
GATE EE 2009
+1
-0.3
A linear Time Invariant system with an impulse response $$h(t)$$ produces output $$y(t)$$ when input $$x(t)$$ is applied. When the input $$x\left( {t - \tau } \right)$$ is applied to a system with response $$h\left( {t - \tau } \right)$$, the output will be
A
$$y\left( t \right)$$
B
$$y\left( {2\left( {t - \tau } \right)} \right)$$
C
$$y\left( {t - \tau } \right)$$
D
$$y\left( {t - 2\tau } \right)$$
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
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 $$\omega$$
4
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
EXAM MAP
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