GATE EE 2008 | Linear Time Invariant Systems Question 34 | Signals and Systems

GATE EE 2008

MCQ (Single Correct Answer)

-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?

Statement $$\left( {\rm I} \right)$$ is correct and Statement $$\left( {\rm II} \right)$$ is wrong

Statement $$\left( {\rm II} \right)$$ is correct and Statement $$\left( {\rm I} \right)$$ is wrong

Both Statement $$\left( {\rm I} \right)$$ and Statement $$\left( {\rm II} \right)$$ are wrong

Both Statement $$\left( {\rm I} \right)$$ and Statement $$\left( {\rm II} \right)$$ are correct

GATE EE 2007

MCQ (Single Correct Answer)

-0.3

Let a signal $${a_1}\,\sin \left( {{\omega _1}t + {\phi _1}} \right)$$ be applied to a stable linear time-invariant system. Let the corresponding steady state output be represented as $${a_2}F\left( {{\omega _2}t + {\phi _2}} \right).$$ Then which of the following statements is true?

$$F$$ is not necessarily a ''sine'' or ''cosine'' function but must be periodic with $${\omega _1} = {\omega _2}.$$

$$F$$ must be a ''sine'' or ''cosine'' function with $${a_1} = {a_2}.$$

$$F$$ must be a ''sine'' function with $${\omega _1} = {\omega _2}.$$ and $${\phi _1} = {\phi _2}.$$

$$F$$ must be a ''sine'' or ''cosine'' function with $${\omega _1} = {\omega _2}.$$

GATE EE 2002

MCQ (Single Correct Answer)

-0.3

$$s(t)$$ is step response and $$h(t)$$ is impulse response of a system. Its response $$y(t)$$ for any input $$u(t)$$ is given by

$${d \over {d\,t}}\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

$$\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

$$\int\limits_0^t {\int\limits_0^\tau s \left( {t - {\tau _1}} \right)\,u\left( {{\tau _1}} \right)\,d{\tau _1}} \,d\tau $$

$${d \over {d\,t}}\int\limits_0^t h \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

GATE EE 1994

Subjective

-0

If $$f(t)$$ is the step-response of a linear time-invariant system, then its impulse response is given by ___________

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