1
GATE EE 2007
MCQ (Single Correct Answer)
+1
-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?
A
$$F$$ is not necessarily a ''sine'' or ''cosine'' function but must be periodic with $${\omega _1} = {\omega _2}.$$
B
$$F$$ must be a ''sine'' or ''cosine'' function with $${a_1} = {a_2}.$$
C
$$F$$ must be a ''sine'' function with $${\omega _1} = {\omega _2}.$$ and $${\phi _1} = {\phi _2}.$$
D
$$F$$ must be a ''sine'' or ''cosine'' function with $${\omega _1} = {\omega _2}.$$
2
GATE EE 2002
MCQ (Single Correct Answer)
+1
-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
A
$${d \over {d\,t}}\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$
B
$$\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$
C
$$\int\limits_0^t {\int\limits_0^\tau s \left( {t - {\tau _1}} \right)\,u\left( {{\tau _1}} \right)\,d{\tau _1}} \,d\tau $$
D
$${d \over {d\,t}}\int\limits_0^t h \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$
3
GATE EE 1994
Subjective
+1
-0
If $$f(t)$$ is the step-response of a linear time-invariant system, then its impulse response is given by ___________
4
GATE EE 1993
MCQ (Single Correct Answer)
+1
-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
A
$${d \over {d\,t}}\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$
B
$$\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$
C
$$\int\limits_0^t {\int\limits_0^\tau s \left( {t - {\tau _1}} \right)\,u\left( {{\tau _1}} \right)\,d{\tau _1}} \,d\tau $$
D
$${d \over {d\,t}}\int\limits_0^t h \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$
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