1
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
$${d \over {d\,t}}\int\limits_0^t h \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$
2
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 ___________
3
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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