GATE EC 2014 Set 1 — Question 29
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Question
A continuous, linear time-invariant filter has an impulse response described byWhen a constant input of value 5 is applied to this filter, the steady state output is _____.
Correct answer
44 to 46
Solution
The steady-state output of a continuous-time LTI system with impulse response for a constant input is given by:where is the DC gain of the system, which is the integral of the impulse response over all time:Given the impulse response:We calculate :Given the constant input , the steady-state output is:Thus, the steady-state output is 45, which falls within the specified range of 44 to 46.
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