Question:
The impulse response of a continuous time system is given by \( h(t) = \delta(t - 1) + \delta(t - 3) \). The value of the step response at \( t = 2 \) is
The impulse response of a continuous time system is given by \( h(t) = \delta(t - 1) + \delta(t - 3) \). The value of the step response at \( t = 2 \) is
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The step response is the integral of the impulse response. If there are no jumps at a given time, the step response will be constant.
Updated On: May 5, 2025
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The Correct Option is C
Solution and Explanation
The step response \( s(t) \) is the integral of the impulse response \( h(t) \). In this case, the impulse response consists of two Dirac delta functions, \( \delta(t-1) \) and \( \delta(t-3) \). The step response will therefore have jumps at \( t = 1 \) and \( t = 3 \). Since we are asked for the step response at \( t = 2 \), which is between these two jumps, the step response is 0. Therefore, the correct answer is option (3).
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