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

• A. 2
• B. 3
• C. 0
• D. 1

Hint:

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.

Answer 1

The Correct Option is C

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).