Question

The impulse response of a continuous time system is given by h(t) = δ (t – 1) + δ (t – 3) . The value of the step response at t = 2 is

Answer 1

Correct Answer - Option 2 : 1

h (t) = δ (t – 1) + δ (t – 3)

From convolution property, we get

x(t) * δ (t – t₀) = x (t – t₀)

Now, for x(t) = u(t)

y(t) = u (t) * h (t)

= u (t) * [ δ (t – 1) + δ (t – 3)]

= u (t -1) + u (t - 3)

At t = 2,

y(2) = u (2 – 1) + u (2 – 3)

= u (1) + u (-1)

= 1 + 0

= 1