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

The convolution of a signal is given by:

y(t) = h(t) * x(t)

Given, h(t) = δ(t-1) + δ(t-3)

and x(t) = u(t) (Step Input)

y(t) = (δ(t-1) +δ(t-3)) * u(t)

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

The required value of y(2) is:

y(2) = u(2-1) + u(2-3) = u(1) + u(-1)

Since u(-1) = 0

∴ y(2) = u(1) = 1