The impulse response g(t) of a system, G, is as shown in

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The impulse response g(t) of a system, G, is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of Gas shown in Figure (b)?

1. 2
  3
2. 3
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3. 4
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4. 1

Correct Option: D

Impulse Response,
H(s) = G(s) · G(s) ...(i)
Taking Inverse Laplace transform both sides,
h(t) = g(t) * g(t) ...(ii)
where g(t) = u(t) – u(t – 1)
h(t) =
= u(t) * u(t) – u(t) * u(t – 1) – u(t) * u (t – 1) + u(t – 1) * u(t – 1)
= r(t) – r(t – 1) – r(t – 1) + r(t – 2)
h(t) = r(t) – 2r (t – 1) + r(t – 2)

Therefore, Max^m value of Impulse Response
h(t)_max = 1