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The unit impulse response of a system in given as f (t) = – 4e– t + 6e– 2t. The response of the same system for t ≥ 0 is equal to—
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- – 3e– 2t + 4e– t + 1
- – 3e– 2t + 4e– t – 1
- – 3e– 2t – 4e– t – 1
- – 3e– 2t + 4e– t – 1
- – 3e– 2t + 4e– t + 1
Correct Option: B
As we know that the unit step response is the integral of unit impulse response, this is due to the fact that a function which is defined for t ≥ 0 is a unit step function.
∴ Unit step response = ∫ t 0 (– 4e– t + 6e–2t) dt
= [ 4e– t – 6 × 1/2 e– 2t]t0
= – 3e– 2t + 4e– t – 1
