The unit impulse response of a linear time invariant system

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The unit impulse response of a linear time invariant system is unit step function u(t). For t > 0, the response of the system to an excitation e^{– at} u(t), a > 0 will be

1. ae^{– at}
2. 1 (1 - ae^-at)
  a
3. a(1 – ae^{– at})
4. 1 – ae^{– at}

Correct Option: B

Given: h(t) = u(t)
x(t) = e^–at u(t)

∴ Y(s) = X(s) H(s) =	1	.	1	=	1		1	-	1
	(s + a)		s		a		s		s + a

y(t) = 1/a (1 – e^{– at}) u(t)