The response h(t) of a linear time invariant system to an

The response h(t) of a linear time invariant system to an impulse δ(t), under initially relaxed condition is h(t) = e^–t + e^–2t. The response of this system for a unit step input u(t) is

1. u(t) + e^–t + e^–2t
2. (e^–t + e^–2t) u(t)
3. (1.5 – e^–t – 0.5e^–2t) u(t)
4. e^–t δ(t) + e^–2t u(t)

Impulse response, H(s) = α h(t)

=	1	+	1
	(s + 1)		(s+ 2)

Step response = L^-1		1	+	1
		(s + 1)		(s+ 2)

= L^-1			1	-	1		+		0.5	-	0.5
			s		s + 2				s		(s + 2)

= (1 – e^–t + 0.5 – 0.5e^–2t)u(t)
= (1.5 – e^–t – 0.5e^–2t)u(t)