The impulse response of a system consists of two delta function

The impulse response of a system consists of two delta function as shown in the given figure.

The input to the system is a unit amplitude square pulse of one unit time duration. Which one of the following depicts the correct output?

Given that impulse response i.e.

h(t) = 1.δ(t) –	1	δ(t – 1)
	2

or H(s) = 1 –	1	e^–s
	2

Also, given x(t) = unit amplitude pulse of one unit time duration i.e.
or x(t) = u(t) – u(t – 1)

or X(s) =	1	-	1	e^–s
	s		s

Now, Y(s) = H(s).X(s)

or Y(s) =		1 -	1	e^–s			1	-	1	e^–s
			s				s		s

or Y(s) =	1	-	1	.	1	e^–s	+	1	1	e^–s
	s		2		s			2	s

or Y(s) =	1	-	1	- e^–s	-	1	1	e^–s	+	1	1	e^–2s
	s		s			2	s			2	s

Taking inverse Laplace transform

or y(t) = u(t) – u(t – 1) – 1/2 · u(t – 1) + 1/2 u(t – 2)
or y(t) = u(t) – 3/2 u(t – 1) + 1/2 u(t – 2)
Hence, alternative (B) is the correct choice.