If the unit step response of a network is (1

If the unit step response of a network is (1 – e^–αt), then its unit impulse response will be—

In order to calculate the unit impulse response first we will obtain transfer function i.e. H (S)
given y (t) = 1 – e^{– α t}

	Y (s) =	1	-	1	=	α
		s		s² (s + α)		s(s + α)

we know that

H (s) =	Y (s)
	X (s)

X (t) = u (t)

X (s) =	1
	s

	so, H (s) =	α	=	α
		S(s + α) 1 / S		s + α

Now, according to the question
x (t) = δ (t)
so, X (s)=1
Y (t)=?
Now, Y (s) = H (S) X (S)

or Y (S) =	α	. 1
	s + α

or Y (S) =	α
	s + α

or Y (t) = α. e^{– αt}

1	e^–t/α
α

1
αe^–t/α