Given two continuous time signals x(t) = e–t and y(t)

Home » Signals and Systems » Signals and systems electrical engineering miscellaneous » Question

Given two continuous time signals x(t) = e^–t and y(t) = e^–2t which exist for t > 0, the convolution z(t) = x(t) * y(t) is

1. e^–t – e^–2t
2. e^–3t
3. e^+t
4. e^–t + e^–2t

Correct Option: A

z(t) = x(t) * y(t), Taking laplace transform both side
Z(s) = X(s).Y(s)

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

L^–1{z(s)} = z(t) = e^–t – e^–2t