Question

Convolve the signals e^-2t  u(t), e^-3t  u(t). Determine the output?

(a) y(t) = (e^-2t – e^-3t)u(t)

(b) y(t) = (e^-2t – e^-3t)

(c) y(t) = (e^-3t – e^-2t)u(t)

(d) y(t) = (e^-t – e^-3t)u(t)

I got this question by my school principal while I was bunking the class.

Query is from Convolution : Impulse Response Representation for LTI Systems in portion Time Domain Representation for LTI Systems of Signals and Systems

Answer 1

The correct answer is (a) y(t) = (e^-2t – e^-3t)u(t)

To explain I would say: By solving the convolution integral

, we get output asy(t) = (e^-2t – e^-3t)u(t).