Question

The impulse response h (t) of an LTI system is given by e^-2t.u(t) . What is the step response?

(a) y(t) = ^1⁄2 (1 – e^-2t) u (t)

(b) y(t) = ^1⁄2 (1 – e^-2t)

(c) y(t) = (1- e^-2t) u (t)

(d) y(t) = ^1⁄2 (e^-2t) u (t)

The question was posed to me in my homework.

This is a very interesting question from Convolution : Impulse Response Representation for LTI Systems topic in division Time Domain Representation for LTI Systems of Signals and Systems

Answer 1

Correct option is (a) y(t) = ^1⁄2 (1 – e^-2t) u (t)

The explanation is: Given x (t) = u (t) and h (t) = e^-2t.u(t). By using convolution integral

We get output y (t) as y(t) = ^1⁄2 (1 – e^-2t) u (t).