Using the Fourier transform, find out output to each of the following input signals.

$i) \space\space x(t) = e^{-t} u(t) \\ ii) \space x(t) = u(t)$

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 10

Year : DEC 2014

Given

$\dfrac {dy(t)}{dt}+2y=x(t)$

By Laplace transform,

$s\space y(s) + 2 y(s) = x (s) \\ y (s) (s+2) = x (s) \\ \dfrac {y(s)}{x(s)} = \dfrac 1{(s+2)} \\ H(s) = \dfrac 1{(s+2)} \\ (i)\space x(t) = e^{-t} u(t) \\ X (s) =\dfrac 1{(s+1)} $

By Laplace transform,

$Y (s) = …