When the input to an LTI system is the pulse $p(t) = 2I_{[-1,1]}(t)$, the output is given
by $g(t) = tI_{[0,1)}(t) + I_{[1,2]}(t) + (3 - t)I_{(2,3]}(t)$.
(a) Sketch $g(t)$.
(b) Can you find the system output when the input is $x(t) = I_{[0,1]}(t) - I_{[2,3]}(t)$. If so, find and
sketch the output. If not, say why not.
(c) Can you find the system output when the input is $x(t) = I_{[0,1]}(t)$. If so, find and sketch the
output. If not, say why not.