Problem $4$: $(15$ points$)$

An LTI system is described by the difference equation

$y[n]=3x[n]-4x[n-1]+2x[n-2]$

Question $4\mathrm{.}1$:

When the input to this system is

$x[n]=\{\begin{array}{cc}0,& n<mn\; id="EditorElement\_81107">0</mn>\\ 4,& n=0,1,& 2\\ 7-n,& n=3,& 4\\ 1,& n5\end{array}$

Compute the values of $y[n]$ over the range $0n10.$

Question $4\mathrm{.}2$:

For the values in $4\mathrm{.}1,$ plot both $x[n]$ and $y[n]($on two separate plots$).$

Question $4\mathrm{.}3$:

Determine the response of this system to a unit impulse input. That is$,$ find the output

$y[n]=h[n]$ when the input is $x[n]=[n].$ Plot $h[n]$ as a function of $n.$