$($DSP$($Digital signal proccess module$))($SOLVE IN PAPER $,$INCLUDE ALL STEPS$)$

$1$ a$)$ A function $g[n]$ is defined by

$x[n]=\{\begin{array}{cc}-2,& n-4\\ n,& -4n1\\ \frac{4}{n},& 1n\end{array}$

Calculate the signal $x[4-n]$ and $x[\frac{n}{3}]$ by direct method, represent the signal in sequence form and sketch the signal.

b$)$ A casual and stable LTI system has its input $x[n]$ and output $y[n]$ related by the linear constant coefficient difference equation,

$y[n]+{\displaystyle \underset{k=1}{\overset{10}{}}}{}_{k}y[n-k]=x[n]+x[n-1]$

Let $h[n]$ be the impulse response. Determine $($i$)h[0]$; $($ii$){}_1$ in terms of $h[0]$ and $h[1].$