$($DSP$($digital signal proccess$))($solve with all steps and skietch the signal in part $($a$))$

a$)$ A digital signal $x(n)$ is defined as $7)].$ Calculate the signal $y(n)=a(-2n+3)$ by direct method, represent the signal in sequence form and sketch the signal.

b$)$ A discrete LTI system has an unit sample response of $h(n)=5(\frac{1}{2}{)}^{n}u(n)-4(\frac{1}{3}{)}^{n-1}u(n)$ and the input to the system is $x(n)=\{\begin{array}{cc}0\mathrm{.}5,& n0\\ 0& \text{e}\text{l}\text{s}\text{e}& \end{array}.$

Determine the output response $y(n)$ of the system using convolution sum.