for the system shown below:

$($a$)$ sketch the spectra W$($e$^$jw$),$ V$($e$^$jw$),$ Z$($e$^$jw$)$ and Y$($e$^$jw$)$ in the range $[-\backslash$pi $,\backslash$pi $].$

$($b$)$ If the sampling period of x$($n$)$ is T$=1$ ms$,$ find the sampling period pf w$($n$),$ v$($n$),$ z$($n$)$ and y$($n$).$

$($c$)$ Develop a new system that changes the sampling period of x$($n$)$ from T$=1$ to T$\text{'}=1\mathrm{.}2$ ms perfectly with no aliasing.