$($a$)$ Crate a new function $[xz,yz,zz]=$ addzeros$($zaas$,$ U$)$ which inputs an antialiased and sampled image zaas. The function outputs the image $zz,$ which contains $U$ zero$-$valued pixels inserted between each pixel from zaas, both horizontally and vertically. It also outputs the new axes $xz$ and $yz.$ Use the function image$\_$system$1$ from Question #$1$ as a guide $($hint: most of the information you need is in this function$).$ Include this new function at the end of the skeleton $m$ file.

$($b$)$ Apply addzeros to your x$64$ anti$-$aliased and sampled image z $64$s in Question #$3$ to obtain zz$.$ Add U$=12$ zeros between each pixel. Use subplot to show side$-$by$-$side images before and after applying the function.

$($c$)$ Your function antialias can be an anti$-$aliasing filter or an interpolation filter! Therefore, apply antialias to your image$-$with$-$zeros zz to obtain zzaa. Use subplot to show side$-$by$-$side images before and after applying the interpolation filter.

$($d$)$ Use a for$-$loop to apply the filter to zz $64$ times to obtain zz$64.$ This results in a $"$x$64$ interpolation filter." Use subplot to show side$-$by$-$side the original high$-$resolution image $z$ and the new interpolated image zz$64.1$

$($e$)$ Answer in your comments: What does the interpolation filter do to the image? Why is this uscful in real$-$world applications?