$($a$)$ Create a new function zaa $=$antialias$(z)$; which inputs a high$-$resolution image $z$ and outputs high$-$resolution anti$-$aliased image zaa. Use the function image$\_$system$2$ from Question #$1$ as a guide. Design the anti$-$aliasing system to compute each point of $z_{aa}[x,y]$ according to the $2D$ difference equation $($i$.$e$.,$ a discrete$-$time system$)$

Include this new function at the end of the skeleton $.m$ file.

$($b$)$ Apply antialias to your high$-$resolution image $z$ to obtain zaa. Use subplot to show side$-$by$-$side images before and after applying the anti$-$aliasing filter.

$($c$)$ Use a for$-$loop to apply the anti$-$aliasing filter to the high$-$resolution image z $64$ times. This applies a $"$x$64$ anti$-$aliasing filter" to get $z64.$ Use subplot to show side$-$by$-$side images with and without the $x64$ anti$-$aliasing filter.

$($d$)$ Use your sample function to sample every $D=12$ pixels of the anti$-$aliased image zaa to obtain output zaas and to the $64x$ anti$-$aliased image $z64$ to obtain output $z64s.$ Use subplot to show side$-$by$-$side sampled images with $1x$ anti$-$aliasing and $64x$ anti$-$aliasing.

$($e$)$ Answer in your comments: What does the anti$-$aliasing filter do to the image? How does this reduce aliasing? Why is this useful in real$-$world applications?

$($f$)$ Answer in your comments: Temporarily uncomment the imread line from the skeleton code to load a "natural" image. Run your code with this. How does the anti$-$aliasing affect this image differently? $($Note: Submit your solution with the sinusoidal image, not this one.$)$

Guide for image$\_$system$2$ is: function$[$za$]=$ image$\_$system$2($z$,$ Sx$,$ Sy$)$