For these threc questions, add your code into the pre$-$made skeleton ee$13135\_$lab$03\_$skeleton.m from Canvas. Include all code $($and functions$)$ in this one MATLAB $m-$file so that everything is published to a single PDF$.$ Use colormap $($gray$)$ to display images in grayscale.

$($a$)$ Write a new function $[xs,ys,zs]=$sample$(z,D)$; that inputs a high$-$resolution image $z$ and samples every $D$ pixels in both the horizontal and vertical direction. It outputs the sampled image zs and the new axes Fxs and ys$.$ 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 sample to the image $z$ in the skeleton code. Sample every D $=10$ pixcls in the horizontal and vertical directions. Use subplot to show side$-$by$-$side images before and after sampling.

$($c$)$ Apply sample to the image z two more times with two different $D$ values: $D=15$ an $D=20.$ Use subplot again to show the side$-$by$-$side for these two different sampling rates.

$($d$)$ Answer in your comments: How does aliasing manifest in the sampled sinusoidal image $($hint: aliasing distorts your signal$)?$ Relate this to your understanding of aliasing from class.

$($e$)$ 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 aliasing manifest in this image differently? $($Note: Submit your solution with the sinusoidal image, not this one.$)$