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EEL 3135 – Lab #03 solution

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EEL 3135 – Lab #03
Submission Notes
• Your laboratory solutions should be submitted on Canvas as a single published MATLAB PDF.
• Use the provided skeleton code as the basis for your solutions (easier for you and the graders).
Question #1: (Image Processing) Download eel3135_lab03_comment.m from Canvas, replace each of the corresponding comments with the corresponding descriptions. This is designed
to show you how to work with images in MATLAB.
Note: You should run the code to help you understand how it works and help you write your
comments. You will use elements of this MATLAB code for the rest of the lab assignment.

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Full Name:
EEL 3135 – Lab #03
Submission Notes
• Your laboratory solutions should be submitted on Canvas as a single published MATLAB PDF.
• Use the provided skeleton code as the basis for your solutions (easier for you and the graders).
Question #1: (Image Processing) Download eel3135_lab03_comment.m from Canvas, replace each of the corresponding comments with the corresponding descriptions. This is designed
to show you how to work with images in MATLAB.
Note: You should run the code to help you understand how it works and help you write your
comments. You will use elements of this MATLAB code for the rest of the lab assignment.
Question #2: (Sampling) The following three questions handle three important processes in
image processing: (1) sampling (converting a large image to a small image), (2) anti-aliasing (reducing distortions from aliasing), and (3) interpolation (converting a small image to a large image).
For these three questions, add your code into the pre-made skeleton eel3135_lab03_skeleton.m
from Canvas. Include all code (and functions) in this one MATLAB m-file so that everything is
published to a single PDF.
(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 xs and ys. Use the function image_system1 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 = 8 pixels 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, first with D = 16 and then D = 24. 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 image (hint:
aliasing distorts your signal)? Relate this to your understanding of aliasing from class.
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Question #3: (Anti-Aliasing)
(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_system2 from
Question #1 as a guide. Design the anti-aliasing system to compute each point of zaa[x, y]
(i.e., the mathematical notation for zaa) according to the two-dimensional difference equation
(i.e., a discrete-time system)
zaa[x, y] = (1/2)z[x, y] + (1/8)(z[x − 1, y] + z[x + 1, y] + z[x, y − 1] + z[x, y + 1])
Include this new function at the end of the skeleton .m file.
(b) Apply antialias to your high-resolution image z. Use subplot to show side-by-side
images before and after applying the anti-aliasing filter.
(c) Use your sample function to sample every D=8 pixels of the anti-aliased image zaa to
obtain output zaas. Use subplot to show side-by-side sampled images with and without
the anti-aliasing filter.
(d) Use a for-loop to apply the anti-aliasing filter to the high-resolution image z 64 times and
then apply sample to obtain a new zaas. This applies a “x64 anti-aliasing filter.” Use
subplot to show side-by-side sampled images with and without the x64 anti-aliasing filter.
(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?
Question #4: (Interpolation)
(a) Create 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_system1 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 x64 anti-aliased and sampled image zaas in Question #3 to obtain
zz. Add U=8 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 a new zzaa. This results in
a “x64 interpolation filter.” Use subplot to show side-by-side the original high-resolution
image z and the new interpolated image zzaa.
(e) Answer in your comments: What does the interpolation filter do to the image? Why is
this useful in real-world applications?
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