Assignment 3 Lunar Eclipse

MATLAB Assignment 3
, Section A
This problem set’s goal is to familiarize you with two useful concepts in MATLAB, functions and
logical indexing, as well as begin getting you used to plotting.
Please submit this homework as .m files (note the plural), with suppressed output (obviously,
the plots will still be displayed). Remember that all lectures and homeworks may be found at
github.com/guybaryosef/ECE210-materials. This homework is due by 4:00 PM on February 12th
to guybymatlab@gmail.com. Remember to also bring a hardcopy in to class!
1. Lunar Eclipse This question guides you through some basic image processing techniques in
MATLAB. You will create interesting images with relational and logical indexing, as well as use
the imshow function to visualize what you have created.
a. Create a 100 × 100 matrix A whose contents are all ones.
b. Create a 100 × 100 matrix B whose contents are all zeros.
c. In matrix A, set the values of entry ai,j equal to 0 if p
(i − 50)2 + (j − 50)2 < 20. Hint :
meshgrid would be useful in creating the indices.
d. In matrix B, set the values of entry ai,j equal to 1 if p
(i − 40)2 + (j − 40)2 < 20.
e. Visualize the following results with figure and imshow. Describe each of the results with one
sentence each, either as a comment or by printing to stdout.
• A
• B
• The intersection between A and B
• The union between A and B
• Complement of the intersection between A and B
• Complement of the union between A and B
2. Sincing Ship Here we will look at a function near and dear to the signal processing community’s
heart - the sinc function. You are going to implement your own functions to find the local extrema
and roots. As we haven’t yet gone over plotting, don’t stress over stylizing your plots beyond what
is asked.
a. Sample a sinc with 10001 linearly spaced points on [−2π, 2π] using the sinc function. Plot your
results, and give the plot a title.
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b. Create a function (either anonymously or in another file) which locates the indices at which the
input vector transitions from one sign to another. Note: This can be done in one line of code
but it is trecherousF F . For one scenario the vector has a positive value followed by a negative
value, i.e. v(n) > 0 and v(n + 1) < 0. In this scenario the root occurs somewhere in between
and you can pick either n or n + 1 as the root. We could loop through the vector and check this
condition at every point - but don’t do that. Instead think of a way to use logical indexing: You
will want to write conditions on the vector and some kind of shifted version of itself. Beware
however, when you do this you will have non-overlapping points. It is up to you to figure out
what to do with them.
c. Apply your function from part (b) to the sinc you created in part (a). Find the roots (x and y
coordinates) and plot them as black circles on top of the sinc using plot(xRoots,yRoots,’ko’).
d. Now we are interested in finding the extrema (local minimums and maximums). Firstly, approximate the derivative by taking the difference between all adjacent elements and dividing by their time spacing. Then apply your roots function to the approximate derivative of
your sinc to obtain the extrama. Finally, plot them as red stars on top of the sinc using
plot(xMinMax,yMinMax,’r*’).
3. Fun with find Write a function to return the value and index of a number in a vector / matrix that is closest to a desired value. The function should be called as [val, ind] =
f indClosest(x, desiredV alue). This function can be accomplished in less than five lines. Show
that the function works by finding the value (and index) closest to 3/2 in sin( linspace(0,5,100)
) + 1. You may find the functions abs, min and/or find useful. Hint: You may have some
trouble using min when x is a matrix- remember that you could convert any matrix to a column
vector using y = X(:).
Bonus (worth 1 extra point): Implement MATLAB’s sub2ind function for the 2-D case. Because
you are only doing this for the 2-D case, the function prototype will look like: linearInd =
sub2ind(matrixSize, rowSub, colSub). You do not need to worry about infinite error checking, but
try to make it at least a plausible implementation.
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