**Assignment (1)**

**Image Processing – Spring
2001**

**Due : Wednesday Jan. 24**

Please note that all the problems must be completed using Matlab. Create a file that contains all parts and print that file and submit it in class. Remove extra blank lines to save some paper. Since you are running Matlab on Unix, you can use an editor to cut and paste the results of your work in Matlab into a file. Then you can print the file.

Problems that are marked with **G.** are for graduate
students __only__. Note that all
problems are related to what you have learned and practiced in Lab (1). Use the values given in Lab (1) for *t, A,
and B*. You can use the Matlab help
or tutorial on our web page to find the commands that you do not know.

**Problem (1) :** *sin(2t) =
2 sin(t).cos(t).* Use Matlab to find
the values for *sin(2t)*using the procedure given in the lab (obtain 2t,
then sin(2t) ) and using *2sin(t).cos(t).* Confirm that both methods generate the same results.

**Problem (1) G.:** (Graduate students only) : *sin2(t) + cos2(t) = *1, use Matlab to
prove this using array operations and array t given in the lab.

**Problem (2)**: If A was a complex matrix, what
procedure would you use to generate its

transpose? What was the outcome of the transpose operation in that case?

**Problem (3)** How do you multiply the corresponding
elements of matrix A and B ?

Please note that I didn't ask you to multiply A * B. I want you to tell me how to

multiply A(1,1) by B(1,1), and A(1,2) by B(1,2), ....? Find the results of your work using A and B that are given in the lab.

**Problem (3) G.** How do you find the cube of matrix
A?

**Problem (4) (Challenging): **Suppose you have the
following 4x4 matrix. Suppose the
values in A were selected from the 0 to 255 range. Assume for now that in that scale, 0 represents the black and 255
represents the white colors. Can you
revert the matrix, i.e., can you covert *x(i,j)* to *255- x(i,j)*. Note that *x(i,j)* represents the value
at each location, *x(1,1)* corresponds to the first value in the
matrix. By reverting the matrix, you
will change the black color to white and white to black. A similar thing will happen to all values in
between.

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