# Second Bonus point opportunity

ECE301, Spring 2013, Prof. Krogmeier

1. Find out what the impulse response is called in the math literature and then find and state some theorems relating the concept to solutions of ODEs.

2. Use Matlab to demonstrate summing of a finite number of terms of a Fourier Series ... pick a fun time function with a discontinuity to illustrate Gibbs phenomena. How does the Gibbs overshoot behave as the number of terms in the FS increases?

3. In this question you will perform spatial filtering operations on an image. The code should be implemented in Matlab. Use the following image. (Hint. Use these functions: imread, fspecial, fftshift, fft2, imfilter, imshow, surf).

a) Read the image

b) Create Gaussian filter of size 5x5 with mean 0 and standard deviation 3.

c) Plot Fourier Transform of filter’s impulse response in 3D.

d) Apply filter to the original image and explain the result

e) Create “unsharp” filter.

f) Plot Fourier Transform of filter’s impulse response in 3D.

g) Apply filter to the original image and explain the result

h) Attach filtered images, and 3D plots of FT.

Post your examples/questions and solutions on a Rhea page, and post a link to your page below. If you do so before 5:00pm on Monday March 11th, you will receive up to 0.5% bonus on your course grade. DO NOT PLAGIARIZE.

Note that you will receive full credit if you do the exercise seriously, following all guidelines, even if your answer is not completely correct. Before you do this exercise, please familiarize yourself with Rhea's copyright policy. By default you can login to Rhea with your Purdue CAREER account. Note that the system keeps track of who writes what/when and this information is available for public view. If you would prefer to participate anonymously, please contact your instructor to obtain a new login name.

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- You must login in order to be able to edit pages.
- Use the wikitext markup language to type your question and answer. (This is the same language as wikipedia.) Click here for help on the wikitext markup language. DO NOT UPLOAD A PDF OR WORD DOCUMENT.
- Clearly state the question on top of the page. Put your answer in a separate section below the question.
- Invite others to share their own answers or comment on your problem/solution towards the bottom of your page.
- Add the following code on top of your page:

- [[Category:ECE301Spring2013JVK]] [[Category:ECE]] [[Category:ECE301]] [[Category:signalandsystems]] [[Category:problem solving]]

- For question #1 add the following code on top of your page:

- [[Category:Impulse Response]]

- For question #2 add the following code on top of your page:

- [[Category:Fourier series]]

- For question #3 add the following code on top of your page:

- [[Category:FFT]]

- At the very bottom of the page, put a link back to this page:

- [[ECE301bonus2|Back to the 2nd bonus point opportunity, ECE301 Spring 2013]]