# 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).

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.

Guidelines:

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[[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]]