Basic Filtering in the Frequency Domain 1 Low-pass Take the Discrete Fourier Tr

Basic Filtering in the Frequency Domain
1 Low-pass
Take the Discrete Fourier Transform (DFT) of an image (use the fft2 command in Matlab) and multiply its spectrum by a circle of a diameter that retains about ¼ of the lowest spatial frequencies. Note: make sure the DC part of the DFT and filter are centered. The center of the circle should have a value of 1 and the remainder 0. Take the inverse DFT of the product and visually verify that the results looks like a low-pass filtered image. This is one version of a low-pass filter.
Compare this low-pass filter’s frequency response to that of the uniform filter in Chap. 3 and note the difference. The circle is in the filter used above is its frequency response. For the uniform filter, put a 3 x 3 array of 1/9 in a matrix, then pad that matrix with zeros until it is the same size as your circle image. Then take it’s DFT and plot it’s absolute value to see its frequency response.
2 High-pass
Filter an image like you did above, but with a circle of that retains about ½ the highest spatial frequencies. In this case, the center of the circle should be 0, and remainder 1.
Compare this filter’s frequency response to the Sobel edge operators. Meaning, add the absolute values of the frequency responses for gx and gy of the Sobel operators. Describe the differences between the two filters, Sobel and circle.
Turn in:
1- Brief description of what you have done
2- Explanation and/or discussion of results
Image and low-pass version from part 1
Frequency response of ideal (circle) low-pass filter
Frequency response of 3 x 3 low-pass filter
Image and high-pass version from part 2
Frequency response of ideal high-pass filter
Frequency response of sum of absolute values of Sobel operators
3- Appendix: program listing
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PLEASE NOTE THAT CONDITIONS:
1. Avoid plagiarism.
2. Do not use artificial intelligence such as ChatGPT, etc.
3. Utilize MATLAB software and attach a screenshot of the codes used within the program for each section.
4. Explain the solution method for each section.
5. The project requires attaching MATLAB results, including codes and images (as required by the project).
6. List the names of the programs used in the project on the last page.
7. Sentence formatting is required.
8. An attachment is provided for further clarification.