Assignment 3 1

Assignment
3
1. DFT Implementation
a. Forward Fourier transform
b. Inverse Fourier transform
c. Magnitude of DFT
2. Spatial Filtering
a. Using Gaussian 5X5 filter
b. Using Laplacian 3X3 filter
3. Frequency filtering
a. Reject noise frequencies by analyzing the DFT

Assignment
3
1. DFT Implementation
a. Forward Fourier transform
b. Inverse Fourier transform
c. Magnitude of DFT
2. Spatial Filtering
a. Using Gaussian 5X5 filter
b. Using Laplacian 3X3 filter
3. Frequency filtering
a. Reject noise frequencies by analyzing the DFT

Part 1: DFT Implementation
1.
Input a matrix of integers (15X15)
1.
Compute forward Fourier transform
2.
Compute inverse Fourier transform
3.
Compute magnitude of DFT

Part
2: Spatial Filtering
The input is an image, and string specifying the type of filter to use
1.
Perform the required zero padding
2.
Create the filter
1.
5X5 Gaussian filter
2.
3X3 Laplacian filter
3.
Perform convolution

Computation of the DFT
•
Fast algorithms for the DFT are collectively referred to as
Fast Fourier Transform (FFT)
•
We will not delve into the design of these, as they are
available in most math library programs.
•
Divide and conquer
•
Exploit Symmetry
•
Reduces complexity from ?(?2)to ?(?log?)

Assignment
3
1. DFT Implementation(15 Pts)
2. Spatial filtering (30 Pts)
3. Frequency filtering (30 Pts)
Total: 75 Pts.

Submission Instructions
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Must use the starter code available in Github
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Submission allowed only through Github
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You will receive an email with invitation to join
Github classroom
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Start by reading the readme.md file.
Instructions are available here
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Github will automatically save the last commit
as a submission before the deadline