2D Frequency Domain Filtering and the 2D DFT
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The 2D DFT:
o The Transforms
o Frequency Content Location
o Properties of 2D DFT
o Examples of Properties

Frequency Domain Image Filters:
o 2D Filtering Concepts
o Smoothing
o Edge Detection
o Sharpening
o Filter Design



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Frequency Content Location A map of the frequency domain.

The DFT coefficients produced by the 2D DFT equations here, are arranged in a somewhat awkward manner as shown in the diagram below.

It is considered much more intuitive to have low frequency content in the center of the image and high frequency contet on the outsides of the image. Due to the periodicity of the content, and the fact that we could have done our DFT over any period of the image, we chose to modify the frequency domain contents representation by interchanging the 1st and 3rd quadrants and 2nd and 4th quadrants. This layout is shown below.

Since typical images have much stronger low frequency content (slowly varying features as opposed to erratic intensity changes), this positions the majority of the content around the center of the frequency spectrum. It also means that the certain properties hold which would not otherwise, and gives a more pleasing symmetry to the relationship between the spatial and frequency domains.