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# Lode's Computer Graphics Tutorial Fourier Transform

Lode's Computer Graphics Tutorial Fourier Transform

## Lode's Computer Graphics Tutorial Fourier

Lode's Computer Graphics TutorialFourier TransformTable of Contents• Introduction• Signals and Spectra• The Fourier Transform• Properties of the Fourier Transform• Programming the 1D Fourier Transform• The Fast Fourier Transform• Filters• The 2D Fourier Transform on Images• The Spectra of Images• 2D Filters• The DC Component• Low Pass Filters: Blurring• High Pass Filters• Band Pass Filters• The Discrete Quaternion Fourier TransformationBack to Indexhttp://student.kuleuven.be/~m0216922/CG/fourier.htmlIntroductionThe Fourier Transform is an important tool in Image Processing, and is directly related to filter theory,since a filter, which is a convolution in the spatial domain (=the image), is a simple multiplication inthe spectral domain (= the FT of the image)!Most other tutorials about Fourier Transforms of images are in boring greyscale. Even, many programsand plugins available that can calculate the FT on images only support greyscale. In times where 24and 32 bit color are getting old, we cannot accept this any longer! This tutorial is in 24-bit color, bydoing the FT on each colorchannel separately. Here's an example where the FT of an image is used tomake a tillable grass texture look better:

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