Discrete Fourier Transformation

This applet demonstrates the discrete Fourier transformation. It provides different interactive tools to test the mathematical background of e.g. low and high pass filters and the sampling theorem. For theoretical aspects (mathematics as well as implementation) of Fourier transformation see  Mathmatical background.

How to use the applet

The first image on the left side shows the input image. You can change it by using the -button.
The two images in the middle represent the Fourier spectrum. upper one shows the amplitude, whereas the lower one shows the phase. Both imagwa can be manipulated manually: First choose the operating tool, indicated by the -button. There are tools like circle, quadrates, lines,etc.. Afterwards move the mouse pointer over  the amplitude or phase picture and cut out the geometric figure you have chosen before. For example if you cut out the low frequencies in the middle of the Fourier spectrum by a black circle, only the high frequencies remain and  therefore you will only see the fine structures  in the output image.You can also manipulate the input image and see what happens in the Fourier spectrum.Another interesting aspect of image processing is the Whitaker-Shannon sampling theorem. When you click on the -button, you are requested to choose a sample rate. Press OK and the input image will be sampled. To reconstruct the original image get the circular-low-pass-tool and cut out one of the clusters in the middle of the amplitude image.. To reset all your changes click on the -button. If you want to visualize a coordinate system press the -button.

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Authors: René Iser, Behrang Karimibabak and Simon Winkelbach

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