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.