1a) Fourier Fun: Selective frequency modifications

The use of Fourier transforms of an image can allow for some intense modifications of an image; most importantly specifying what type of frequency to keep in the resulting output. The following are examples of taking the Fourier transform of an image (fft2), shifting the image to an easy to modify form (ffshift), modifying the Fourier map, then pushing it all back to a modified image (ifft2(iffshift)).

Source Image

Source Fourier Transform
(log(abs(ffshift(fft2(source))))*.2)


Effect

Modified Fourier Map

Output

Removing the high Frequencies
Removing the low Frequencies
Preserving lower right quadrant.
Preserving upper right quadrant.
Preserving upper left quadrant.
Preserving lower left quadrant.
Preserving the non off-angle signals.
Preserving just the right angle signals.
It is interesting to note the amount of information that is still passed through on the "right angle" transform, as compared to the lack of information passed through the "off-angle" transformation.
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