Fourier Transform and Frequency Filters

Fourier transform allows us to smoothen or sharpen images using filters. An image is first converted from spatial to frequency domain (high components=edges; low components=smooth regions) using Fourier transform then it is multiplied with a filter function (lowpass, highpass, bandpass filter) in a pixel-by-pixel fashion, and converted back to spacial domain.
For example, a lowpass filter will reduce high frequencies and retain low frequencies resulting to a smoother image.

https://www.tutorialspoint.com/dip/introduction_to_frequency_domain.htm
http://paulbourke.net/miscellaneous/imagefilter/
http://homepages.inf.ed.ac.uk/rbf/HIPR2/freqfilt.htm

original image

resulting image after applying lowpass filter

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