Editing Spatial anti-aliasing (section)

==Signal processing approach to anti-aliasing==
In this approach, the ideal image is regarded as a ''signal''.  The image displayed on the screen is taken as samples, at each (''x,y'') pixel position, of a filtered version of the signal. Ideally, one would understand how the human brain would process the original signal, and provide an on-screen image that will yield the most similar response by the brain.

The most widely accepted analytic tool for such problems is the [[Fourier transform]]; this decomposes a signal into [[basis function]]s of different frequencies, known as frequency components, and gives us the [[amplitude]] of each frequency component in the signal. The waves are of the form:

:<math>\ \cos (2j \pi x) \cos (2k \pi y)</math>

where ''j'' and ''k'' are arbitrary non-negative [[integer]]s. There are also frequency components involving the [[sine]] functions in one or both dimensions, but for the purpose of this discussion, the [[cosine]] will suffice.

The numbers ''j'' and ''k'' together are the ''frequency'' of the component: ''j'' is the frequency in the ''x'' direction, and ''k'' is the frequency in the ''y'' direction.

The goal of an anti-aliasing filter is to greatly reduce frequencies above a certain limit, known as the [[Nyquist frequency]], so that the signal will be accurately represented by its samples, or nearly so, in accordance with the [[sampling theorem]]; there are many different choices of detailed algorithm, with different filter [[transfer function]]s. Current knowledge of [[human visual perception]] is not sufficient, in general, to say what approach will look best.