Window function: Difference between revisions

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Two-dimensional windows are commonly used in image processing to reduce unwanted high-frequencies in the image Fourier transform.<ref name=Hovden/> They can be constructed from one-dimensional windows in either of two forms.<ref name=Bernstein/> The separable form, <math>W(m,n)=w(m)w(n)</math> is trivial to compute. The [[Radial function|radial]] form, <math>W(m,n)=w(r)</math>, which involves the radius <math>r=\sqrt{(m-M/2)^2+(n-N/2)^2}</math>, is [[Isotropy|isotropic]], independent on the orientation of the coordinate axes. Only the [[#Gaussian_window|Gaussian]] function is both separable and isotropic.<ref name=Awad/> The separable forms of all other window functions have corners that depend on the choice of the coordinate axes. The isotropy/[[anisotropy]] of a two-dimensional window function is shared by its two-dimensional Fourier transform. The difference between the separable and radial forms is akin to the result of [[diffraction]] from rectangular vs. circular apertures, which can be visualized in terms of the product of two [[sinc function]]s vs. an [[Airy function]], respectively.

== A listExamples of window functions ==

Conventions''':'''