Window Function - Two-dimensional Windows

Two-dimensional Windows

Two-dimensional windows are utilized in, e.g., image processing. They can be constructed from one-dimensional windows in either of two forms.

The separable form, is trivial to compute but creates corners that depend on the (arbitrary) orientation of the coordinate axes. The unseparable form, involves the radius . In terms of their frequency response, the separable form will be direction-dependent while the nonseparable form will be isotropic. This is akin to the result of diffraction from rectangular vs. circular appertures, which can be visualized in terms of the product or two sinc function vs. an Airy function, respectively.