3-D digital filter design using symmetrical decomposition technique

The authors explore ways of decomposing a 3D response into a number of components and designing a 3D filter by designing each component individually. The authors first list the types of 3D symmetries and antisymmetries that can be present in 3D filter responses. The types of symmetries studied are spatial centro symmetry, single, double, and triple planar quadrantal, diagonal, four-fold rotational, and octagonal symmetries. Then, based on these symmetry and antisymmetry definitions, procedures and examples are given to decompose a 3D function into various symmetrical and antisymmetrical components. A filter design example illustrating the application and efficiency of the method is presented