Planar symmetries in 3-D filter responses and their application in 3-D filter design

Symmetry definitions are extended to 3-D frequency responses, and single planar, double planar, and triple planar symmetries are defined. Necessary and sufficient conditions on 3-D s- and z-domain functions to possess various 3-D symmetries in magnitude responses are derived. The application of symmetry results in the design of 3-D filters is discussed.<
>