Two-Dimensional Filters Designed in Polar Coordinates

This paper proposes a design method for a class of two-dimensional filters with a shape specified in polar coordinates in the frequency plane. The design starts from a desired 1-D prototype filter, to which a frequency transformation is applied, which leads to the 2D filter with desired shape. The designed filter have the useful zero-phase property. A section of the paper approaches a particular case of this class of filters, namely filters with regular polygonal section. The filters were formally approached here as analog filters implemented with cellular neural networks (CNNs), but the technique can be also used for designing digital 2-D filters.