Design approach for a class of 2D recursive filters

This paper proposes an analytical design method for a class of two-dimensional recursive zero-phase filters with a shape specified in polar coordinates in the frequency plane. The design is based on applying a frequency transformation to a given 1D prototype filter, which leads to the 2D filter with a desired shape. For each particular 2D filter, the design consists in finding the appropriate frequency transformation. The resulted filters are efficient, of low order and relatively high selectivity. Simulation results are provided for one type of filter, to show its capabilities in image filtering.