Efficient design of adjustable circular IIR 2D filters

This paper proposes an analytical design method for 2D zero-phase recursive filters with a circularly-symmetric frequency response. The design is based on a maximally-flat low-pass prototype filter, whose transfer function is transformed using a specific 1D to 2D frequency mapping. An efficient pre-warping is applied before using the bilinear transform, which allows to obtain filters having a central frequency close to the frequency plane margins, and still with an accurate circular shape, without any distortions. Finally the general filter matrices are obtained. The filter is adjustable in the sense that its bandwidth is specified by a parameter which appears explicitly in the filter coefficients.