Parametric 2D Gaussian circular band-pass filters

This paper approaches an analytical design method for a type of 2D band-pass circularly-symmetric Gaussian-shaped recursive filters. The method is based on a Gaussian 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 yet with an accurate circular shape, without any distortions. Finally the filter matrices are obtained, which include the filter parameters - central frequency and bandwidth.