Two-dimensional filter design based on frequency mapping of analog prototype filters

In this work an analytical design method for two types of 2D recursive filters is proposed. The design starts from a given analog prototype filter with specified parameters and a transfer function which is factorized into elementary (biquad) functions. Applying adequate frequency transformations to these functions, the desired 2D filters are directly obtained in a factorized form, preserving the selectivity properties of their 1D counterparts. The types of 2D filters approached here are narrow orientation-selective filters with a specified orientation and maximally-flat low-pass filters with circular symmetry. Design examples starting from imposed specifications and simulation results are provided.