Equiripple stopband characteristic for circularly symmetric 2-D recursive filters

Abstract

A circularly symmetric 2-D recursive digital filter whose magnitude-squared response approximates a Gaussian function in the two frequency variables has a separable transfer function. Such a circularly symmetric filter has a monotonic frequency response. One may, therefore, want to sharpen the response in the transition band. Due to the separability feature, it is shown how to obtain an equiripple characteristic in the stopband without affecting the circular symmetry in the passband. This reduces the transition bandwidth.