Design of 2-D IIR digital filters with circular symmetry by transformation of the variable

This paper deals with the design of 2-D IIR digital filters having circular symmetry in the 2-D plane. The design is based on the transformation of the variable z of 1-D IIR digital filter into a function f of two variables z1and z2to obtain a 2-D filter. The transformation proposed is such that the resulting 2-D filter has an elliptical symmetry in the 2-D plane. In order to obtain a circular symmetry, one has to cascade two filters rotated with respect to each other by 90°. The rotation is achieved by a suitable choice of the transformation f(z1,z2). It is also shown how to choose the values of the coefficients of the transformation f(z1,z2) so that circular symmetry can be obtained. Stability test is easy to carry out since the filter is assumed to be in cascade form.