Study of elliptical symmetry in 2D IIR Butterworth digital filters

This paper proposes a study of the presence of elliptical symmetry in 2D designed digital filters by parameter modifications. IIR filters have been considered for this purpose due to their capability of approximating the required response with low-order filters and also their flexibility in terms of altering filter parameters to obtain new filters. The filters must be checked for stability before analysis. The design makes use of the fact that varying the feedback factor "k" in an IIR filter produces a near-elliptical symmetric response for certain values of "k₁" and "k₂" between specific magnitude ranges. Butterworth filters have been chosen to illustrate the objective of the paper.