Design of three‐dimensional recursive digital filters with symmetry

This paper discusses a useful design method for three-dimensional recursive digital filters approximating the desired amplitude response with spherical or cubic symmetry and the constant group delay. the filter structure is chosen so that the denominator is of a separable form, composed of one-dimensional polynomials of the same form, and the numerator is composed of a mirror- image three-dimensional polynomial with 48- hedral symmetry. In the filter design, the denominator and the numerator approximate the phase and the amplitude responses, respectively, which are designed independently. the proposed method is advantageous since the required computation is relatively small and the numerator is determined by solving a linear equation. the stability of the filter is ensured by its structure.