Design of three dimensional spherically symmetric infinite impluse response digital filters

Three-dimensional (3-D) signal processing offers many advantages over two-dimensional (2-D) processing, because it preserves 3-D correlation. In this paper, the method of 2- D rotated filters is extented to 3-D and used for the design of stable 3-D lowpass (LP) digital filters, with approximately spherically symmetric magnitude responses. In the proposed technique, a number of 3-D rotated filters is cascaded. These filters are designed by rotating an one-dimensional (1-D) digital filter in the 3-D space. The stability of the rotated filters is extensively discussed. Stable realizations of the spherically symmetric filters are proposed. The relation between the radius of the sphere that the designed filter approximates and the 1-D filter used in the design is discussed. Finally, configurations that result in highpass (HP) and bandpass (BP) filters are proposed. Examples of LP, HP and BP filters designed on the basis of the method proposed, are presented.