Design of three- dimensional recursive digital filters

Three types of three-dimensional (3-D) recursive digital filters are first defined under different radial symmetry constraints in the 3-D coordinate axes: the symmetrical filter, the nonsymmetrical filters I and II. A design technique is then outlined for these 3-D recursive digital filters whose magnitude responses can be decomposed into several cubic pass- and stopbands. The filter designed by the present approach can be realized by cascading and paralleling of the well-known one-dimensional (1-D) component transfer functions so that the stability test is simple and the filter can be implemented easily. Three examples are included to illustrate the design procedure for each type of 3-D filter.