Design of three-dimensional spherically symmetric digital filters

A method is presented for the design of 3-D recursive digital filters with approximately spherically symmetric magnitude frequency response. The desired 3-D recursive filter is obtained by cascading a number of 3-D transformed filters which can be designed by rotating a 1-D analog filter and using the triple bilinear z-transformation. The stability of the 3-D filters is discussed in detail, and a theorem which gives the sufficient conditions for stable 3-D filters is derived