Design of three-dimensional digital filters using two-dimensional rotated filters

Two techniques for the design of three-dimensional (3-D) filters are introduced in this paper. The first one is based on coefficient transformations of two-dimensional (2-D) circularly symmetric filters. These filters can be designed by cascading 2-D rotated filters. Stability of the 3-D filters designed is discussed and a stabilization procedure based on cepstrum analysis, is proposed. Stable implementation schemes are introduced. The second technique is based on cascade arrangements of 2-D rotated filters and results in 3-D spherically symmetric filters. Examples of 3-D filters designed on the basis of both techniques introduced are presented. Finally, some comparisons among several 3-D design techniques are given.