The use of Symmetrics in the Design of Multidimensional Digital filters

Symmetries have been successfully used in the design of two-dimensional digital filters. This results in a reduction of the required optimization and in better response characteristics of the filters designed. Since the number of parameters of a filter increases by an order of magnitude for every increase by one of the filter dimensionality, the use of symmetries in the design of multidimensional filters is essential. This paper introduces various multidimensional symmetries and applies them to the computer-aided design of some useful three-dimensional digital filters.