Recursibility of N-dimensional IIR digital filters

A simple theorem giving the necessary and sufficient conditions for the recursibility of N-D IIR digital filters is proven. This theorem is used to develop a linear programming technique to test the recursibility of a given filter. The concept of N-D sector is introduced and used to model the structure of N-D recursive filters. These results lead to a method for checking the compatibility of a desired recursion direction with respect to the specified filter output mask structure.