Design of multidimensional separable-denominator digital filters in the spatial domain

Based on a concept of minimal decomposition and balanced realization, a novel technique is developed for designing multidimensional (M-D) separable-denominator digital filters in the spatial domain. This is done by decomposing a desired M-D FIR filter into M parts and by representing it by a cascade connection of M 1-D filters. The minimal decomposition treated here can be viewed as an extension of that in 2-D separable-denominator case in some sense. However, the proposed technique differs from the existing one even in 2-D case and is simpler. The amount of calculation required here is relatively small and the stability of the filter is always guaranteed