Approximation and implementation of multidimensional digital filters

The approximation and optimal implementation of a single-input single-output multidimensional digital filter with fixed-point arithmetic is investigated. Based on balanced and optimal realizations, a novel structure which minimizes the error due to the order approximation and output round-off noise is obtained. It is shown that for the class of M-D completely separable-in-denominator filters, optimum order structure exhibits some favorable properties such as robustness of the filter's constant coefficients. A numerical example is presented to illustrate the proposed technique.<>