Abstract
The optimal synthesis of a single-input single-output (SISO) multidimensional (M-D) digital filter with fixed-point arithmetic is investigated. The necessary and sufficient conditions for optimal realizations for both optimal and equal wordlength registers are established. It is shown that these optimality conditions always can be satisfied for an arbitrary M-D filter. It is proven that optimal structures possess some favorable properties such as low coefficient sensitivity. It is found that the optimal realizations of a multidimensional filter demonstrate a remarkable property in needed number of multipliers per sample output is comparison to one dimensional (1-D) optimal structures. Two numerical examples are presented to illustrate the design procedure and usefulness of the proposed scheme.
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