Analysis and minimization of roundoff noise in separable denominator multidimensional digital filters

This paper studies the analysis and minimization of roundoff noise in separable denominator multidimensional (SD M‐D) digital filters on the basis of state‐space representations. First, the roundoff noise in SD M‐D digital filters is analyzed and the l₂‐norm dynamic range constraint is discussed. Using the results, a synthesis method of optimal realizations (with respect to roundoff noise) is proposed. Further, the simple relation between balanced realizations and optimal realizations of SD M‐D digital filters is obtained and an efficient method for synthesizing optimal realizations from balanced realizations is proposed. In addition, this paper also proves that optimal realizations are free of overflow oscillations under zero input conditions. Finally, the synthesis procedure is illustrated by a numerical example.