APPROXIMATION AND MINIMUM ROUNDOFF NOISE SYNTHESIS OF 3-D SEPARABLE-DENOMINATOR RECURSIVE DIGITAL-FILTERS

In respect to a state-space model for causal three-dimensional (3-D) recursive digital filters, a necessary and sufficient condition is derived for a 3-D separable-denominator recursive model to be separately locally controllable and separately locally observable. To approximate a given 3-D digital filter by a 3-D separable-denominator recursive model, a technique is developed via singular value decomposition of three finite Hankel matrices. A roundoff noise analysis and a scaling on state variables are discussed for 3-D separable-denominator recursive models. A technique is then presented for the synthesis of an optimal 3-D separable-denominator recursive model which minimizes the output noise due to roundoff subject to a scaling condition on the state variables. Finally, two examples are given to illustrate the utility of the proposed techniques.