Abstract
AbstractA roundoff noise analysis is presented for three‐dimensional (3‐D) local state‐space digital filters with separable denominator. It is clarified that the output‐noise power and the signal scaling condition are closely related to three, and three positive‐definite matrices, respectively. A procedure is also developed for the synthesis of an optimal 3‐D local state‐space digital filter with separable denominator which minimizes the output‐noise due to roundoff subject to a scaling condition on the state variables. The optimal state‐space realization can be obtained through the 3‐D similarity transformation by individually solving three 1‐D optimization problems.
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