Minimization of roundoff noise in state-space digital filters using error feedback and coordinate transformation

A systematic approach is developed to obtain the optimal coordinate transformation matrix that minimizes the roundoff noise in state-space digital filters, under the l₂-norm, dynamic-range constraints. This is an alternative approach to Hwang´s method for constructing the optimal realization with minimum roundoff noise, and is much simpler than the conventional method. Next, error feedback is applied to both the optimal realization and the input-balanced realization. Finally, a numerical example is given to illustrate the utility of the proposed technique.