Joint optimization of error feedback and coordinate transformation for roundoff noise minimization in state-space digital filters

An iterative approach for joint optimization of a scalar error-feedback matrix and a coordinate transformation matrix is developed to minimize the roundoff noise subject to the l₂-norm dynamic-range scaling constraints. When the iterative algorithm converges and the optimal coordinate transformation matrix is obtained, the diagonal error-feedback matrix is derived to minimize the noise gain in the optimal state-space realization. This diagonal error-feedback matrix enables one to produce more reduction of the noise gain. Finally, a numerical example is given to illustrate the utility of the proposed technique.