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. 1