Optimal design of state - space digital filters by simultaneous minimization of sensitivity and roundoff noise

The relation between a newly defined sensitivity measure and the noise power gain for scaled filters is given. By means of this relation it is shown that the necessary and sufficient condition to minimize the noise power gain is to minimize the sensitivity measure for unsealed filters. It is shown that the minimization of this sensitivity measure can be carried out without taking into account the dynamic range constraint. A procedure for the simultaneous minimization of the sensitivity measure and the noise power gain is also given.