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The problem of minimizing an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints for state-space digital filters is formulated. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form formula for gradient evaluation. The coordinate transformation matrix obtained is then used to construct the optimal state-space filter structure that minimizes the L2-sensitivity measure subject to the scaling constraints. A numerical example is presented to illustrate the utility of the proposed technique.
Circuits and Systems II: Express Briefs, IEEE Transactions on (Volume:52 , Issue: 10 )
Date of Publication: Oct. 2005