L/sub 2/-sensitivity minimization for a class of 2D digital filters using a quasi-Newton method

The minimization problem of an L₂-sensitivity measure subject to L₂-norm dynamic-range scaling constraints is formulated for a class of two-dimensional (2D) state-space digital filters. First, the problem is 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 synthesize the optimal 2D state-space filter structure that minimizes the L₂ -sensitivity measure subject to the L₂-scaling constraints. Finally, a numerical example is presented to illustrate the utility of the proposed technique