Optimal Synthesis of a Class of 2-D Digital Filters with Minimum L2-Sensitivity and No Overflow Oscillations

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