Abstract
The joint optimization problem of error feedback and realization for two-dimensional (2-D) state-space digital filters to minimize the effects of roundoff noise at the filter output subject to L2-norm dynamic-range scaling constraints is investigated. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem at hand is then solved iteratively by applying an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. Analytical details are given as to how the proposed technique can be applied to the cases where the error-feedback matrix is a general, block-diagonal, diagonal, or block-scalar matrix. A case study is presented to illustrate the utility of the proposed technique
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