The dual parameterization approach to optimal least square FIR filter design subject to maximum error constraints

This paper is concerned with the design of linear-phase finite impulse resp onse (FIR) digital filters for which the weighted least square error is min imized, subject to maximum error constraints. The design problem is formula ted as a semi-infinite quadratic optimization problem, Using a newly develo ped dual parameterization method in conjunction with the Caratheodory's dim ensional theorem, an equivalent dual finite dimensional optimization proble m is obtained. The connection between the primal and the dual problems is e stablished. A computational procedure is devised for solving the dual finit e dimensional optimization problem, The optimal solution to the primal prob lem can then be readily obtained from the dual optimal solution. For illust ration, examples are solved using the proposed computational procedure.