A general method is proposed for the design of optimal 1D IIR digital filters via linear programming. The method is based upon the formulation of an appropriate linear problem which assures satisfactory approximation error for the filter's magnitude response. The linear problem does not require differential correction methods or other iterative techniques for its solution, thus resulting in a computationally efficient algorithm. Analytical examples are presented to illustrate the efficiency of the method for the design of stable 1D recursive digital filters.
This paper presents new linear programming techniques for the design of optimal 1D IIR digital filters. The first method is based on a linear minimax criterion and leads to a linear approximation problem whose optimal solution is attained by a new fast algorithm. Next, the linear minimax approximation problem is extended and formulated as two linear integer programming problems which permit the design of 1D IIR digital filters with coefficients of finite word length. The first of these methods is formulated as a mixed integer linear programming problem. The second method is formulated as a power of two coefficients integer linear programing problem. The feasibility of the proposed algorithms is illustrated with detailed solutions or numerical examples.
