Minimax design of stable IIR digital filter using iterative linear programming method

In this paper, we present an iterative linear programming approach to design stable IIR digital filters with prescribed magnitude and phase responses. At each iteration. The complex error of frequency response is transformed into a linear form by treating the denominator polynomial obtained from the preceding iteration as a part of the weighting function, and the pole radii are constrained to lie in the unit circle by using the positive real condition of the denominator. After solving the standard linear programming problem at each iteration, the design algorithm converges to the minimax solution. Design examples demonstrate that our method provides better design results than the conventional linear programming method.