Minimax design of stable IIR digital filter with prescribed magnitude and phase responses

In this work, an iterative linear programming approach is presented to design stable IIR digital filters with prescribed magnitude and phase responses. At each iteration, the complex error of the 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 poles restricted inside the unit circle by using a set of linear constraints. 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