Least P-Norm Design of IIR Filters with a Pole Radius Constraint

In this paper, the least p-norm criterion is adopted to design the Infinite Impulse Response (IIR) digital filters that meet simultaneously on prescribed magnitude and phase responses with a pole radius constraint. The parameterizations of direct form and cascade of second-order factors are employed to represent the denominators. For both parameterizations, the pole radii are constrained within a prescribed circle centered at the origin of the complex plane. The positive realness condition and an internal stability triangle are used to constrain the pole radii of direct form and cascade form denominators respectively. We incorporate the benefits of less nonlinearity of direct form denominator and the necessary and sufficient property on controlling the pole radii of cascade form denominator to design the IIR filter that converges to the true local optimum solution. That is, the direct form is first carried out to search a good solution, and then the results are used as the initial point of the cascade form to search true local optimum. This paper develops a robust and stable algorithm to design IIR digital filters with acceptable results.