IIR Digital Filter Design With New Stability Constraint Based on Argument Principle

This paper presents a weighted least squares (WLS) method for IIR digital filter design using a new stability constraint. Utilizing the reweighting technique, an iterative second-order cone programming (SOCP) method is employed to solve the design problem, such that either linear or second-order cone constraints can be further incorporated. In order to guarantee the stability of designed IIR digital filters, a new stability constraint with a prescribed pole radius is derived from the argument principle (AP) of complex analysis. As compared with other frequency-domain stability constraints, the AP-based stability constraint is both sufficient and necessary. Since the derived stability constraint cannot be directly incorporated in the iterative SOCP method, the similar reweighting technique is deployed to approximate the stability constraint in a quadratic form, which is then combined with the WLS iterative design process. Filter design examples are presented to demonstrate the effectiveness of the proposed iterative SOCP method.