Iterative design of IIR variable fractional delay digital filters

In this paper, an iterative algorithm is proposed to design IIR variable fraction delay (VFD) digital filters in the weighted least-squares (WLS) sense. The original IIR VFD filter design problem is nonconvex. As an attempt to tackle this difficulty, an iterative procedure is introduced, and the Steiglitz-McBride (SM) reweighting technique is employed at each iteration to transform the original approximation error into a (convex) quadratic form. The stability of designed IIR VFD filters can be ensured by imposing a set of linear stability constraints based on the positive realness. The proposed algorithm can be applied to design IIR VFD filters with either fixed or variable denominator. Two examples are presented to illustrate the effectiveness of the proposed algorithm.