R-cos&thetas; adaptive IIR filter algorithm

P.C. Ching and C.C. Goodyear and Ching (1980) proposed a FIR filter adaptation algorithm in which the transfer function zeros were implemented in a cascade structure of modified second-order filter sections. The modification allowed the radius and angle of the complex conjugate zero pairs to be adapted independently and was successfully applied to speech prediction. In this paper, an adaptive IIR filter is proposed which uses the modified filter sections for implementation of transfer function poles. The adaptation algorithm is derived for an IIR filter structure in which the transfer function poles have been implemented using modified second-order filter sections. The modification decouples the radius and angle of the poles and enables them to be adapted independently. A second-order filter example is presented to highlight advantages that may be gained using the modified filter sections rather than the standard canonic form. The performance of the r-cosθ filter is particularly beneficial if the target poles are in the region of z=+/-1, when the sensitivity of direct form coefficients is greatly increased