Convergence studies of the analog hyperstable adaptive recursive filter

An adaptive recursive filter, which has both adaptive zeros and adaptive poles, can offer a reduced computational load compared to non-recursive filters, which have only adaptive zeros, for a given level of performance. Most applications of adaptive filtering are implemented using digital components. The digital implementation is appropriate in narrowband applications, such as in the telephone channel. However, in wideband and high-data-rate applications, a digital implementation may result in an undesirable and often infeasible system design. The analog implementation can overcome these difficulties. In recent years, research has been carried out in analog adaptive filtering. In the research of continuous-time hyperstable adaptive recursive filtering (CTHARF), there is an assumption, the validity of which is not shown, in the proof of convergence of the algorithm (Larimore et al. 1980 and Cornett, 1992). In order to gain insight into convergence, the present paper considers the convergence properties of the CTHARF with practical structures. The structures are discussed, and the convergence properties are investigated by way of computer simulations