SHARF: An algorithm for adapting IIR digital filters

The concept of adaptation in digital filtering has proven to be a powerful and versatile means of signal processing in applications where precise a priori filter design is impractical. Adaptive filters have traditionally been implemented with FIR structures, making their analysis fairly straightforward but leading to high computation cost in many cases of practical interest (e.g, sinusoid enhancement). This paper introduces a class of adaptive algorithms designed for use with IIR digital filters which offer a much reduced computational load for basically the same performance. These algorithms have their basis in the theory of hyperstability, a concept historically associated with the analysis of closed-loop nonlinear time-varying control systems. Exploiting this theory yields HARF, a hyperstable adaptive recursive filtering algorithm which has provable convergence properties. A simplified version of the algorithm, called SHARF, is then developed which retains provable convergence at low convergence rates and is well suited to real-time applications. In this paper both HARF and SHARF are described and some background into the meaning and utility of hyperstability is given, in addition, computer simulations are presented for two practical applications of IIR adaptive filters: noise and multi-path cancellation.