A fast converging and self-adjusting SHARF algorithm

Adaptive infinite impulse response (IIR) or recursive filters are less attractive mainly because of the stability and the difficulties associated with their adaptive algorithms. Hyperstability is a concept from nonlinear stability theory and its convergence is directly related to strictly positive real (SPR) transfer functions. The simple hyperstable adaptive recursive filters (SHARF) is a simplified version of hyperstable recursive filters designed for real time applications. In this paper, SHARF is investigated using the constraint recursive least-squares (RLS) method with SPR transfer functions designed without any a priori knowledge of the parameters of the filter by the pole-zero placement on the unit circle method. To demonstrate its fast convergence and self-adjustment, the SHARF algorithm is applied to a pure four-pole autoregressive process.