A Self-Adjusting Simple Hyperstable Adaptive Recursive Algorithm

Abstract

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 theory when simplified and adapted for digital signal processing offers a new class of IIR filters, simple hyperstable adaptive recursive filters (SHARFs), which is directly related to strictly positive real (SPR) transfer functions. One of the most important drawbacks of the SHARF algorithm is the presence of the unknown denominator in the transfer function that must be SPR in order to ensure convergence. In this paper, SHARF is investigated with SPR transfer functions designed without any priori knowledge of the filter parameters by the pole–zero placement on the unit circle method and made self-adjusting. To demonstrate self-adjustment of the algorithm, SHARF algorithm using constraint least-mean square (LMS) method is applied to a pure four-pole autoregressive process.