An analysis of the convergence condition for narrowband FxLMS

Abstract

This letter discusses the convergence condition of the narrowband FxLMS (NFxLMS) algorithm in Z-domain. First, two new concepts about NFxLMS root locus, that is critical start point (CSP) and critical cross point (CCP), are introduced and defined. For NFxLMS with the simplest case, a special characteristic of the root locus is observed that the CCP always locates itself near the CSP in the Z plane. By exploiting this characteristic, directly solving the root locus equation is eliminated from the stability analysis, and the upper bound of the step size for NFxLMS is eventually estimated as a function of the reference frequency.