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.