Open AccessAn analysis of the convergence condition for narrowband FxLMS
Author(s) -
Wen Haoxiang,
Luo Huan,
Yang Senquan
Publication year - 2022
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
eISSN - 1350-911X
pISSN - 0013-5194
DOI - 10.1049/ell2.12378
Subject(s) - root locus , locus (genetics) , narrowband , mathematics , control theory (sociology) , pole–zero plot , complex plane , mathematical analysis , upper and lower bounds , critical point (mathematics) , transfer function , computer science , telecommunications , engineering , control system , gene , biochemistry , chemistry , control (management) , artificial intelligence , electrical engineering
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.