A Note on the Convergence Analysis of LMS Adaptive Filters with Gaussian Data

Abstract

Necessary and sufficient conditions fur the convergence of LMS adaptive filters with Gaussian data have been established by Horowitz and Senne [3], with the recent support of Feuer and Weinstein [4]. A feature of both of these studies is the necessity to investigate hounds on the roots of rather unwieldy characteristic equations. This note shows how such an investigation can be avoided through the use of a theorem of Gantmacher [SI. In formally applying this theorem, similar results to those of the above studies are obtained in a precise and straightforward manner.