Weak Convergence and Asymptotic Properties of Adaptive Filters with Constant Gains

摘要

This paper illustrates the power of weak convergence methods through the analysis of the basic algorithm of adaptive filtering. Except for the simplest cases (e.g., when (y sub n, psi sub n) are mutually independent), the analysis of the algorithm for fixed epsilon is difficult. However, asymptotic analysis (epsilon approaches limit of O) via weak convergence methods provides much information, relatively painlessly.