Weak Convergence and Asymptotic Properties of Adaptive Filters with Constant Gains.
BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
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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.
- Theoretical Mathematics