Title :
An easy demonstration of the optimum value of the adaptation constant in the LMS algorithm [FIR filter theory]
Author :
Soria-Olivas, Emilio ; Calpe-Maravilla, Javier ; Guerrero-Martinez, Juan F. ; Martinez-Sober, Marcelino ; Espi-Lopez, J.
Author_Institution :
Fac. de Fisica, Valencia Univ., Spain
fDate :
2/1/1998 12:00:00 AM
Abstract :
The least mean squares (LMS) is the most widely used algorithm among those proposed to adapt the coefficients of an FIR filter in order to minimize the mean-square error (MSE) between its output and the desired signal. Since the introduction of the LMS algorithm, many variants have been proposed to improve its performance. Doubtless, the most popular is the normalized LMS algorithm, which uses a value for the adaptation constant that assures the fastest convergence. This correspondence shows a new demonstration of the algorithm based on a mathematical approach easier than that usually proposed
Keywords :
FIR filters; convergence of numerical methods; filtering theory; least mean squares methods; FIR filter; adaptation constant; coefficients adaptation; computational performance; fast convergence; least mean squares algorithm; mathematical demonstration approach; mean-square error; normalized LMS algorithm; Adaptive filters; Convergence; Equations; Finite impulse response filter; Lagrangian functions; Least squares approximation; Minimization methods; Real time systems; Robustness; Stability;
Journal_Title :
Education, IEEE Transactions on
