Title :
The spectral dynamics of evolving LMS adaptive filters
Author_Institution :
Hydrotronics, Inc., San Diego, California
Abstract :
It is well known that the time constants governing the learning curves of LMS adaptive filters are determined by the eigenvalues of the input correlation matrix. In this paper it is shown that for sufficiently long filters, a transformation to the frequency domain diagonalizes the matrix. As a consequence it is possible to obtain a simple representation of the spectrum of the LMS filter as a function of time (i.e., during convergence). The theoretical results are compared with a computer simulation.
Keywords :
Adaptive filters; Computer simulation; Convergence; Discrete Fourier transforms; Discrete transforms; Eigenvalues and eigenfunctions; Equations; Frequency domain analysis; Least squares approximation; Mean square error methods;
Conference_Titel :
Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '79.
DOI :
10.1109/ICASSP.1979.1170651
