Analytical probability density functions for LMS adaptive filters using the Fokker-Planck equation

Author

Alexander, S.T. ; Stonic, V.L.

Author_Institution

Dept. of Electr. & Comput. Eng., North Carolina State Univ., Raleigh, NC, USA

fYear

1991

fDate

14-17 Apr 1991

Firstpage

2117

Abstract

Analytical expressions for the theoretical probability density function (pdf) of the LMS (least mean square) adaptive filter weights are obtained for the steady state. The LMS update is formulated as a stochastic differential equation and the weight PDF is derived as the solution to the Fokker-Planck equation. The application of systems identification is examined, and closed-form solutions are obtained for the steady-state PDF for the LMS weights. Only the steady-state PDFs are found for a system identification problem, although the theory developed can also be applied to finding the time-varying PDFs during the adaptation phase

Keywords

adaptive filters; differential equations; digital filters; identification; least squares approximations; probability; Fokker-Planck equation; LMS adaptive filters; LMS update; LMS weights; PDF; closed-form solutions; least mean square; probability density functions; steady state; stochastic differential equation; systems identification; Adaptive arrays; Adaptive filters; Density functional theory; Differential equations; Jitter; Least squares approximation; Partial differential equations; Probability density function; Steady-state; Stochastic processes;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference on

Conference_Location

Toronto, Ont.

ISSN

1520-6149

Print_ISBN

0-7803-0003-3

Type

conf

DOI

10.1109/ICASSP.1991.150824

Filename

150824