Title :
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
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;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference on
Conference_Location :
Toronto, Ont.
Print_ISBN :
0-7803-0003-3
DOI :
10.1109/ICASSP.1991.150824
