article · 1991

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

Cited by 2Abstract and details only

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

Cite this paper

APA 7

Alexander, S., & Stonic, V. (1991). Analytical probability density functions for LMS adaptive filters using the Fokker-Planck equation. https://doi.org/10.1109/icassp.1991.150824

MLA 9

Alexander, S.T., and V.L. Stonic. “Analytical probability density functions for LMS adaptive filters using the Fokker-Planck equation.” 1991, pp. 2117–2120 vol.3, https://doi.org/10.1109/icassp.1991.150824.

Chicago

Alexander, S.T., and V.L. Stonic. 1991. “Analytical probability density functions for LMS adaptive filters using the Fokker-Planck equation.” https://doi.org/10.1109/icassp.1991.150824.

Harvard

Alexander, S. and Stonic, V. (1991) ‘Analytical probability density functions for LMS adaptive filters using the Fokker-Planck equation’. Available at: https://doi.org/10.1109/icassp.1991.150824.

BibTeX

@article{alexander1991analytical,
  title = {{Analytical probability density functions for LMS adaptive filters using the Fokker-Planck equation}},
  author = {Alexander, S.T. and Stonic, V.L.},
  pages = {2117--2120 vol.3},
  year = {1991},
  doi = {10.1109/icassp.1991.150824}
}

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