Signal, Image and Video Processing

, Volume 8, Issue 1, pp 133–142 | Cite as

Stochastic analysis of the least mean fourth algorithm for non-stationary white Gaussian inputs

  • Eweda EwedaEmail author
  • Neil J. Bershad
  • Jose C. M. Bermudez
Original Paper


This paper studies the stochastic behavior of the least mean fourth (LMF) algorithm for a system identification framework when the input signal is a non-stationary white Gaussian process. The unknown system is modeled by the standard random-walk model. A theory is developed which is based upon the instantaneous average power and the instantaneous average squared power in the adaptive filter taps. A recursion is derived for the instantaneous mean square deviation of the LMF algorithm. This recursion yields interesting results about the transient and steady-state behaviors of the algorithm with time-varying input power. The theory is supported by Monte Carlo simulations for sinusoidal input power variations.


Adaptive filters Analysis Least mean fourth algorithm Stochastic algorithms 


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Eweda Eweda
    • 1
    Email author
  • Neil J. Bershad
    • 2
  • Jose C. M. Bermudez
    • 3
  1. 1.National Knowledge CenterAbu DhabiUnited Arab Emirates
  2. 2.Department of Electrical Engineering and Computer ScienceUniversity of California, IrvineNewport BeachUSA
  3. 3.Department of Electrical EngineeringFederal University of Santa CatarinaFlorianopolisBrazil

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