### Abstract

Filtered-x Least Mean Squares (FXLMS) algorithm is a
well-known method for adapting feedforward FIR filters to
compensate selected disturbances in the system output.
However, the nonlinearities in the algorithm complicates
its analysis. Nevertheless, it can be shown that if a
periodic, synchronously sampled reference signal is
considered, FXLMS algorithm can be analyzed by a LTP
system to which the conventional linear analysis tools
can be applied. Earlier, this method has been applicable
only for systems, in which the model of the plant is
unity. This paper extends the analysis to cover also
systems with an arbitrary, linear plant model. The new
approach relieves some of the other assumptions made in
the earlier analysis. The effect of filter length,
convergence coefficient, and model errors to the
stability and to the rate of convergence of FXLMS are
also studied by using the LTP representation

Original language | English |
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Title of host publication | Proceedings |

Subtitle of host publication | 18th International Congress on Sound and Vibration 2011, ICSV 19 |

Editors | Malcolm J. Crocker, Marek Pawelczyk, Nickolay Ivanov |

Publisher | International Institute of Acoustics and Vibration IIAV |

Pages | 203-210 |

Volume | 1 |

ISBN (Print) | 978-1-61839-259-6 |

Publication status | Published - 2011 |

MoE publication type | A4 Article in a conference publication |

Event | 18th International Congress on Sound & Vibration, ICSV18 - Rio de Janeiro, Brazil Duration: 10 Jul 2011 → 14 Jul 2011 |

### Conference

Conference | 18th International Congress on Sound & Vibration, ICSV18 |
---|---|

Abbreviated title | ICSV18 |

Country | Brazil |

City | Rio de Janeiro |

Period | 10/07/11 → 14/07/11 |

### Keywords

- FxLMS
- convergence
- active vibration control

## Fingerprint Dive into the research topics of 'Linear time-periodic representation for periodic-reference, discrete-time filtered-x LMS algorithm'. Together they form a unique fingerprint.

## Cite this

Haarnoja, T., Tammi, K., & Zenger, K. (2011). Linear time-periodic representation for periodic-reference, discrete-time filtered-x LMS algorithm. In M. J. Crocker, M. Pawelczyk, & N. Ivanov (Eds.),

*Proceedings: 18th International Congress on Sound and Vibration 2011, ICSV 19*(Vol. 1, pp. 203-210). International Institute of Acoustics and Vibration IIAV.