### Abstract

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 |
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Abbreviated title | ICSV18 |

Country | Brazil |

City | Rio de Janeiro |

Period | 10/07/11 → 14/07/11 |

### Fingerprint

### Keywords

- FxLMS
- convergence
- active vibration control

### Cite this

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

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*Proceedings: 18th International Congress on Sound and Vibration 2011, ICSV 19.*vol. 1, International Institute of Acoustics and Vibration IIAV, pp. 203-210, 18th International Congress on Sound & Vibration, ICSV18, Rio de Janeiro, Brazil, 10/07/11.

**Linear time-periodic representation for periodic-reference, discrete-time filtered-x LMS algorithm.** / Haarnoja, Tuomas; Tammi, Kari; Zenger, Kai.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Linear time-periodic representation for periodic-reference, discrete-time filtered-x LMS algorithm

AU - Haarnoja, Tuomas

AU - Tammi, Kari

AU - Zenger, Kai

N1 - Project code: 26153

PY - 2011

Y1 - 2011

N2 - 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

AB - 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

KW - FxLMS

KW - convergence

KW - active vibration control

UR - http://www.proceedings.com/13257.html

M3 - Conference article in proceedings

SN - 978-1-61839-259-6

VL - 1

SP - 203

EP - 210

BT - Proceedings

A2 - Crocker, Malcolm J.

A2 - Pawelczyk, Marek

A2 - Ivanov, Nickolay

PB - International Institute of Acoustics and Vibration IIAV

ER -