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

Tuomas Haarnoja, Kari Tammi, Kai Zenger

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

3 Citations (Scopus)


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 languageEnglish
Title of host publicationProceedings
Subtitle of host publication18th International Congress on Sound and Vibration 2011, ICSV 19
EditorsMalcolm J. Crocker, Marek Pawelczyk, Nickolay Ivanov
PublisherInternational Institute of Acoustics and Vibration (IIAV)
ISBN (Print)978-1-61839-259-6
Publication statusPublished - 2011
MoE publication typeA4 Article in a conference publication
Event18th International Congress on Sound & Vibration, ICSV18 - Rio de Janeiro, Brazil
Duration: 10 Jul 201114 Jul 2011


Conference18th International Congress on Sound & Vibration, ICSV18
Abbreviated titleICSV18
CityRio de Janeiro


  • FxLMS
  • convergence
  • active vibration control


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