### Abstract

Original language | English |
---|---|

Pages (from-to) | 121-130 |

Number of pages | 10 |

Journal | IEEE Transactions on Signal Processing |

Volume | 62 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A1 Journal article-refereed |

### Fingerprint

### Keywords

- active noise control (ANC)
- convergence analysis
- convergent control (CC)
- filtered-x least mean square (FxLMS)
- higher harmonic control (HHC)
- multichannel FxLMS
- narrowband FxLMS
- state-space representation

### Cite this

*IEEE Transactions on Signal Processing*,

*62*(1), 121-130. https://doi.org/10.1109/TSP.2013.2285513

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*IEEE Transactions on Signal Processing*, vol. 62, no. 1, pp. 121-130. https://doi.org/10.1109/TSP.2013.2285513

**Exact LTP representation of the generalized periodic-reference FxLMS algorithm.** / Haarnoja, Tuomas; Tammi, Kari; Zenger, K.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Exact LTP representation of the generalized periodic-reference FxLMS algorithm

AU - Haarnoja, Tuomas

AU - Tammi, Kari

AU - Zenger, K.

N1 - Project code: 26153

PY - 2014

Y1 - 2014

N2 - The analysis of the Filtered-x Least Mean Square (FxLMS) algorithm can be based either on a stochastic or deterministic approach. One of the drawbacks of the stochastic analysis is that it relies on several assumptions which are not justified if the reference signal is time periodic. To overcome these limitations, several deterministic methods have been suggested. However, useful results have been reported only for setups with certain filter length, secondary path model, or reference signal. In this paper, an exact Linear Time-Periodic (LTP) representation is proposed assuming only that the reference is synchronously-sampled. The representation is derived for a general FxLMS system, which also covers the multichannel topology of several parallel filters and its common narrowband modification. The representation is found to have a Linear Time-Invariant (LTI) form if the filter length is suitably chosen. The usability of the method is demonstrated in a numerically computed example by comparing it to an approximate LTI model.

AB - The analysis of the Filtered-x Least Mean Square (FxLMS) algorithm can be based either on a stochastic or deterministic approach. One of the drawbacks of the stochastic analysis is that it relies on several assumptions which are not justified if the reference signal is time periodic. To overcome these limitations, several deterministic methods have been suggested. However, useful results have been reported only for setups with certain filter length, secondary path model, or reference signal. In this paper, an exact Linear Time-Periodic (LTP) representation is proposed assuming only that the reference is synchronously-sampled. The representation is derived for a general FxLMS system, which also covers the multichannel topology of several parallel filters and its common narrowband modification. The representation is found to have a Linear Time-Invariant (LTI) form if the filter length is suitably chosen. The usability of the method is demonstrated in a numerically computed example by comparing it to an approximate LTI model.

KW - active noise control (ANC)

KW - convergence analysis

KW - convergent control (CC)

KW - filtered-x least mean square (FxLMS)

KW - higher harmonic control (HHC)

KW - multichannel FxLMS

KW - narrowband FxLMS

KW - state-space representation

U2 - 10.1109/TSP.2013.2285513

DO - 10.1109/TSP.2013.2285513

M3 - Article

VL - 62

SP - 121

EP - 130

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 1

ER -