### Abstract

Original language | English |
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Title of host publication | Proceedings of 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 |

Publisher | Institute of Electrical and Electronic Engineers IEEE |

Pages | 3777-3780 |

ISBN (Electronic) | 978-1-4673-0046-9 |

ISBN (Print) | 978-1-4673-0045-2, 978-1-4673-0044-5 |

DOIs | |

Publication status | Published - 2012 |

MoE publication type | Not Eligible |

Event | IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Kyoto, Japan Duration: 25 Mar 2012 → 30 Mar 2012 |

### Conference

Conference | IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 |
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Abbreviated title | ICASSP 2012 |

Country | Japan |

City | Kyoto |

Period | 25/03/12 → 30/03/12 |

### Fingerprint

### Keywords

- LMS algorithm
- monodromy matrix
- estimator for the eigenvalues
- convergence rate

### Cite this

*Proceedings of 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012*(pp. 3777-3780). Institute of Electrical and Electronic Engineers IEEE. https://doi.org/10.1109/ICASSP.2012.6288739

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*Proceedings of 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012.*Institute of Electrical and Electronic Engineers IEEE, pp. 3777-3780, IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012, Kyoto, Japan, 25/03/12. https://doi.org/10.1109/ICASSP.2012.6288739

**An estimator for the eigenvalues of the system matrix of a periodic-reference 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 - An estimator for the eigenvalues of the system matrix of a periodic-reference LMS algorithm

AU - Haarnoja, Tuomas

AU - Tammi, Kari

AU - Zenger, Kai

N1 - Project code: 26153

PY - 2012

Y1 - 2012

N2 - The convergence analysis of the Least Mean Square (LMS) algorithm has been conventionally based on stochastic signals and describes thus only the average behavior of the algorithm. It has been shown previously that a periodic-reference LMS system can be regarded as a linear time-periodic system whose stability can be determined from the monodromy matrix. Generally, the monodromy matrix can only be solved numerically and does not thus reveal the actual factors behind the dynamics of the system. This paper derives an estimator for the eigenvalues of the monodromy matrix. The estimator is easy to calculate, and it also reveals the underlying reason for the bad convergence of the LMS algorithm in some special cases. The estimator is confirmed by comparing it to the precise eigenvalues of the monodromy matrix. The estimator is found to be accurate for the eigenvalues close to unity

AB - The convergence analysis of the Least Mean Square (LMS) algorithm has been conventionally based on stochastic signals and describes thus only the average behavior of the algorithm. It has been shown previously that a periodic-reference LMS system can be regarded as a linear time-periodic system whose stability can be determined from the monodromy matrix. Generally, the monodromy matrix can only be solved numerically and does not thus reveal the actual factors behind the dynamics of the system. This paper derives an estimator for the eigenvalues of the monodromy matrix. The estimator is easy to calculate, and it also reveals the underlying reason for the bad convergence of the LMS algorithm in some special cases. The estimator is confirmed by comparing it to the precise eigenvalues of the monodromy matrix. The estimator is found to be accurate for the eigenvalues close to unity

KW - LMS algorithm

KW - monodromy matrix

KW - estimator for the eigenvalues

KW - convergence rate

U2 - 10.1109/ICASSP.2012.6288739

DO - 10.1109/ICASSP.2012.6288739

M3 - Conference article in proceedings

SN - 978-1-4673-0045-2

SN - 978-1-4673-0044-5

SP - 3777

EP - 3780

BT - Proceedings of 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012

PB - Institute of Electrical and Electronic Engineers IEEE

ER -