### Abstract

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Periodic signals are encountered in many applications. Such signals can be modelled by a weighted sum of sinusoidal components whose frequencies are integer multiples of a fundamental frequency. Given a data set, the fundamental frequency can be estimated in many ways including a maximum likelihood (ML) approach. Unfortunately, the ML estimator has a very high computational complexity, and the more inaccurate, but faster correlation-based estimators are therefore often used instead. In this paper, we propose a fast algorithm for the evaluation of the ML cost function for complex-valued data over all frequencies on a Fourier grid and up to a maximum model order. The proposed algorithm significantly reduces the computational complexity to a level not far from the complexity of the popular harmonic summation method which is an approximate ML estimator.

Original language | English |
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Title of host publication | 23rd European Signal Processing Conference (EUSIPCO), 2015 |

Publisher | IEEE Press |

Publication date | 1 Sep 2015 |

Pages | 589 - 593 |

ISBN (Electronic) | 978-0-9928626-3-3 |

DOIs | |

Publication status | Published - 1 Sep 2015 |

Event | 2015 23rd European Signal Processing Conference (EUSIPCO) - Nice, France Duration: 31 Aug 2015 → 4 Sep 2015 |

### Conference

Conference | 2015 23rd European Signal Processing Conference (EUSIPCO) |
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Country | France |

City | Nice |

Period | 31/08/2015 → 04/09/2015 |

Series | Proceedings of the European Signal Processing Conference |
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ISSN | 2076-1465 |

### Cite this

*23rd European Signal Processing Conference (EUSIPCO), 2015*(pp. 589 - 593). IEEE Press. Proceedings of the European Signal Processing Conference https://doi.org/10.1109/EUSIPCO.2015.7362451

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*23rd European Signal Processing Conference (EUSIPCO), 2015.*IEEE Press, Proceedings of the European Signal Processing Conference, pp. 589 - 593, Nice, France, 31/08/2015. https://doi.org/10.1109/EUSIPCO.2015.7362451

**A Fast Algorithm for Maximum Likelihood-based Fundamental Frequency Estimation.** / Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper Rindom; Christensen, Mads Græsbøll; Jensen, Søren Holdt.

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - A Fast Algorithm for Maximum Likelihood-based Fundamental Frequency Estimation

AU - Nielsen, Jesper Kjær

AU - Jensen, Tobias Lindstrøm

AU - Jensen, Jesper Rindom

AU - Christensen, Mads Græsbøll

AU - Jensen, Søren Holdt

PY - 2015/9/1

Y1 - 2015/9/1

N2 - PrintRequest PermissionsPeriodic signals are encountered in many applications. Such signals can be modelled by a weighted sum of sinusoidal components whose frequencies are integer multiples of a fundamental frequency. Given a data set, the fundamental frequency can be estimated in many ways including a maximum likelihood (ML) approach. Unfortunately, the ML estimator has a very high computational complexity, and the more inaccurate, but faster correlation-based estimators are therefore often used instead. In this paper, we propose a fast algorithm for the evaluation of the ML cost function for complex-valued data over all frequencies on a Fourier grid and up to a maximum model order. The proposed algorithm significantly reduces the computational complexity to a level not far from the complexity of the popular harmonic summation method which is an approximate ML estimator.

AB - PrintRequest PermissionsPeriodic signals are encountered in many applications. Such signals can be modelled by a weighted sum of sinusoidal components whose frequencies are integer multiples of a fundamental frequency. Given a data set, the fundamental frequency can be estimated in many ways including a maximum likelihood (ML) approach. Unfortunately, the ML estimator has a very high computational complexity, and the more inaccurate, but faster correlation-based estimators are therefore often used instead. In this paper, we propose a fast algorithm for the evaluation of the ML cost function for complex-valued data over all frequencies on a Fourier grid and up to a maximum model order. The proposed algorithm significantly reduces the computational complexity to a level not far from the complexity of the popular harmonic summation method which is an approximate ML estimator.

U2 - 10.1109/EUSIPCO.2015.7362451

DO - 10.1109/EUSIPCO.2015.7362451

M3 - Article in proceeding

T3 - Proceedings of the European Signal Processing Conference

SP - 589

EP - 593

BT - 23rd European Signal Processing Conference (EUSIPCO), 2015

PB - IEEE Press

ER -