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Abstract

Joint fundamental frequency and model order esti- mation is an important problem in several applications. In this paper, a default estimation algorithm based on a minimum of prior information is presented. The algorithm is developed in a Bayesian framework, and it can be applied to both real- and complex-valued discrete-time signals which may have missing samples or may have been sampled at a non-uniform sampling frequency. The observation model and prior distributions corre- sponding to the prior information are derived in a consistent fashion using maximum entropy and invariance arguments. Moreover, several approximations of the posterior distributions on the fundamental frequency and the model order are derived, and one of the state-of-the-art joint fundamental frequency and model order estimators is demonstrated to be a special case of one of these approximations. The performance of the approximations are evaluated in a small-scale simulation study on both synthetic and real world signals. The simulations indicate that the proposed algorithm yields more accurate results than previous algorithms. The simulation code is available online.
Original languageEnglish
JournalI E E E Transactions on Audio, Speech and Language Processing
Volume21
Issue number3
Pages (from-to)598-610
Number of pages13
ISSN1558-7916
DOIs
Publication statusPublished - Mar 2013

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approximation
time signals
simulation
Invariance
estimators
invariance
Entropy
sampling
entropy
Sampling

Keywords

  • Fundamental frequency estimation
  • Bayesian model comparison
  • Zellner's g-prior

Cite this

@article{4de67ed7abdc4c47a1bb646f0e126cab,
title = "Default Bayesian Estimation of the Fundamental Frequency",
abstract = "Joint fundamental frequency and model order esti- mation is an important problem in several applications. In this paper, a default estimation algorithm based on a minimum of prior information is presented. The algorithm is developed in a Bayesian framework, and it can be applied to both real- and complex-valued discrete-time signals which may have missing samples or may have been sampled at a non-uniform sampling frequency. The observation model and prior distributions corre- sponding to the prior information are derived in a consistent fashion using maximum entropy and invariance arguments. Moreover, several approximations of the posterior distributions on the fundamental frequency and the model order are derived, and one of the state-of-the-art joint fundamental frequency and model order estimators is demonstrated to be a special case of one of these approximations. The performance of the approximations are evaluated in a small-scale simulation study on both synthetic and real world signals. The simulations indicate that the proposed algorithm yields more accurate results than previous algorithms. The simulation code is available online.",
keywords = "Fundamental frequency estimation, Bayesian model comparison, Zellner's g-prior",
author = "Nielsen, {Jesper Kj{\ae}r} and Christensen, {Mads Gr{\ae}sb{\o}ll} and Jensen, {S{\o}ren Holdt}",
year = "2013",
month = "3",
doi = "10.1109/TASL.2012.2229979",
language = "English",
volume = "21",
pages = "598--610",
journal = "IEEE/ACM Transactions on Audio, Speech, and Language Processing",
issn = "2329-9290",
publisher = "IEEE Signal Processing Society",
number = "3",

}

Default Bayesian Estimation of the Fundamental Frequency. / Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt.

In: I E E E Transactions on Audio, Speech and Language Processing, Vol. 21, No. 3, 03.2013, p. 598-610.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Default Bayesian Estimation of the Fundamental Frequency

AU - Nielsen, Jesper Kjær

AU - Christensen, Mads Græsbøll

AU - Jensen, Søren Holdt

PY - 2013/3

Y1 - 2013/3

N2 - Joint fundamental frequency and model order esti- mation is an important problem in several applications. In this paper, a default estimation algorithm based on a minimum of prior information is presented. The algorithm is developed in a Bayesian framework, and it can be applied to both real- and complex-valued discrete-time signals which may have missing samples or may have been sampled at a non-uniform sampling frequency. The observation model and prior distributions corre- sponding to the prior information are derived in a consistent fashion using maximum entropy and invariance arguments. Moreover, several approximations of the posterior distributions on the fundamental frequency and the model order are derived, and one of the state-of-the-art joint fundamental frequency and model order estimators is demonstrated to be a special case of one of these approximations. The performance of the approximations are evaluated in a small-scale simulation study on both synthetic and real world signals. The simulations indicate that the proposed algorithm yields more accurate results than previous algorithms. The simulation code is available online.

AB - Joint fundamental frequency and model order esti- mation is an important problem in several applications. In this paper, a default estimation algorithm based on a minimum of prior information is presented. The algorithm is developed in a Bayesian framework, and it can be applied to both real- and complex-valued discrete-time signals which may have missing samples or may have been sampled at a non-uniform sampling frequency. The observation model and prior distributions corre- sponding to the prior information are derived in a consistent fashion using maximum entropy and invariance arguments. Moreover, several approximations of the posterior distributions on the fundamental frequency and the model order are derived, and one of the state-of-the-art joint fundamental frequency and model order estimators is demonstrated to be a special case of one of these approximations. The performance of the approximations are evaluated in a small-scale simulation study on both synthetic and real world signals. The simulations indicate that the proposed algorithm yields more accurate results than previous algorithms. The simulation code is available online.

KW - Fundamental frequency estimation

KW - Bayesian model comparison

KW - Zellner's g-prior

U2 - 10.1109/TASL.2012.2229979

DO - 10.1109/TASL.2012.2229979

M3 - Journal article

VL - 21

SP - 598

EP - 610

JO - IEEE/ACM Transactions on Audio, Speech, and Language Processing

JF - IEEE/ACM Transactions on Audio, Speech, and Language Processing

SN - 2329-9290

IS - 3

ER -