Fast fundamental frequency estimation: Making a statistically efficient estimator computationally efficient

Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper; Christensen, Mads Græsbøll; Jensen, Søren Holdt

doi:10.1016/j.sigpro.2017.01.011

Cited by 54 publications

(79 citation statements)

References 28 publications

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“…Signals displaying harmonic structures arise in a wide set of applications, ranging from speech processing [1] to machinery fault detection [2], with the fundamental frequency, or pitch [3], often being used as a characterizing feature for the signal [4]. The problem of finding statistically efficient, as well as computationally feasible [5], estimators of the fundamental frequency constitutes an active field of research, including recent efforts for addressing multi-pitch signals [6], [7]. The assumption underlying the derivation of such methods is that of perfect harmonicity, i.e., the frequencies of the sinusoids constituting each pitch group should be exact integer multiples of a corresponding fundamental [3].…”

Section: Introductionmentioning

confidence: 99%

On Harmonic Approximations of Inharmonic Signals

Elvander

Ding

Jakobsson

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this work, we present the misspecified Gaussian Cramér-Rao lower bound for the parameters of a harmonic signal, or pitch, when signal measurements are collected from an almost, but not quite, harmonic model. For the asymptotic case of large sample sizes, we present a closed-form expression for the bound corresponding to the pseduo-true fundamental frequency. Using simulation studies, it is shown that the bound is sharp and is attained by maximum likelihood estimators derived under the misspecified harmonic assumption. It is shown that misspecified harmonic models achieve a lower mean squared error than correctly specified unstructured models for moderately inharmonic signals. Examining voices from a speech database, we conclude that human speech belongs to this class of signals, verifying that the use of a harmonic model for voiced speech is preferable.

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Section: Introductionmentioning

confidence: 99%

On Harmonic Approximations of Inharmonic Signals

Elvander

Ding

Jakobsson

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…YIN and RAPT compute autocorrelation functions from short frames of sound signals in the time domain. However, they are not robust against noise [13] and suffer from pitch octave errors (that is, a rational multiple of the true pitch) [3]. To reduce the pitch octave errors, SWIPE uses the cross-correlation function against a sawtooth signal combined with the spectrum of the signal, and exploits only the first and prime harmonics of the signal.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, by adopting a fully Bayesian approach to model weights and observation noise variances, the overfitting can be avoided. By assigning a proper transition pdf for the weights, fast NLS [13] can be easily incorporated into the proposed algorithm, leading to low computational and storage complexities.…”

Section: Introductionmentioning

confidence: 99%

Robust Bayesian Pitch Tracking Based on the Harmonic Model

Shi

Nielsen

Jensen

et al. 2019

IEEE/ACM Trans. Audio Speech Lang. Process.

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Fundamental frequency is one of the most important characteristics of speech and audio signals. Harmonic modelbased fundamental frequency estimators offer a higher estimation accuracy and robustness against noise than the widely used autocorrelation-based methods. However, the traditional harmonic model-based estimators do not take the temporal smoothness of the fundamental frequency, the model order, and the voicing into account as they process each data segment independently. In this paper, a fully Bayesian fundamental frequency tracking algorithm based on the harmonic model and a first-order Markov process model is proposed. Smoothness priors are imposed on the fundamental frequencies, model orders, and voicing using first-order Markov process models. Using these Markov models, fundamental frequency estimation and voicing detection errors can be reduced. Using the harmonic model, the proposed fundamental frequency tracker has an improved robustness to noise. An analytical form of the likelihood function, which can be computed efficiently, is derived. Compared to the state-of-the-art neural network and non-parametric approaches, the proposed fundamental frequency tracking algorithm has superior performance in almost all investigated scenarios, especially in noisy conditions. For example, under 0 dB white Gaussian noise, the proposed algorithm reduces the mean absolute errors and gross errors by 15% and 20% on the Keele pitch database and 36% and 26% on sustained /a/ sounds from a database of Parkinson's disease voices. A MATLAB version of the proposed algorithm is made freely available for reproduction of the results 1 .

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“…Cristensen et al [6] proposed joint estimation of fundamental frequency and number of harmonics based on MUSIC criterion. Recently, Nielsen et al [14] provided a computationally efficient estimator of the unknown parameters of the model (1). A more general model with presence of multiple fundamental frequencies has been considered by Christensen et al [7] and Zhou [16].…”

Section: Introductionmentioning

confidence: 99%

Estimating the fundamental frequency using modified Newton–Raphson algorithm

Nandi

Kundu

2018

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In this paper, we propose a modified Newton-Raphson algorithm to estimate the frequency parameter in the fundamental frequency model in presence of an additive stationary error. The proposed estimator is super efficient in nature in the sense that its asymptotic variance is less than the asymptotic variance of the least squares estimator.With a proper step factor modification, the proposed modified Newton-Raphson algorithm produces an estimator with the rate O p (n − 3 2 ), the same rate as the least squares estimator. Numerical experiments are performed for different sample sizes, different error variances and for different models. For illustrative purposes, two real data sets are analyzed using the fundamental frequency model and the estimators are obtained using the proposed algorithm.It is observed the model and the proposed algorithm work quite well in both cases.2000 Mathematics Subject Classification. 62J02; 62E20; 62C05.

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Fast fundamental frequency estimation: Making a statistically efficient estimator computationally efficient

Cited by 54 publications

References 28 publications

On Harmonic Approximations of Inharmonic Signals

On Harmonic Approximations of Inharmonic Signals

Robust Bayesian Pitch Tracking Based on the Harmonic Model

Estimating the fundamental frequency using modified Newton–Raphson algorithm

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