TY - GEN
T1 - On Harmonic Approximations of Inharmonic Signals
AU - Elvander, Filip
AU - Ding, Jie
AU - Jakobsson, Andreas
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Fundamental frequency estimation
KW - inharmonicity
KW - misspecified Cramér-Rao lower bound
U2 - 10.1109/ICASSP40776.2020.9054139
DO - 10.1109/ICASSP40776.2020.9054139
M3 - Paper in conference proceeding
AN - SCOPUS:85089222292
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5360
EP - 5364
BT - 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
PB - IEEE - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020
Y2 - 4 May 2020 through 8 May 2020
ER -