Estimating parameters in multichannel fundamental frequency with harmonics model

Abstract

In this paper, we introduce a special multichannel model in the class of multichannel sinusoidal model. In multichannel sinusoidal model, the inherent frequencies from distinct channels are the same with different amplitudes. The underlying assumption here is that there is a fundamental frequency that is the same in each channel and the effective frequencies are harmonics of this fundamental frequency. We name this model as multichannel fundamental frequency with harmonics model. It is assumed that the errors in individual channel are independently and identically distributed whereas the signal from different channels are correlated. We propose generalized least squares estimators which become the maximum likelihood estimators also, when the error distribution of the different channels follows a multivariate Gaussian distribution. The proposed estimators are strongly consistent and asymptotically normally distributed. We have provided the implementation of the generalized least squares estimators in practice. Special attention has been taken when the number of channels is two and both have equal number of components. Simulation experiments have been carried out to observe the performances of the proposed estimators. Real data sets have been analysed using a two-channel fundamental frequency model.

Keywords:

• Multichannel model
• fundamental frequency model
• least squares estimator
• generalized least squares estimators
• consistency
• asymptotic normality

Mathematics Subject Classifications:

• 62J02
• 62E20
• 62C05

Acknowledgements

The authors would like to thank the Associate editor and two reviewers for their constructive comments, which have helped to improve the manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the author(s).