Bayesian modelling of the speech spectrum using mixture of Gaussians

This paper presents a method for modelling the speech spectral envelope using a mixture of Gaussians (MOG). A novel variational Bayesian (VB) framework for Gaussian mixture modelling of a histogram enables the derivation of an objective function that can be used to simultaneously optimise both model parameter distributions and model structure. A histogram representation of the STRAIGHT spectral envelope, which is free of glottal excitation information, is used for parametrisation using this MOG model. This results in a parameterisation scheme that purely models the vocal tract resonant characteristics. Maximum likelihood (ML) and variational Bayesian (VB) solutions of the mixture model on histogram data are found using an iterative algorithm. A comparison between ML-MOG and VB-MOG spectral modelling is carried out using spectral distortion measures and mean opinion scores (MOS). The main advantages of VB-MOG highlighted in this paper include better modelling using fewer Gaussians in the mixture resulting in better correspondence of Gaussians and formant-like peaks, and an objective measure of the number of Gaussians required to best fit the spectral envelope.