A Simple, Quasi-linear, Discrete Model of Vocal Fold Dynamics.pdf

A Simple, Quasi-linear, Discrete Model of Vocal Fold Dynamics Max Little1,
, Patrick McSharry2, Irene Moroz1, and Stephen Roberts3 1 Applied Dynamical Systems Research Group, Oxford Centre for Industrial and Applied Mathematics, Oxford University, UK littlem@maths.ox.ac.uk http://www.maths.ox.ac.uk/ads 2 Oxford Centre for Industrial and Applied Mathematics, Oxford University, UK 3 Pattern Analysis Research Group, Engineering Science, Oxford University, UK Abstract. In current speech technology, linear prediction dominates. The linear vocal tract model is well justified biomechanically, and lin- ear prediction is a simple and well understood signal processing task. However, it has been established that, in voiced sounds, the vocal folds exhibit a high degree of nonlinearity. Hence there exists the need for an approach to modelling the behaviour of the vocal folds. This paper presents a simple, nonlinear, biophysical vocal fold model. A comple- mentary discrete model is derived that reflects accurately the energy dynamics in the continuous model. This model can be implemented eas- ily on standard digital signal processing hardware, and it is formulated in such a way that a simple form of nonlinear prediction can be carried out on vocal fold signals. This model could be of utility in many speech technological applications where low computational complexity synthesis and analysis of vocal fold dynamics is required. 1 Introduction The linear signal processing of speech is a well developed science, having a long history of association with the science of linear acoustics. Referring to Fig. 1, the use of linear acoustics is well justified biophysically, since a realistic representa- tion of the vocal organs is obtained by assuming that the influence of the vocal tract is that of an acoustic tube that acts as a linear resonator, amplifying or attenuating the harmonic components of the vocal folds during voiced sounds. This resonator can be represented in discrete-time as a