Real-time dynamic articulations in the 2-D waveguide mesh vocal tract model

Time domain articulatory vocal tract modeling in one-dimensional (1-D) is well established. Previous studies into two-dimensional (2-D) simulation of wave propagation in the vocal tract have shown it to present accurate static vowel synthesis. However, little has been done to demonstrate how such a model might accommodate the dynamic tract shape changes necessary in modeling speech. Two methods of applying the area function to the 2-D digital waveguide mesh vocal tract model are presented here. First, a method based on mapping the cross-sectional area onto the number of waveguides across the mesh, termed a widthwise mapping approach is detailed. Discontinuity problems associated with the dynamic manipulation of the model are highlighted. Second, a new method is examined that uses a static-shaped rectangular mesh with the area function translated into an impedance map which is then applied to each waveguide. Two approaches for constructing such a map are demonstrated; one using a linear impedance increase to model a constriction to the tract and another using a raised cosine function. Recommendations are made towards the use of the cosine method as it allows for a wider central propagational channel. It is also shown that this impedance mapping approach allows for stable dynamic shape changes and also permits a reduction in sampling frequency leading to real-time interaction with the model.