Application of a Non-Uniform Structured Mesh in a Three-Dimensional Digital Waveguide Model of the Vocal Tract

Abstract

For accurate modelling of the vocal tract, higher dimensional digital waveguide modeling is being used successfully with the structured and uniform grid of the same delay lines. The current work extends the standard methodology in the three-dimensional digital waveguide model using the structured and non-uniform mesh. In the previous work, the delay lines were the same due to uniform grid orientation. However, the current work typically introduces two specific types of delay lines coded with smaller- and larger-delay lines. To eliminate fractional delay for the transfer function of the vocal tract, the larger-delay line is generated by considering the double of the smaller-delay line. This approach also performs efficient simulations of wave propagation in a digital three-dimensional waveguide model of the vocal tract. In this work, the non-uniform rectilinear grid is generated by using the blend of larger- and smaller-delay lines with the various combinations in the directional axes. For example, the larger-delay lines may be operated solely along the x-axis, while the smaller-delay lines are used in the y- and z-axes. Another example may be taken by the using of larger-delay lines in both x- and y-axes and smaller-delay lines in the z-axis. For the practical demonstration of the present work, the vowels /ɔ/ and /ɑ/ have been taken for the simulations and comparison has been given by the standard three-dimensional digital waveguide model which is considered our benchmark model.