A vocal tract model based on a digital waveguide is presented in which the vocal tract has been decomposed into uniform cylindrical segments of variable lengths. We present a model for the real-time numerical solution of the digital waveguide equations in a uniform tube with the temporally varying cross section. In the current work, the uniform cylindrical segments of the vocal tract may have their different lengths, the time taken by the sound wave to propagate through a cylindrical segment in an axial direction may not be an integer multiple of each other. In such a case, the delay in an axial direction is necessarily a fractional delay. For the approximation of fractional-delay filters, Lagrange interpolation is used in the current model. Variable length of the individual segment of the vocal tract enables the model to produce realistic results. These results are validated with accurate benchmark model. The proposed model has been devised to elongate or shorten any arbitrary cylindrical segment by a suitable scaling factor. This model has a single algorithm and there is no need to make section of segments for elongation or shortening of the intermediate segments. The proposed model is about 23% more efficient than the previous model.

Simulation of wave propagation in the three-dimensional (3D) modeling of the vocal tract has shown significant promise for enhancing the accuracy of speech production. Recent 3D waveguide models of the vocal tract have been designed for better accuracy but require a lot of computational tasks. A high computational cost in these models leads to novel work in reducing the computational cost while retaining accuracy and performance. In the current work, we divide the geometry of the vocal tract into four equal symmetric parts with the introduction of two axial perpendicular planes, and the simulation is performed on only one part. A novel strategy is defined to implement symmetric conditions in the mesh. The complete standard 3D digital waveguide model is assumed as a benchmark model. The proposed model is compared with the benchmark model in terms of formant frequencies and efficiency. For the demonstration, the vowels /O/, /i/, /E/, /A/, and /u/ have been selected for the simulations. According to the results, the benchmark and current models are nearly identical in terms of frequency profiles and formant frequencies. Still the current model is three times more effective than the benchmark model.