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The structured and uniform meshing is the big limitation for the implementation of the two-dimensional digital waveguide model in the modelling of the vocal tract. In other word, the length of each edge of the mesh must be same to keep the same delay lines in the digital waveguide of the vocal tract meshing. The same approach with structured and non-uniform meshing has been used in the current work for the simulations of the two- dimensional waveguide modelling of the vocal tract. For this purpose, two types of delay lines are introduced with the coded names of smaller-and larger-delay lines. The larger-delay lines are chosen as the double of the smaller-delay lines and this approach leads to no need of fractional delays. The effective simulations of sound wave propagation in the two- dimensional waveguide modeling of the vocal tract are also given by this method. In the current work, the construction of the non-uniform rectilinear mesh is bases on the combination of larger-and smaller-delay lines. The vowel /ɔ, /ɑ/, /ɛ/, /i/ and /u/have been chosen for the demonstration of the proposed work. In all vowels of the current work, the central part of the meshing of the vocal tract has been taken with dense mesh while coarser mesh is implemented in the other parts of the meshing. For the validation of the proposed work, the standard two-dimensional waveguide model with the uniform grid is considered as our benchmark model.
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