Two-dimensional vocal tracts with three-dimensional behavior in the numerical generation of vowels

Two-dimensional (2D) numerical simulations of vocal tract acoustics may provide a good balance between the high quality of three-dimensional (3D) finite element approaches and the low computational cost of one-dimensional (1D) techniques. However, 2D models are usually generated by considering the 2D vocal tract as a midsagittal cut of a 3D version, i.e., using the same radius function, wall impedance, glottal flow, and radiation losses as in 3D, which leads to strong discrepancies in the resulting vocal tract transfer functions. In this work, a four step methodology is proposed to match the behavior of 2D simulations with that of 3D vocal tracts with circular cross-sections. First, the 2D vocal tract profile becomes modified to tune the formant locations. Second, the 2D wall impedance is adjusted to fit the formant bandwidths. Third, the 2D glottal flow gets scaled to recover 3D pressure levels. Fourth and last, the 2D radiation model is tuned to match the 3D model following an optimization process. The procedure is tested for vowels /a/, /i/, and /u/ and the obtained results are compared with those of a full 3D simulation, a conventional 2D approach, and a 1D chain matrix model.