How far are vowel formants from computed vocal tract resonances?
  We compare numerically computed resonances of the human vocal tract with formants that have been extracted from speech during vowel pronunciation. The geometry of the vocal tract has been obtained by MRI from a male subject, and the corresponding speech has been recorded simultaneously. The resonances are computed by solving the Helmholtz partial differential equation with the Finite Element Method (FEM).   Despite a rudimentary exterior space acoustics model, i.e., the Dirichlet boundary condition at the mouth opening, the computed resonance structure differs from the measured formant structure by $\approx$ 0.7 semitones for [i] and [u] having small mouth opening area, and by $\approx$ 3 semitones for vowels [a] and [ae] that have a larger mouth opening. The contribution of the possibly open velar port has not been taken into considaration at all which adds the discrepancy for [a] in the present data set. We conclude that by improving the exterior space model and properly treating the velar port opening, it is possible to computationally attain four lowest vowel formants with an error less than a semitone. The corresponding wave equation model on MRI-produced vocal tract geometries is expected to have a comparable accuracy. 
Daniel Aalto, Antti Huhtala, Atle Kivel\"a, Jarmo Malinen, Pertti   Palo, Jani Saunavaara, Martti Vainio
math.DS cs.SD