Finite element computation of elliptical vocal tract impedances using the two-microphone transfer function method
This work provides a computational tool for speech acoustics researchers, but it is incremental as it adapts an existing method to a numerical context with specific optimizations.
The paper adapted the experimental two-microphone transfer function method to numerically compute radiation and input impedances for three-dimensional vocal tracts with elliptical cross sections, addressing issues like wall absorption and frequency range extension, and demonstrated results for vowels /a/, /i/, and /u/.
The experimental two-microphone transfer function method (TMTF) is adapted to the numerical framework to compute the radiation and input impedances of three-dimensional vocal tracts of elliptical cross section. In its simplest version, the TMTF method only requires measuring the acoustic pressure at two points in an impedance duct and the postprocessing of the corresponding transfer function. However, some considerations are to be taken into account when using the TMTF method in the numerical context, which constitute the main objective of this paper. In particular, the importance of including absorption at the impedance duct walls to avoid lengthy numerical simulations is discussed and analytical complex axial wave numbers for elliptical ducts are derived for this purpose. It is also shown how the plane wave restriction of the TMTF method can be circumvented to some extent by appropriate location of the virtual microphones, thus extending the method frequency range of validity. Virtual microphone spacing is also discussed on the basis of the so called singularity factor. Numerical examples include the computation of the radiation impedance of vowels /a/, /i/ and /u/ and the input impedance of vowel /a/, for simplified vocal tracts of circular and elliptical cross sections.