Printed and finite element models.

<p>(A) Different views of the 3D-printed model of /a/. (B), (C) and (D) Finite element models of /a/, /u/ and /i/. For each model, the surface was partitioned into three regions representing the glottis, the lip region and the vocal tract walls.</p

How to precisely measure the volume velocity transfer function of physical vocal tract models by external excitation

<div><p>Recently, 3D printing has been increasingly used to create physical models of the vocal tract with geometries obtained from magnetic resonance imaging. These printed models allow measuring the vocal tract transfer function, which is not reliably possible in vivo for the vocal tract of living humans. The transfer functions enable the detailed examination of the acoustic effects of specific articulatory strategies in speaking and singing, and the validation of acoustic plane-wave models for realistic vocal tract geometries in articulatory speech synthesis. To measure the acoustic transfer function of 3D-printed models, two techniques have been described: (1) excitation of the models with a broadband sound source at the glottis and measurement of the sound pressure radiated from the lips, and (2) excitation of the models with an external source in front of the lips and measurement of the sound pressure inside the models at the glottal end. The former method is more frequently used and more intuitive due to its similarity to speech production. However, the latter method avoids the intricate problem of constructing a suitable broadband glottal source and is therefore more effective. It has been shown to yield a transfer function similar, but not exactly equal to the volume velocity transfer function between the glottis and the lips, which is usually used to characterize vocal tract acoustics. Here, we revisit this method and show both, theoretically and experimentally, how it can be extended to yield the precise volume velocity transfer function of the vocal tract.</p></div

Theoretical model of the measurement setup.

<p>Equivalent acoustic circuits for the measurement situations in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193708#pone.0193708.g001" target="_blank">Fig 1A and 1B</a>, respectively.</p

Amplitudes in dB of the simulated and measured transfer functions and their absolute deviations in dB.

<p>Amplitudes in dB of the simulated and measured transfer functions and their absolute deviations in dB.</p

Formant frequencies in Hz of the simulated and measured transfer functions and their relative deviations in %.

<p>Formant frequencies in Hz of the simulated and measured transfer functions and their relative deviations in %.</p

Bandwidths in Hz of the simulated and measured transfer functions and their absolute deviations in Hz.

<p>Bandwidths in Hz of the simulated and measured transfer functions and their absolute deviations in Hz.</p

Experimental setup for measuring the vocal tract transfer function.

<p>(A) The mouth of the vocal tract model is open and the pressure <i>P</i>₁ is measured at the glottis. (B) The mouth of the model is closed and the pressure <i>P</i>₃ is measured right in front of the closed mouth.</p

Experimentally determined pressure ratios at the lips.

<p>Ratio of the pressure spectra measured in front of the closed mouth (<i>P</i>₃) and without the models (<i>P</i>_ref) for all four models.</p

Calculated measures.

<p>Transfer functions <i>P</i>₁/<i>P</i>₃, <i>P</i>₁/<i>P</i>_ref, and the simulated transfer functions <i>H</i>_FEM for the models /a/ (A), /u/ (B), /i/ (C) and /Ə/ (D).</p

Measured signals.

<p>Spectra of pressure signals measured at the glottis (<i>P</i>₁), in front of the closed mouth (<i>P</i>₃) and without the models (<i>P</i>_ref) for the models /a/ (A), /u/ (B), /i/ (C) and /Ə/ (D).</p