Joint estimation of vocal tract and nasal tract area functions from speech waveforms via auto-regression moving-average modeling and a pole assignment method

Nasal resonance is utilized in certain languages to differentiate word meanings. The joint filtering effect by the vocal tract and the nasal tract can be modeled by the auto-regression moving-average (ARMA) approach. However, unlike all-pole (i.e., AR) modeling, it has been difficult to derive the equivalent vocal-tract area function directly from an ARMA model due to the nonlinear nature in the relation between model coefficients and vocal-tract geometry. In this paper, we propose a method to decompose an ARMA model approximately into α/C(z) + β/D(z); in our context, 1/C(z) and 1/D(z) represent the filtering effects of the oral and the nasal tract, respectively. Once the decomposition is performed, equivalent oral-tract and nasal-tract area functions can be obtained by converting C(z) and D(z) to their respective lattice representation. The proposed method was applied to non-nasalized and nasalized vowels produced by three speakers, and it was found that the ratio r = β/α tends to be higher in nasalized vowels than in their non-nasalized counterparts. The vocal-tract area function estimated by the present approach was also fairly stable for sustained vowels.