## 2 Methodology
### Voice Source Signal  
Voice source signals were generated according to the LF model [12]. Specifically, [PERSON]'s implementation [22] was chosen to obtain aliasing-free glottal flow derivative waveforms \(u^{\prime}_{g}(t)\). The shape of a glottal pulse is controlled by the parameters \(T_{p}\), \(T_{e}\), \(T_{a}\), \(T_{c}\), and \(T_{0}\) (see Figure 3). Figure 2: Vocal tract transfer function magnitude \(|H(f)|\) of vowels [a], [i], and [u] for realistic and simplified vocal tract geometries. However, this control can be simplified as described in the transformed LF model [16]. The latter reduces parameter redundancy in the glottal pulse description. To this end, a global waveshape parameter, \(R_{d}\), is introduced as:  
\[R_{d}=\frac{T_{d}}{T_{0}}\frac{1}{110}=\frac{U_{0}}{E_{e}}\frac{F0}{110}\quad, \tag{4}\]  
where \(T_{d}\) is the declination time, \(T_{0}\) the period, and \(F0\) the fundamental frequency. The declination time \(T_{d}\) corresponds to the quotient between the glottal flow peak \(U_{0}\) and the negative amplitude of the differentiated glottal flow \(E_{e}\). The scale factor was chosen so as to make the numerical value of \(R_{d}\) the same as the declination time in seconds for \(F0=110\) Hz [16]. The glottal shape parameter \(R_{d}\) was integrated into [PERSON]'s implementation, thereby allowing us to simulate from a tense, very adducted phonation (\(R_{d}=0.3\)) to a lax, very abducted phonation (\(R_{d}=2.7\)). \(T_{p}\), \(T_{e}\), and \(T_{a}\) are derived from \(R_{d}\) according to the equations in [16] and \(T_{c}\) is set to \(T_{0}\). The glottal flow \(u_{g}(t)\) is computed by performing the cumulative integration of \(u_{g}^{\prime}(t)\) using the composite trapezoidal rule [23]. Furthermore, the voice source model was extended to incorporate aspiration noise, \(S_{AH}(t)\), which is added to the glottal flow \(u_{g}(t)\). To this end, the method presented in [24] was implemented. This consists of automatically generating the temporal dynamics of \(S_{AH}(t)\) according to the voice source parameters as follows:  
\[S_{AH}(t)=AH\ E_{e}^{1.35}F0^{1.05}\ n(t)\sqrt{\frac{U_{ac}}{U_{0}}u_{g}(t)+U_{ dc}}, \tag{5}\]  
where \(U_{ac}=(379/R_{d})-91,\ U_{dc}=83T_{d}+34\) and \(T_{d}=110\ T_{0}R_{d}\), according to [24]. The noise amplitude factor \(AH\) was perceptually adjusted to \(3\times 10^{-14}\). The noise signal \(n(t)\) was generated by filtering white Gaussian noise with a 2 nd order Butterworth bandpass filter with cutoff frequencies of 300 and 3000 Hz as in [1]. Finally, a SoX resampling ([[http://sox.sourceforge.net/SoX/Resampling](http://sox.sourceforge.net/SoX/Resampling)]([http://sox.sourceforge.net/SoX/Resampling](http://sox.sourceforge.net/SoX/Resampling))) was incorporated to adapt the glottal flow signals originally generated at 44,100 Hz to the sampling rate at which the speech signals were synthesised (24 kHz). The glottal flow signals generated for this work cover the \(R_{d}\) range \([0.3,2.7]\)[16], considering 49 logarithmically spaced values of \(R_{d}\) (24 steps from 0.3 to 1 and 24 more steps from 1 to 2.7). Regarding \(F0\), a pitch contour was extracted from a real sustained vowel lasting for 2 s. This curve was successively pitch-shifted from a \(F0\) mean value of 75.6 Hz to 240 Hz in 81 steps of 0.25 semitones, thereby covering the male speech range [25]. For each possible combination of \(R_{d}\) and \(F0\) values, two glottal flow versions were obtained with and without aspiration noise. The pulse amplitude, \(U_{0}\), was selected to have 70 dBSPL with the realistic geometry, \(F0=120\) Hz and \(R_{d}=1\), which resulted in values \(U_{0}=6.296\times 10^{-5}\) m\({}^{3}\)/s for vowel [a], \(U_{0}=3.455\times 10^{-5}\) m\({}^{3}\)/s for [i] and \(U_{0}=6.657\times 10^{-5}\) m\({}^{3}\)/s for [u]. Figure 3: Glottal flow \(u_{g}(t)\) and its time derivative \(u_{g}^{\prime}(t)\) according to the LF (Liljencrants–Fant) model [12].