## 1 Introduction  
Voice can be generated simulating acoustic wave propagation within the vocal tract. For years only plane waves were considered, which allowed the use of 1D vocal tract models to produce a voice of fairly good quality (see e.g., [1, 2]). Nonetheless, the accuracy of 1D models is limited up to about 4-5 kHz, depending on the generated sound (see e.g., [3] which compares vowels and diphthongs generated in 1D and 3D). Beyond this frequency, higher order modes also exist, resulting in resonances and anti-resonances that cannot be predicted in 1D and which strongly modify the high frequency energy (HFE) content of the spectrum [4, 5]. Until now, however, little attention has been paid to the high frequency range. An exception is found in some recent works that point out that HFE may be important for voice quality, speech localisation, speaker recognition, and intelligibility (see [6] and references therein). Plane wave propagation along the vocal tract midline is not a constraint for 3D acoustic models. Some examples of the latter can be found, for instance, in [7] where the finite element method (FEM) was used to study the production of Czech vowels using 3D vocal tracts, reconstructed from magnetic resonance imaging (MRI) data. In [8], a finite-difference time-domain method was adopted to analyse the MRI-based vocal tracts of Japanese vowels. Moreover, the results of the simulations were validated through experiments performed in physical models constructed from the same MRI data. Similarly, in [9], measurements on 3D-printed mechanical replicas presented very close results to those from 3D FEM acoustic simulations on MRI-based vocal tracts. Nevertheless, the use of a 3D acoustic model does not necessarily entail the propagation of higher-order modes. For instance, these will rarely appear in a straight, axisymmetric vocal tract excited at the glottis, as observed in [5]. In fact, several geometric simplifications were analysed in [5] which preserved the cross-sectional areas of the vocal tract but introduced modifications in their cross-sectional shapes and midline curvature. Results showed a similar behaviour for the analysed configurations in frequencies below 4-5 kHz but very large deviations beyond that value. This highlights the limits of the plane wave assumption and also shows that changes in the vocal tract shape modify the HFE content. Nonetheless, there are other important factors that must be considered to determine the HFE content of a voice such as phonation type. In [10] for instance, loud and soft phonations of sustained vowels showed significant differences in HFE content. Moreover, results showed that modifications of HFE levels are more easily detected by listeners in a loud phonation case. In this work, we study the contribution of the glottal source excitation in the 3D numerical synthesis of vowels, paying special attention to HFE content. 3D realistic vocal tracts for vowels [a], [i], and [u] were considered for this purpose, as well as their simplified counterparts consisting of straight ducts of varying circular cross-section [5]. The latter allowed us to mitigate the onset of higher order modes and thus examine their influence on HFE by comparison with the 3D realistic outputs. Vocal tract impulse responses have been computed from FEM simulations in the time domain [11]. Vowels have finally been synthesised by convolving impulse responses with the desired glottal source excitations. An LF (Liljencrants-Fant) model [12] enhanced with aspiration noise has been employed to generate the latter. Although this model does not take into account the interaction between the vocal tract and the vocal folds [13; 14], it has proven useful to explore the phonatory tense-lax continuum [15] by controlling the \(R_{d}\) glottal shape parameter [16]. The \(R_{d}\) parameter has thus been incorporated in the LF model and used to examine different phonation types, ranging from a lax to a tense phonation.