## 2 Analysis-by-Synthesis Methodology  
Figure 2 depicts the proposed GlottDNN-based analysis-by-synthesis methodology designed to evaluate the contribution of both the vocal tract and the glottal source spectral cues to the synthesis of expressive speech vowels. Specifically, the analysis of expressive speech is based on the inverse filtering of a parallel speech corpus composed of utterances in the expressive style of interest, as well as their neutral counterparts (as reference). In order to focus exclusively on the voice quality differences between expressive and neutral speech, the prosody from the expressive utterance (F0, duration, and energy) is transplanted into the corresponding neutral pair. The resulting utterance is considered as the baseline in the comparisons between the different synthesis configurations, labelled as GSS\({}_{\mathrm{X}}\)VT\({}_{\mathrm{Y}}\), where \(X\) and \(Y\) denote the origin of the GSS and VT cues applied to the utterance vowels, respectively, which can be either borrowed from the time-scaled neutral utterance (N), or from the target expressive component (E).  
The main steps of the process are described as follows. As a first step, the GlottDNN vocoder is applied to parameterise each speech frame of the neutral-expressive utterance pair (see Figure 2b), obtaining their fundamental frequency (F0 in Hz) and energy (EN in dB). Moreover, the corresponding glottal source and VT cues are estimated through a quasi-closed phase (QCP) inverse filtering approach, whose result is subsequently parameterised using line spectral frequencies (LSF). Moreover, the harmonic-to-noise ratio (HNR) of the glottal source estimate is also computed at the frame level (the reader is referred to [21] for further details of this process). It is worth noting that the obtained QCP-based spectral tilt is compensated for to minimise the presence of residual spectral cues from the glottal source on the vocal tract estimation, following [22].  
Secondly, the prosody of the neutral utterance is replaced by the one borrowed from its expressive pair. To this aim, the neutral GlottDNN-based features (marked with \({}^{\prime}\) on Figure 2a) are time scaled to fit the expressive target according to the temporal alignment obtained through dynamic time warping. Next, F0\({}_{\mathrm{N}}\) and EN\({}_{\mathrm{N}}\) are respectively replaced by the corresponding values from the expressive utterance, i.e., F0\({}_{\mathrm{E}}\) and EN\({}_{\mathrm{E}}\). Finally, depending on the tested combination, GSS\({}_{\mathrm{E}}\) and/or VT\({}_{\mathrm{E}}\) are also transplanted into the neutral vowels.  
The final step corresponds to the GlottDNN-based expressive synthesis. Following [21], the parameters of voiced frames are inserted into a simple feed-forward deep neural network to generate a zero-padded, two-pitch-period, glottal flow-derivative pulse, while a white noise excitation is used for unvoiced frames. The amplitude of these excitation signals is adjusted to fit EN\({}_{\mathrm{E}}\) and concatenated through the classic pitch-synchronous overlap and add algorithm [39]. Subsequently, the HNR\({}_{\mathrm{N}}\) parameter is used to adjust the noise component of the excitation in the spectral domain, besides modifying its spectrum to match the target \(\text{GSS}_{X}\). Finally, the excitation signal is filtered according to the considered \(\text{VT}_{\text{Y}}\) to obtain the synthetic speech output. The GlottDNN-based pulse generation model trained with the neutral speech corpus and \(\text{HNR}_{\text{N}}\) are considered in the synthesis of the expressive utterances. This is due to the fact that the designed analysis methodology only focuses on evaluating the spectral characteristics of the glottal source, leaving the analysis of these two features of the glottal source for future works.