# Evaluation of Glottal Inverse Filtering Techniques on
## 1 Introduction  
Voice generation based on articulatory speech synthesis has been significantly improved by considering three-dimensional (3D) source-filter models, surpassing the limitations of their one-dimensional counterparts [1, 2]. These advanced models have demonstrated their ability to generate various speech utterances, including vowels [3], diphtongs [4, 5], and vowel-consonant-vowel sequences incorporating fricatives [6, 7]. Despite these accomplishments, the exploration of expressive voice synthesis using these 3D-based numerical simulations is still in its early stages due to its great complexity. In fact, expressiveness in speech, which implies the communication of non-linguistic information about emotions, speaking styles, and mood, among other things, can be conveyed through prosodic (including the modification of the fundamental frequency, F0, duration and energy of phonemes) and voice quality modelling (embracing factors ranging from formant tuning due to vocal tract variations to the modification of the parameters of the glottal source, such as phonation or aspiration noises) (see [8] for a comprehensive review). A preliminary endeavour in this direction was presented by [PERSON] et al. in [9], where the authors introduced a method that modified the spectral tilt of the glottal flow signal produced using the Liljencrants-Fant (LF) model's [10] input to vocal tract geometriesobtained from magnetic resonance imaging [4], aiming to generate happy and aggressive /a/ vowels. Building upon this initial work, a following study emphasised the importance of accurately simulating higher-order modes to achieve expressiveness [11], especially for tense phonations and high fundamental frequencies. Additionally, the manipulation of the vocal tract characteristics using simulations based on finite element methods (FEM) has enabled the production of effects such as the singing formant in 3D-based articulatory voice generation [12]. Therefore, from these works, it can be concluded that, for the production of expressive speech, a proper model and adjustment of the vocal tract response and the glottal source signal is of paramount importance, as is considering their varying relevance depending on the target speaking style [13; 14]. The estimation of the glottal source (GS) and the vocal tract (VT) transfer function from speech signals therefore becomes instrumental. Glottal inverse filtering (GIF) methods have been widely used for this purpose, although alternative approaches based on a joint estimation process have also been proposed [15; 16]. Female voices are known to be especially difficult to analyse compared to males [17], especially due to the higher mean fundamental frequency of the GS as well as the smaller larynx and slightly shorter VT [18], which entail formant-frequency differences between both sexes [19], among other effects. The GIF techniques can be broadly categorized into three main groups, as outlined by [PERSON] et al. [17]: mixed-phase decomposition, iterative and adaptive inverse filtering, and closed-phase inverse filtering. Among the GIF techniques based on mixed-phase decomposition, complex cepstrum decomposition (CCD) [20] and zeros of the z-transform [21] are notable approaches. CCD relies on the cepstral decomposition of the source-filter model; that is, it entails working on the so-called quefrency domain. On the other hand, zeros of the z-transform distinguishes the VT and GS components of speech by analyzing the location of zeros on the unit circle. Zeros inside the unit circle correspond to the VT resonances, while those outside the circle represent the GS response, which contains the maximum-phase component of speech, i.e., the glottal open phase [17]. However, despite the effectiveness of these straightforward approaches, more advanced techniques have emerged, albeit at the cost of increased complexity in their tuning and implementation. The iterative adaptive inverse filtering (IAIF) algorithm proposed by [PERSON] et al.