## 3 Preliminaries  
In this Section, we describe and discuss some preliminary considerations that are founding our research.  
In this work, we generate synthetic speech with the well known Cascade-Parallel formant synthesizer [46]. The synthesizer is driven by the following minimum set of eight acoustic parameters: \((AV,AF,F1,F2,F3,B1,B2,B3)\), namely the amplitudes for voicing and frication, three formant frequencies with the respective bands. It is well known that this is a quite old yet very simple approach to produce artificial speech. Indeed, the speech obtained in this way does not sound natural but rather, it is perceived as highly robotic.  
The talking head produces artificial speech from unrestricted text. One of the first attempts to generate speech from arbitrary text is synthesis from concatenation approach [47], where sets of basic speech units are defined. Each speech unit contains at least a transition between phonemes (diphone).  
In conclusion, our unrestricted text is generated by diphone concatenation where each diphone (transition) is modeled with the minimum set of eight acoustic parameters. The motivation of this simple approach is that, as regards the small number of parameters which drive the synthesizer to produce transitions, the small number of acoustic parameters simplify the fuzzy rule development process. As regards the diphone concatenation approach, by concatenation of basic speech units, the motivation is that that the goal of this work is not to produce good artificial speech but to estimate good articulatory parameters, and concatenated speech is enough for that purpose.  
In Figure 3 we show an example of transition of the first formant frequency between the two phonemes in a speech unit. For simplicity, each of the speech units we selected contain a single transition, thus leading to the minimum set of speech units for speech generation. In our set, we consider consonant-vowel and vowel-consonant transitions, affricate-vowel and vowel-affricate transitions and diphthongs transitions. The total number of basic speech units is 192, namely 140 consonant-vowel transitions and viceversa, 20 affricate-vowels transition and viceversa, 10 vowel-silence transitions and viceversa, 8 diphthongs, that is, vowel-vowel transitions and 14 transitions between silence and a consonant.  
As shown in Figure 3, any transition is described by the _Initial, Duration, Final_ and _Locus_ values, we call \([I(.),D(.),F(.)L_{1}(.),L_{2}(.)]\).  
Using the \([I(.),D(.),F(.)L_{1}(.),L_{2}(.)]\) parameters, the transitions can be easily concatenated. An example of concatenation of two trajectories is shown in Figure 4.  
Along with the acoustic parameters that are used to synthesize the signal, we also store in the knowledge base the corresponding articulation configurations. The acoustic parameters are the transitions of formants and amplitudes (i.e., \([I(.),D(.),F(.)L_{1}(.),L_{2}(.)]\)). We considered the following twelve places of articulation: _(rounded, open, front, voiced, bilabial, labidotental, alveolar, prepalatal, palatal, vibrant, dental, velar)_.  
Articulatory parameters are the genetically optimized degrees of membership of the places of articulation. The knowledge base of articulatory parameters is reported in Figure 5. Therefore, the knowledge base describes the membership values of all the possible transitions in the selected language for the operator who acts as trainer. Please note that the symbol _Sil_ means silence (therefore _/Sil-a/_ is an initial part of a sentence starting with the _/a/_ vowel). Moreover, note that the symbols on the vertical axis are selected from the IPA alphabet.  
Figure 4: Formant trajectories concatenation example.  
Figure 5: Basic speech units knowledge base.  
Figure 3: F1 transition trajectory example.