## 3 Proposed Method
### \(F_{0}\) Contour Modeling
#### 3.1.2 Sampling-Based Representation of \(F_{0}\)  
Several studies have used parametric models, such as the Fujisaki model and DCT [26; 39; 40]. [PERSON] et al. [39] used the Fujisaki model to generate contours of \(F_{0}\) without any modification, but this model does not perform as well as rule-based and frame-based approaches. This suggests that the parameters of the Fujisaki model are complex and challenging to predict. [PERSON] et al. [40] used coefficients of DCT to represent the template of an \(F_{0}\) contour, but this approach still requires frame-level features to generate a smooth output of the \(F_{0}\) contour. Instead of converting values of \(F_{0}\) into parameters of other domains (e.g., the Fujisaki model and DCT), we propose a sampling-based approach to represent the \(F_{0}\) contour. The main idea of the sampling-based model of \(F_{0}\) is to represent the \(F_{0}\) contour within syllables by sampling it with an appropriate number of points. Dynamic features are included to provide temporal information concerning values of \(F_{0}\) in the given syllable and adjacent syllables. The use of dynamic features guarantees that the sampling-based method can produce a smooth output of the \(F_{0}\) contour. The output of the process is used as features for training the RNN. Details of the proposed method of representation of \(F_{0}\) are described as follows. Before modeling a given \(F_{0}\) contour, interpolation and smoothing must be performed. The interpolation process fills artificial values of \(F_{0}\) between its intermediate values where unvoiced speech segments or short pauses occur. The unusual values of \(F_{0}\) (e.g., error points and micro-prosody) from regions of unvoiced speech are eliminated automatically using the phoneme region described in \begin{table}
\begin{tabular}{l l} \hline \hline
**Feature Category** & **Description** \\ \hline Tone features & Tone identities of previous/current/next syllable. \\ \hline Duration feature & Duration of current syllable. \\  & Duration of initial consonant/vowel/final consonant of current syllable. \\ \hline Phoneme features & Phoneme identities of initial consonant/vowel/final consonant of current syllable. \\  & Phoneme categories of initial consonant/vowel/final consonant of current syllable. \\ \hline Positional features & Position of the current syllable in the current word. \\  & Number of syllables in the current phrase. \\  & Position of the current syllable in the current intermediate phrase. \\  & Number of syllables in the current phrase. \\  & Position of the current syllable in the current intermediate phrase. \\  & Number of syllables in the current intermediate phrase. \\  & Position of the current word in the current phrase. \\  & Number of words in the current phrase. \\  & Position of the current word in the current intermediate phrase. \\  & Number of words in the current intermediate phrase. \\  & Position of the current phrase in the utterance. \\  & Number of words in the current phrase. \\  & Position of the current intermediate phrase in the current phrase. \\  & Number of intermediate phrases in the current phrase. \\  & Syllable section in the current word (silence, single, begin, middle, end). \\  & Syllable section in the current intermediate phrase (silence, single, begin, middle, end). \\  & Syllable section in the current phrase (silence, single, begin, middle, end). \\  & Word section in the current intermediate phrase (silence, single, begin, middle, end). \\  & Word section in the current phrase (silence, single, begin, middle, end). \\  & Intermediate phrase section in the current phrase (silence, single, begin, middle, end). \\  & Phase section in the utterance (silence, single, begin, middle, end). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Linguistic features for training the proposed model. the label files. Unvoiced speech segments are interpolated using piecewise cubic interpolation [41] and smoothed by a median filter. Note that we manipulate \(F_{0}\) in the logarithmic domain.