## 5 Evaluation Results and Discussion
### Objective Evaluation
#### 5.1.4 Phase Distortion Deviation  
Recent progress in synthesized speech showed that the phase distortion of the signal carries all of the crucial information relevant to the shape of glottal pulses [71]. As the noise component in our continuous vocoder is parameterized in terms of time envelopes and computed for every pitch-synchronous residual frame, we compared the vocoded sentences to the natural and baseline by measuring mean phase distortion deviation (M-PDD). Originally, PDD could be calculated based on early [PERSON]'s standard-deviation [72]. However, [71] showed two issues related to variance and source shape in voiced segments. By avoiding these limitations, M-PDD can be estimated in this experiment at 5 ms frame shift as  
\[MPDD=\mu_{i}(f)=\lambda\left(\frac{1}{N}\sum_{n\in C}e^{jPD_{n}(f)}\right) \tag{29}\]  
where \(C=\left\{i-\frac{N-1}{2},\ldots,i+\frac{N-1}{2}\right\}\), \(N\) is the number of frames, PD is the phase difference between two consecutive frequency components, and we denote the phase by \(\angle\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Pitch Algorithm** \\ \hline Proposed \#1 & adContF0-based adaptive Kalman filter \\ Proposed \#2 & adContF0-based adaptive Time-warping \\ Proposed \#3 & adContF0-based adaptive StoneMask \\ \hline \hline \end{tabular}
\end{table}
Table 4: An overview of the three proposed methods based on HNR parameters.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Metric** & **Speaker** & **Baseline** & **Proposed\#1** & **Proposed\#2** & **Proposed\#3** & **STRAIGHT** \\ \hline \multirow{3}{*}{fwSNRseg} & BDL & 8.083 & 11.812 & 11.807 & 13.033 & 15.062 \\  & JMK & 6.816 & 9.505 & 9.784 & 10.621 & 13.094 \\  & SLT & 7.605 & 9.906 & 9.736 & 11.079 & 15.295 \\ \hline \multirow{3}{*}{NCM} & BDL & 0.650 & 0.850 & 0.854 & 0.913 & 0.992 \\  & JMK & 0.620 & 0.847 & 0.860 & 0.906 & 0.963 \\  & SLT & 0.673 & 0.850 & 0.854 & 0.910 & 0.991 \\ \hline \multirow{3}{*}{ESTOI} & BDL & 0.642 & 0.856 & 0.861 & 0.892 & 0.923 \\  & JMK & 0.620 & 0.831 & 0.847 & 0.873 & 0.895 \\  & SLT & 0.679 & 0.848 & 0.846 & 0.894 & 0.945 \\ \hline \multirow{3}{*}{LLR} & BDL & 0.820 & 0.457 & 0.456 & 0.453 & 0.219 \\  & JMK & 0.814 & 0.635 & 0.631 & 0.628 & 0.391 \\  & SLT & 0.744 & 0.639 & 0.640 & 0.636 & 0.194 \\ \hline \multirow{3}{*}{WSS} & BDL & 48.569 & 32.875 & 32.559 & 24.013 & 22.144 \\  & JMK & 51.788 & 36.236 & 32.175 & 26.238 & 29.748 \\ \cline{1-1}  & SLT & 58.043 & 42.789 & 45.254 & 26.906 & 23.614 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average scores performance based on synthesized speech signal per each speaker.  
Figure 9 shows the means of the PDD values of the three speakers grouped by the 6 variants. As can be seen, the M-PDD values of the baseline system are significantly lower in BDL and SLT speakers and higher in JMK speaker compared to natural speech. It can also be noted from the JMK speaker that proposed #3 appears to match the M-PDD value of natural speech, followed by proposed #2. Similarly, the closed M-PDD value to natural speech is shown in proposed #3 and #2 for the female speaker. For the BDL speaker, proposed #3 is the only one that is not different from the natural samples, while the others seem to give lower M-PDD values. In summary, the various experiments result in different M-PDD values, but in general they are closer to the natural speech than the STRAIGHT and baseline vocoders.