# Evaluation of Glottal Inverse Filtering Techniques on
## 4 Results
### Global Results  
Figure 2 depicts the global boxplot distributions of the evaluation error metrics for the speech signals of the dataset for each GIF method divided in two columns by sex. Moreover, their median values are included in Tables 2 and 3 to aid in their quantitative comparison.  
As a general trend, for both sexes, it can be observed that QCP-based approaches obtain lower error metrics than the IAIF-based techniques, with 98 out of the 100 pair-to-pair comparisons being statistically significant, as can be seen in Table 14. When it comes to comparing the performance of the five GIF approaches with respect to sex, it can be observed that the error metrics obtained in the female speech corpus are, in general  
\begin{table}
\begin{tabular}{l c c c c c} \hline  & **IAIF** & **IOP-IAIF** & **GFM-IAIF** & **QCP** & **ST-QCP** \\ \hline RMS distance (\%) & 13.45 & 15.41 & 15.16 & **3.97** & 4.44 \\ NAQ error (\%) & 10.53 & 9.94 & 9.71 & **7.74** & 7.87 \\ H1H2 error (dB) & 2.81 & 2.07 & 2.1 & **0.27** & 0.41 \\ HRF error (dB) & 0.84 & 0.87 & 0.8 & 0.64 & **0.6** \\ ST error & 12.31 & 7.93 & 6.79 & 8.38 & **6.55** \\ (dB/decade) & & & & & \\ \hline \end{tabular}
\end{table}
Table 2: Median of the 5 error measures between the estimated glottal flow and the ground-truth (original glottal flow) signals for male vowels, computed at the pulse level for the 14.096 considered pulses. The best result per error metric is highlighted in bold.  
\begin{table}
\begin{tabular}{l c c c c c} \hline  & **IAIF** & **IOP-IAIF** & **GFM-IAIF** & **QCP** & **ST-QCP** \\ \hline RMS distance (\%) & 15.06 & 15.7 & 17.79 & **3.74** & 4.74 \\ NAQ error (\%) & 16.8 & 16.91 & 15.48 & **6.99** & 9.25 \\ H1H2 error (dB) & 1.22 & 0.93 & 1.51 & **0.25** & 0.34 \\ HRF error (dB) & 1.34 & 1.26 & 1.39 & **0.75** & 0.85 \\ ST error & 19.58 & 15.02 & 16.62 & **8.8** & 9.9 \\ (dB/decade) & & & & & \\ \hline \end{tabular}
\end{table}
Table 3: Median of the 5 error measures between the estimated glottal flow and the ground-truth (original glottal flow) signals for female vowels, computed at pulse level for the 14.097 considered pulses. The best result per per error metric is highlighted in bold.  
Figure 2: Distributions and median of error measures of RMS, NAQ, H1H2, HRF, and ST between the estimated glottal flow and the ground-truth signals for each GIF method evaluated as boxplots with whiskers from 5% up to 95%. Columns shows results for the male and female subsets, respectively.  
terms, despite H1H2, higher than those obtained in the male speech data. Moreover, the QCP-based approaches present quite a more stable response in terms of sex variation than IAAF-based counterparts. Moreover, it is worthwhile to note that QCP presents the most stable performance across sexes (with the lowest median RMS, NAQ, and H1H2 for female speech, while ST-QCT presents the lowest HFR and ST-QCP for the male data), while GFM-IAIF is more sensitive, as shown by the increases in the HRF and ST error medians as well as the wider distributions in the female dataset.  
In particular, for the male corpus, QCP presents the lowest RMS, NAQ, and H1H2 errors, while ST-QCP outperforms the original version of the technique in terms of the HRF and ST error metrics. Moreover, it is worth mentioning that, for this sex, the IOP and GFM variants of IAAF outperform IAAF in terms of the NAQ, H1H2, and ST error, with the latter also being lower than that obtained by QCP. In the female speech corpus, QCP-based approaches surpass IAAF-based approaches for all error metrics, with the QCP method presenting the lowest values of all methods, even outperforming ST-QCP in the ST error metric. For this sex, both the IOP and GFM variants improve the original IAIF in terms of the ST error, as does H1H2 plus HRF for IOP and NAQ for GFM, respectively.