# Evaluation of Glottal Inverse Filtering Techniques on
## 4 Results
### Vowels  
Figure 5 depicts the results grouped per vowel. It can be seen how, in terms of RMS, the best results are obtained by QCP-based approaches for both sexes, with these being the most stable across all vowels, as shown in Figure A1. IAIF and its variants behave considerably worse, especially for /i/ and /u/ for male speech and /i/. /e/, and /ae/ for female speech. When looking at H1H2 outcomes, again, QCP and ST-QCP behaviours are the best and are also very stable across vowels for both sexes. The NAQ errors show lower error values for IAIF-based methods and are, in most cases, comparable to those obtained by QCP, except for /i/ for both male and female and /e/ and /ae/ for female speech. For the HRF measure, the results of IAIF-based methods are again closer to those obtained by QCP-based techniques. These results are quite stable with some exceptions, such as IOP-IAIF for /u/ and /o/ for the male case and the three IAIF methods for /i/, /e/, and /ae/ for female data. Finally, it is interesting to notice how the ST error shows a very different result for male and female speech. In the first case, all the methods behave in a very stable manner across the vowels, with ST-QCP having the best response, closely followed by IOP-IAIF with the best result for /e/ and GFM-IAIF for /a/ and /u/, while IAIF obtains the worst ST values. On the other hand, QCP presents the best results for vowels with lower formant frequencies, and the IAIF variants demonstrate the worst results. For higher-formant-frequency vowels, on the contrary, IOP-IAIF and GFM-IAIF are the methods with lower errors. Figure 5: 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 shown as boxplots with whiskers from 5% to 95% grouped by vowel. Columns show results for the male and female subsets, respectively. In terms of statistics, this case had the lowest statistically significant differences for the pair-to-pair Wilcoxon analysis and was significantly different for 92% out of the 300 pairs for the male subset and 96% in the case of the female subset. It is also apparent, as shown in Table A6, that the NAQ measure has the most non-significant number of pairs, with 11 out of 60 for male data and 4 for female data. Figure 6 shows two examples of both normalised glottal flow output signals and spectra of ground-truth and GS estimations obtained for the optimised versions of each GIF method. The two chosen examples correspond to an /i/ vowel for male and female data, respectively, because there is a clear difference between GIF results within these two subsets, as can be appreciated in Figure 5. In particular, for each subset (i.e., /i/ for the male subset and /i/ for the female subset), the selected example is the one that obtained a lower sum of distances between its MAE-Wave value and the corresponding MAE-Wave mean value of each of the five GIF methods. The /i/ of the male example corresponds to a signal with breathy phonation and an F0 value of 360 Hz, while the /i/ of the female example has a normal phonation and an F0 value of 220 Hz. As can be seen in Figure 5(a), the two selected examples show clearly worse results for the female estimated signal in comparison to the male counterpart for all GIF methods, which is also visible in the /i/ region of Figure 5. Specifically, the female example obtains mean relative increments with regard to the male example of 47.7% for MAE-Wave, 521.7% for NAQ, 88.2% for H1H2, 67.8% for HRF, and 167.1% for ST. In addition, mean relative increments of each of the GIF methods across the five error measures are 120.4% for IAIF, 111% for IOP-IAIF, 130.4% for GFM-IAIF, 65.2% for QCP, and 465.5% for ST-QCP. Figure 6: Ground-truth and normalised glottal flow signal outputs and spectra of the five GIF methods for a male /i/ with breathy phonation and F0 of 360 Hz on the left column and a female /i/ with normal phonation and F0 of 220 Hz on the right column.