## 5 Results
### Results Obtained by Using F\({}_{0}\) Modification  
Compared to adult speakers, children typically use higher \(F_{0}\) values and they also vary the \(F_{0}\) of their speech over a larger \(F_{0}\) range [52,53]. This phenomenon is show in Figure 3, which shows \(F_{0}\) histograms computed from adults' speech signals taken from the WSJCAM0 database (panel (a)) and from children's speech signals taken from the PFSTAR database (panel (b), gray color). For this analysis, 100,000 frames of speech were collected from adults' and children's speech. The figure shows that for the adults' speech signals, there are two peaks close to 100 Hz and 200 Hz corresponding to the average \(F_{0}\) of male and female speakers, respectively. The peak in the children's \(F_{0}\) histogram is higher (around 250 Hz) but the histogram also shows a clearly larger spread of the \(F_{0}\) values compared to the adults' \(F_{0}\) values. When the children's speech signals were processed with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Noise Type**} & \multirow{2}{*}{**SNR (dB)**} & \multicolumn{5}{c}{**WER (\%)**} \\ \cline{3-6}  & & \multicolumn{3}{c}{**Data Augmentation Scenario**} \\ \cline{3-6}  & & & **Same** & **Different** & **All** \\ \hline \multirow{4}{*}{Babble} & 0 dB & 53.35 & 47.05 & 76.35 & 50.90 \\ \cline{2-6}  & 5 dB & 36.43 & 34.37 & 55.42 & 33.68 \\ \cline{2-6}  & 10 dB & 30.29 & 29.16 & 43.10 & 25.75 \\ \cline{2-6}  & 15 dB & 26.46 & 25.18 & 35.76 & 23.64 \\ \hline \multirow{4}{*}{White} & 0 dB & 43.22 & 40.18 & 54.71 & 46.48 \\ \cline{2-6}  & 5 dB & 30.15 & 28.59 & 42.90 & 37.35 \\ \cline{2-6}  & 10 dB & 26.11 & 24.86 & 36.05 & 31.83 \\ \cline{2-6}  & 15 dB & 24.30 & 23.04 & 33.66 & 30.77 \\ \hline \multirow{4}{*}{Factory} & 0 dB & 65.51 & 54.75 & 81.05 & 58.46 \\ \cline{2-6}  & 5 dB & 42.47 & 38.01 & 59.23 & 34.59 \\ \cline{2-6}  & 10 dB & 30.90 & 29.03 & 42.67 & 25.09 \\ \cline{2-6}  & 15 dB & 26.30 & 25.18 & 33.23 & 20.65 \\ \hline \multirow{4}{*}{Volvo} & 0 dB & 21.09 & 18.95 & 38.85 & 23.48 \\ \cline{2-6}  & 5 dB & 20.20 & 18.44 & 36.62 & 22.59 \\ \cline{1-1} \cline{2-6}  & 10 dB & 19.53 & 18.32 & 35.60 & 21.82 \\ \cline{1-1} \cline{2-6}  & 15 dB & 18.92 & 18.11 & 32.36 & 21.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: WERs obtained using data augmentation in recognizing noisy children’s speech of four noise types in four SNR categories. Results obtained with the baseline system, which was trained without data augmentation using solely the noise-corrupted speech of the corresponding condition, are shown in the third column. WERs obtained using the three data augmentation scenarios described in Section 2 are shown in the fourth, fifth, and sixth column. the RTISI-LA method described in Section 3 using \(q=0.80\), the \(F_{0}\) histogram shown in orange in panel (b) was obtained. By comparing panels (a) and (b), it can be clearly seen that RTISI-LA succeeded in converting the original \(F_{0}\) histogram of children's speech much closer to that of adults' speech. To evaluate the effect of \(F_{0}\) modification on the ASR performance, the RTISI-LA method was used to modify all the validation data of children's speech that were noise-corrupted with four different noises with varying SNR values. In these tests, we used the same value for \(q\) for all the data in all the noise conditions. This \(q\) value was determined by varying the parameter between 0.95 and 0.75 (in steps of 0.05) for the different noise types and SNR categories and by searching for the \(q\) value that yielded the lowest WER value in each case. This optimization method was selected because it is straightforward and has low computational cost. These experiments, demonstrated in Figure 4, indicated that the lowest WER value was achieved in most cases with \(q=0.80\). Therefore, we fixed the \(F_{0}\) modification parameter to \(q=0.80\) and processed the noisy children's test data using this parameter value with the RTISI-LA method.