## 5 Results
### Results Obtained by Using Speaking Rate Modification  
In addition to \(F_{0}\), speaking rate is another major factor for the mismatch between children's and adults' speech. Children typically speak at slower rates compared to  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{**WER (\%)**} \\ \hline
**Noise Type** & **SNR (dB)** & **Baseline** & **With \(F_{0}\) Modification** \\ \hline \multirow{4}{*}{Babble} & 0 dB & 53.35 & 38.36 \\ \cline{2-4}  & 5 dB & 36.43 & 23.69 \\ \cline{2-4}  & 10 dB & 30.29 & 18.28 \\ \cline{2-4}  & 15 dB & 26.46 & 16.25 \\ \hline \multirow{4}{*}{White} & 0 dB & 43.22 & 33.85 \\ \cline{2-4}  & 5 dB & 30.15 & 20.34 \\ \cline{2-4}  & 10 dB & 26.11 & 17.77 \\ \cline{2-4}  & 15 dB & 24.30 & 16.38 \\ \hline \multirow{4}{*}{Factory} & 0 dB & 65.51 & 47.50 \\ \cline{2-4}  & 5 dB & 42.47 & 31.59 \\ \cline{2-4}  & 10 dB & 30.90 & 17.89 \\ \cline{2-4}  & 15 dB & 26.30 & 15.87 \\ \hline \multirow{4}{*}{Volvo} & 0 dB & 21.09 & 13.83 \\ \cline{2-4}  & 5 dB & 20.20 & 13.16 \\ \cline{1-1} \cline{2-4}  & 10 dB & 19.53 & 12.82 \\ \cline{1-1} \cline{2-4}  & 15 dB & 18.92 & 12.61 \\ \hline \hline \end{tabular}
\end{table}
Table 4: WERs obtained in recognizing noisy children’s speech of four noise types in four SNR categories using \(F_{0}\) modification. The baseline system is the same as in Table 3.  
Figure 4: WERs as a function of the \(F_{0}\) modification factor \(q\) for each of the four noise types and four SNR categories using the validation set. Note that the smaller the value of \(q\) (i.e., towards the right end of the x-axis), the larger the strength of the \(F_{0}\) modification.  
adults [35; 52; 53]. The effect of the speaking rate modification algorithm described in Section 3 is demonstrated in Figure 5, which shows the histograms of the number of phonemes per second. For this analysis, 500 utterances of adult speech and 500 utterances of child speech were taken from the WSJCAMO and PFSTAR databases, respectively, and the speaking rate of the latter was modified with the RTISI-LA algorithm described in Section 3 by using \(\alpha=0.74\). The difference in the histograms between the adults and children can be noted easily in Figure 5: the children's utterances show clearly smaller numbers of phonemes per time unit compared to the adults' utterances, that is, the children speak at a lower rate. The lower panel of Figure 5 shows the effect of the RTISI-LA algorithm when the speaking rate of the children was modified. By comparing the histograms shown in this panel with the histogram shown in the upper panel of Figure 5, it can be observed that the histogram of the rate-modified child utterances has become closer to that of the adults' utterances compared to the histogram computed from the original children's utterances.  
To evaluate the effect of the speaking rate modification on the ASR performance, the RTISI-LA algorithm was applied to the noise-corrupted children's speech of the entire validation set. We first varied the speaking rate modification factor \(\alpha\) from 0.83 and 0.68 (in steps of 0.03) in the same noise conditions and evaluated the corresponding WER value for all the data. As demonstrated in Figure 6, the lowest WER value was obtained using \(\alpha=0.74\) for most of the noise types and SNR categories. Therefore, we fixed \(\alpha=0.74\) and modified the speaking rate of the children's speech test data in all noise conditions. The results of these ASR experiments are shown in Table 5. From Table 5, it can be noted that the speaking rate modification algorithm improved the system performance over the baseline system for all the noises of varying SNR levels.  
Figure 5: Number of phonemes per second as histograms for (**a**) adults’ speech, (**b**) children’s speech and modified children’s speech processed by the speaking rate modification method.