## 4 Conclusions  
Conventionally, automatic estimation of the speaking F0 range of a given speaker is conducted simply by a direct F0 analysis, which is effective only when a lengthy speech input is available. In contrast, human listeners are able to estimate the underlying pitch range of a given speaker from even a very brief speech and hence to normalize their pitch perception. Although there was an earlier speculation that spectrum plays role in pitch perception, it was not yet clear which spectral parameters can be used directly for the automatic estimation of F0 range until a recent study of ours proposed an LSTM-based model to estimate F0 range using the FBANKs from a brief speech input as short as 300 ms. This model can in a sense mimic the human auditory mechanism of pitch perception. Figure 3: Results of the refined model for the 18 speakers (on the abscissa, where JF and JM indicate female and male Japanese speakers, respectively), with estimates from the Japanese utterances (in triangles) and from the Chinese utterances (in dots). The actual values (in bars) are calculated by direct F0 analysis from all speech data. The three panels from top to bottom indicate the estimates of ceiling, mean and floor, respectively. The present study further refined the model by using a modified measurement of F0 range (with three parameters: ceiling, mean and floor) which can better describe the distribution of F0. Experimental results showed a more accurate estimate than the initial model. Through another experiment conducted on a Japanese-Chinese parallel speech corpus, we found that the F0 range parameters estimated from the same speaker's L1 and L2 speech data were nearly identical, which verified that the estimated F0 range is closer to the speaker-specific underlying F0 range instead of the surface F0 range of the present speech sample. It was also found that the accuracy of estimation in female speakers was lower than in male speakers, though the training data were almost gender-balanced. Thus, in future study we may set different model configurations to male and female speakers and train separate models for them to further improve the estimation accuracy. In sum, the present study has demonstrated that the proposed spectrum-based model is capable of capturing the underlying F0 range of a speaker from a 300 ms-long speech input. In principle, this method can potentially be applied to speech technologies where there is a need for F0 normalization, but no lengthy speech data is available; for example, to help a Mandarin learning application with the F0 normalization for its first-time users. F0 normalization is vital for the evaluation of tone productions but for a new user there is no previous speech which can be used for F0 range estimation. Conceptualization, W.Z., Y.X. and J.Z. ; methodology, W.Z., Y.X., B.L. and L.W. ; formal analysis, W.Z. ; writing--original draft preparation, W.Z. ; writing--review and editing, W.Z., Y.X., B.L., L.W. and J.Z. ; supervision, J.Z. ; Resources, Y.X. and J.Z. All authors have read and agreed to the published version of the manuscript. This study was supported by the Science Foundation and Special Program for Key Basic Research fund of Beijing Language and Culture University (the Fundamental Research Funds for the Central Universities)(20 YJ04002), advanced Innovation Center for Language Resource and Intelligence (KYR17005), and Wutong Innovation Platform of Beijing Language and Culture University (19 PT04). Not applicable. The open-accessed AISHELL Corpus can be found here: [[https://www.openslr.org/33/](https://www.openslr.org/33/)]([https://www.openslr.org/33/](https://www.openslr.org/33/)) (accessed on 24 June 2022), and the THCHS-30 corpus here: [[https://arxiv.org/abs/1512.01882](https://arxiv.org/abs/1512.01882)]([https://arxiv.org/abs/1512.01882](https://arxiv.org/abs/1512.01882)) (accessed on 24 June 2022). Part of this work was presented at the virtual conference of the 10 th International Conference on Speech Prosody, Tokyo, 2020.