## 5 Results
### Quantitative Analysis: Modulation Spectral Features and Vocal-Emotion-Recognition Results  
The results of the highest similarity (over all modulation-frequency channels or over all acoustic-frequency channels) between each MSF and the vocal-emotion-recognition results in clean/noisy/reverberant/noisy reverberant environments are shown in Figure 9. We also selected \(\text{SNR}=5\) dB, \(T_{\text{R}}=1.0\) s, \(\text{SNR}=10\) dB, and \(T_{\text{R}}=0.5\) s as the representative conditions for each environment. The horizontal axis denotes the ten types of MSFs extracted from the modulation spectrograms. The value of each bar denotes the similarity between the vocal-emotion-recognition results and MSFs. The higher the value, the higher the similarity between these results and MSFs. If the similarity exceeds 0.4, it is generally considered that the similarity is high. As illustrated in Figure 9b-d, there are 8, 7, and 10 MSFs that have similarity with the vocal-emotion-recognition results of over 0.4, respectively. This suggests that the contribution of the MSFs to NVS vocal emotion recognition cannot be affected by daily noise and reverberation. It also means that MSFs can be used to explain the vocal-emotion-recognition results in daily noisy reverberant environments. The bar graphs for the highest similarity in all daily noisy reverberant environments are not shown due to the page limitation, but we still want to clarify the following two issues: (1) whether the conclusion of high similarity between vocal-emotion-recognition results and MSFs still exists in all daily environments, and (2) whether there exist common MSFs in all daily environments. To investigate the similarity between MSFs and vocal-emotion-recognition results in all daily environments and further determine common features in these environments, we plotted radar charts, as shown in Figure 10. The different axes represent 10 MSFs, and the values on each axis represent the similarity values between the vocal-emotion-recognition results and MSFs. In Figure 10a-f, different colored lines represent different environments; the results for daily environments are shown with solid lines, and extremely high noisy and/or reverberant environments are shown with dashed lines. In Figure 10g,h, all conditions were for daily environments, so that all of the results are represented as solid lines. This is the same for the bar graphs; the higher the value, the higher the similarity between the vocal-emotion-recognition results and MSFs. The reason for the existence of negatively similarity values is shown in Equations (16)-(18). When a certain emotion's discriminability index of the vocal-emotion-recognition results or MSFs is lower than the average discriminability index of all five emotion categories, the similarity calculated using Equation (16) is negative. The thick black line denotes the similarity of 0.4. The MSFs in red circles mean that they have similarities with the vocal-emotion-recognition results over 0.4 in all daily environments. These MSFs are considered common MSFs. As shown in Figure 10a,b, \(\text{MSSP}_{m}\), \(\text{MSKT}_{m}\), \(\text{MSKT}_{k}\), and \(\text{MSTL}_{k}\) were common MSFs in all daily noisy environments. As shown in Figure 10c,d, \(\text{MSKK}_{m}\), \(\text{MSKT}_{k}\), \(\text{MSTL}_{k}\), and \(\text{MSK}_{k}\) were common MSFs in all daily reverberant environments. As shown in Figure 10e,f, MSCR\({}_{m}\), \(\text{MSTL}_{m}\), \(\text{MSK}_{m}\), \(\text{MSKT}_{k}\), \(\text{MSTL}_{k}\), \(\text{MSCR}_{k}\), and \(\text{MSK}_{k}\) were common MSFs in all daily noisy reverberant environments. As shown in Figure 10g,h, \(\text{MSKT}_{k}\) and \(\text{MSTL}_{k}\) were common MSFs in all daily environments. Combining all the above radar chart results, the conclusion of high similarity between the vocal-emotion-recognition results and MSFs exist in all noisy reverberant environments. We also clarified that there are two common MSFs: \(\text{MSKT}_{k}\) and \(\text{MSTL}_{k}\).