## 5 Results  
Qualitative Analysis: Modulation Spectrogram and Discrimination Index of Vocal-Emotion-Recognition Results  
From the analysis of the modulation spectrogram and vocal emotion recognition results, we can initially clarify the relationship between these results and the modulation spectrum. We have to turn the time-averaged modulation spectrogram mentioned in Section 4 into a three-dimensional modulation representation to analyze the energy change over the modulation- and acoustic-frequency channels. According to the conclusions of [PERSON] et al. 's study that daily noise and reverberation cannot affect vocal emotion recognition [PERSON] et al. (2017), we 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 daily conditions of the noisy, reverberant, and noisy reverberant environments. The results are shown in Figure 8. Figure 8a-d represents the four environments (including that with no noise or reverberation, i.e., clean), and in each environment, the results of the time-averaged modulation representations are displayed from left to right in the order of neutral, Joy, cold anger, sadness, and hot anger. The x-axis denotes six modulation-frequency channels, the y-axis denotes four acoustic-frequency channels, and the values of the z-axis denote the RMSs of modulation spectrograms, where each one is the average over all the time frames for an emotion. Figure 8: Time-average modulation representation in (**a**) a clean environment, (**b**) noisy environment (\(\text{SNR}=5\) dB), (**c**) reverberant environment (\(T_{\text{R}}=1.0\) s), and (**d**) noisy reverberant environment (\(\text{SNR}=10\) dB, \(T_{\text{R}}=0.5\) s). MF channel denotes six modulation-frequency channels, AF channel denotes four acoustic-frequency channels. As Figure 8 illustrates, in the clean environment, neutral speech produced a peak of power around the first and second modulation-frequency channels (frequency range: 0 to 4 Hz), which is consistent with previous research; the power is mostly concentrated at the lower modulation-frequency channel with a peak at 4 Hz for neutral emotion [21; 22; 23], and the peak shifted to a higher modulation-frequency channel for joy and hot anger, indicating that joy and hot anger have faster speaking rates and higher RMSs. In all environments, neutral, joy, cold anger, and hot anger speech had the same power pattern over acoustic-frequency channels, which is shaped like a mountain. In the second and third acoustic-frequency channels, these four categories of emotional speech had higher power, but lower power in the first and four acoustic-frequency channels. Due to the same power patterns, these emotional speeches may not be easily distinguishable in subsequent analysis. However, neutral, joy, cold anger, and hot anger speech also had the same power patterns over all modulation-frequency channels, which are lower and stable. For sad speech in all environments, RMSs in the second and third acoustic-frequency channels were lower than in the first and fourth acoustic-frequency channels. The RMS patterns for sadness are shaped like a valley. In other words, sad speech has a different power pattern from the other four categories of emotional speech, which indicates that sad speech might also be easily recognized in subsequent analysis. To explain how challenging it was people to distinguish different emotional speeches in the vocal-emotion-recognition experiments, as shown in Tables 1 and 2, we calculated the confusion matrix and discrimination index of the vocal emotion recognition results in the noisy reverberant environment (under the conditions mentioned in Section 2, which do not affect vocal emotion recognition). In Table 1, there are four sub-tables for the four environments.