## 2 Materials and Methods
### Method  
#### 2.1.1 Calculation of Emotional Temperature  
First, a voice activity detector (VAD) was applied to each of the recordings using MATLAB(r) software (R2019a). Once the different frames were obtained from the VAD, the six following features were extracted: two prosodic features (related to pitch) and four paralinguistic features (related to spectral energy).  
To calculate the ET, we used as prosodic parameters two linear regression coefficients (\(a\) and \(b\)) from Equation (1) that model the pitch contour \(p(n)\) of an audio sample \(\{w(n)\}\)[24].  
\[Min(a,b)=\sum_{i=1}^{n}(p_{i}(n)-a-bx_{i}(n))^{2} \tag{1}\]  
Coefficients \(a\) and \(b\) were calculated using the least squares method. Coefficient \(a\) represents the pitch, while \(b\) is related to the tone trend. For this purpose, a pitch estimation algorithm (YIN) [40] was used.  
To calculate the paralinguistic features, four voice spectral energy balances (\(EB0\), \(EB1\), \(EB2\), and \(EB3\)) were used, which were quantified using four energy concentration percentages in four frequency bands, \(Bi\) (where \(i\in[0,3]\)). Thus, with a sampling rate greater than 16 kHz, the frequency bands were divided into the following ranges: B\({}_{0}\) = [0 Hz-400 Hz], B\({}_{1}\) = [400 Hz-2 kHz], B\({}_{2}\) = [2 kHz-5 kHz], and B\({}_{3}\) = [5 kHz-8 kHz]. The percentage of energy in each \(EBi\) frequency band, in turn, was obtained using Equation (2).  
\[E_{Bi}=\frac{\sum_{f=B_{i}}\left|X(f)\right|^{2}}{\sum_{f=0}^{8\text{kHz}} \left|X(f)\right|^{2}}\text{, where }0\;\leq\;i\;\leq\;3 \tag{2}\]  
where \(\left|X(f)\right|^{2}\) corresponds to a period of the temporal voice frame, \(w(n)\).  
Once the six prosodic and paralinguistic features were obtained, to carry out the emotional temperature calculation, a support vector machine (SVM) classifier was used, specifically the LIBSVM library in MATLAB(r). In the first phase, each emotional segment was classified into the following two types: high activation and low activation. The decision threshold (Th1) was calculated based on the equal error rate (EER) obtained from the training data. In the second phase, the complete speech signal was classified as high activation if the percentage of the emotional segments classified as high activation in the previous phase was higher than a second threshold (Th2). This second threshold (Th2) was calculated from the EER obtained from the validation data inserted into LIBSVM (which estimates the minimum percentage of high activation segments required for the signal to be classified as such). The resulting scale within this framework was linear and normalised. Generally, a voice signal was classified as high activation when ET \(\geq\) 50 (emotional speech) and as low activation otherwise.  
Finally, the discrete emotional temperature (\(ET_{d}\)), which is a number value, provides information based on the entire recording about whether the speech is emotional (\(ET_{d}\)\(>\) 50). On the other hand, the continuous emotional temperature segments the recording into different fragments and, from each one, obtains an emotional temperature value, thus obtaining a vector from which different descriptive statistics are calculated: mean value, variance, skewness, and kurtosis.