## 3 Methodology
### Acoustic Features  
Acoustic features of a speech signal can be extracted from the whole utterance or a small part of a speech signal, which is called a frame. The acoustic features obtained from the entire utterance are called statistical acoustic features. Statistical acoustic features include the arithmetic mean, the standard deviation, the maximum, and the minimum. The advantage of these acoustic features is their amount. Because it is faster to apply a feature selection algorithm, their classification time is shorter. On the other hand, they may not be sufficient to optimize the parameters of complex classifiers, such as NN. Another group of acoustic features is local acoustic features, which are extracted from frames. These acoustic features can also be subdivided into frequency (pitch, jitter, formants), spectral (spectral slope, spectral flux, spectral energy), harmonic (harmonic energy, inharmonicity), and cepstral (MFCC) features, based on the domain extracted. For instance, MFCC is extracted after converting the time-amplitude signal into a time-frequency-magnitude signal and then into cepstrum. It is extracted from the cepstrum of a speech signal. Therefore, it is classified as a cepstral feature. Many researchers have proved that MFCC is useful for distinguishing emotions on both the arousal and the valence dimension. It is estimated from the frequency domain using the mel scale, which is related to the human ear scale. The human ear scale is approximately linear up to around 1000 Hz, and logarithmic for frequencies above 1000 Hz [35]. To compute the MFCC feature vector, a speech signal is overtaken first through a filter to intensify the energy of a speech signal at a higher frequency. Then it is divided into frames (usually 30 ms  
Figure 2: General speech emotion recognition system. short-time speech segments), and each frame is windowed with a hamming window to retain the continuity of the speech signal (1), where \(w[n]\) is the filter coefficient of the hamming window, \(L\) is the total amount of samples, and \(n\) is the current sample. After that, to convert the time domain speech signal into the frequency domain, as well as to obtain the magnitude frequency, Fast Fourier Transform (FFT) is performed. The next step is applying the mel-scale filter bank (2), where \(f\) is the frequency in Hertz, which is derived from a windowed frame of a speech signal. \[w[n]=\left\{ \begin{array}{ll}0.54-0.46\cos\left(\frac{2\tau n}{L}\right)&0 \leq n\leq L-1\\ 0&\text{otherwise}\end{array} \right. \tag{1}\]  
\[\text{mel}(f)=1127\ln(1+f/700) \tag{2}\]  
Then the log value of each of the mel spectrum is taken. Finally, a discrete cosine transform (DCT) is carried out to acquire the MFCC feature vector. The complete process of extracting the MFCC feature vector is shown in Figure 3.  
Spectral features are derived from the spectral domain by converting a time-amplitude signal into a complex time-frequency-magnitude form using a short-term Fourier transform (STFT). STFT is calculated by performing a sliding window analysis over the speech signal. Next, the extraction method of the spectral features, which are analyzed in this work, is given. We indicate a speech signal with \(s(n)\) or \(s(t)\), where \(n\) is the sample number, \(t=n/sr\) is the time expressed in seconds, and \(sr\) is the sampling rate. We also indicate the frequency and magnitude of the spectrum of the speech signal as \(f(k)\) and \(a(t)\), respectively, where \(k\) is the frequency value between one and \(sr\). The normalized form of \(a(t)\) is calculated with Equation (3). \[p(t)=\frac{a(t)}{\sum_{k=1}^{K}a(t)} \tag{3}\]  
Spectral centroid is one of the statistical moments of the spectrum. It represents the spectral center of gravity and is computed with Equation (4). \(p_{k}(t)\) is the normalized value of the magnitude STFT at frequency \(k\) and time \(t\). \[u_{cnt}(t)=\sum_{k=1}^{K}f(k)\;p_{k}(t) \tag{4}\]  
Spectral spread is another statistical moment of the spectrum. It is the spread of the spectrum around its mean value.