3.2. Power Spectral (Frequency Domain)

Spectral features are the characteristics obtained from the EEG signal in frequency domain. In order to get meaningful information about the EEG, it is important to check the segmentation process of EEG to get stationary signal. Thus, some of the more widely used spectral features and processing techniques are described below.

Power spectral density (PSD) pursues to find power distribution for time-domain EEG signal over frequency range and this provides significant information about cortical activation. In particular, PSD is useful in describing stochastic process of the signal and evaluating short data records [78]. There are several methods applied to estimating the PSD, for example, fast Fourier transform (FFT), Welch, Burg, Yule walker, welch method and periodogram [54]. Several studies have demonstrated the effectiveness of using PSD to estimate the level of stress. For example, study in [79], reported that mental stress decreased the EEG power spectral density in the alpha band. Likewise, the study in [20] found a significant decrease in alpha rhythm when increasing the level of stress from level 1 to level 2 (based on increasing the complexity/difficulty of the math task), and then increasing from levels 2 to level 3. In particular, the difficulty of the math task was increased from level 1 up to 3 by increasing the integer numbers and operands that were used in the math operation. Meanwhile, according to [20], the most dominant cortical structure that is involved in stress detection is the right prefrontal cortex. For detailed mathematical formulations of the PSD method, refer to [80].

Other studies utilized absolute power (AP) as an indicator of stress. The AP at a particular band is calculated by dividing the absolute value of fast Fourier transform of the EEG signal by the signal’s length [81]. Meanwhile, studies in [59,82] used the relative power (RP) to check the rhythm of EEG signal by finding the ratio between the power of each band and the power of the total bands. Subhani et al. [45] and Arsalan et al. [83] found that applying AP on stress/non-stress detection shows a significant difference regarding theta EEG band (4–7 Hz) compared to other bands, whereas in the case of RP, they reported that when stress levels increased, the RP decreased [45]. Consequently, RP showed a better performance compared to the AP in spite of its sensitivity to the noise and memory recall [81]. The detailed math expressions for the AP and RP methods are identified by study [45].

Studies in [26,79] utilized powers from the wavelet transform (WT) coefficients to extract features that are highly correlated with mental stress. They found that the mean alpha rhythm power has significantly decreased from one stress level to the next higher one. Moreover, WT is an appropriate method for multi-resolution time-frequency analysis. This is done by decomposing the EEG signal into its frequency bands retaining information in both: frequency and time domain. Then, from wavelet coefficients, the average power and energy can be estimated. Even though the Fourier transform (FT) provides a frequency domain representation of the signal, the wavelet transform creates a time and frequency domain representation, providing a quick access to the localized information of the signal. In particular, since EEG signals are nonstationary, using the FT may result in tiny changes in the spectrum, and the analysis may alter depending on the duration of data. Thus, WT is preferable to FT [84]. The mathematical formulations of the employed WT can be found in [85].

Other studies used Gaussian mixtures of EEG spectrogram to detect stress by analyzing the changing of spectral density of the EEG signal related to time domain. Moreover, this data analysis method involves short-time Fourier transform (STFT) to calculate the spectrogram of the time signal. After computing spectrogram, Gaussian mixture model (GMM), which is a linear combination of Gaussian pdfs, can be estimated to find the density [51]. The obvious role of this model is extracting the symmetric and asymmetric EEG signal; however, some drawbacks of considering infinite range and symmetric nature are reported [86]. Khosrowabadi et al. [51,87] have used this technique to quantify chronic mental stress. They found that GMM has a lower accuracy than MSC, but higher than FD features when using SVM classifier. The detailed math expressions for the Gaussian method are identified by studies [87].

The study in [88] quantified mental stress by using spectral moments (SM). SM was processed to detect three power spectral moments from each EEG segment, that are related to different root square moments with orders of zero, two and four. These moments are found depending on the phase excluded power spectrum and the EEG length. Attallah in [88] verified the effectiveness of spectral moment in differentiating stress/non-stress cases and between several stress levels and reported high accuracy for SM with a linear discriminant analysis (LDA) classifier. The full mathematical expressions of the SM method can be found in [89].