# Using the \(\beta\)/\(\alpha\) Ratio to Enhance Odor-Induced EEG Emotion Recognition
## 2 Materials and Methods
### Spectral Decomposition  
The power spectral density (PSD) was estimated using the Welch method, employing a Hanning window of 2 s for segmentation and an overlap of 256 samples (50% overlap rate). The number of discrete Fourier transform (DFT) points was 1024.  
Since high-frequency signals are often doped with electromyographic (EMG) artifacts, these are difficult to remove cleanly in long-term monitoring [31], which, in turn, affects the experimental results. The 1-30 Hz range is a common EEG study frequency band range which can provide most of the emotional information [32]. Therefore, this study focused on the PSD within the 1-30 Hz frequency range, which constitutes the band of interest. Given the distinct biological significance of EEG signal frequency bands [8; 9; 10; 33; 34], the 1-30 Hz range was segmented into six sub-bands, namely delta (8, 1-4 Hz), theta (8, 4-8 Hz), alpha1 (\(\alpha\)1, 8-10 Hz), alpha2 (\(\alpha\)2, 10-13 Hz), beta1 (81, 13-20 Hz), and beta2 (82, 20-30 Hz). The PSD of all frequency points within each frequency band at each electrode was averaged to obtain the mean PSD value for that band. Additionally, we introduced the \(\beta/\alpha\) ratio as a new metric, since it reflects the level of brain arousal [13; 14; 15]. Subsequently, we averaged the PSD of the \(\beta/\alpha\) ratio across all electrodes. It should be noted that in the \(\beta/\alpha\) ratio, \(\beta\) represents the entire \(\beta\) frequency band (13-30 Hz), while \(\alpha\) represents the entire \(\alpha\) frequency band (8-13 Hz).  
The brain was divided into five regions of interest (ROIs), namely F-ROI, T-ROI, C-ROI, P-ROI, and O-ROI, with electrodes in each ROI distinguished by unique colors (refer to the \"Channel Locations\" module in Figure 1B). Given that this study focuses exclusively on the arousal dimension of emotions, the \(\alpha\) frequency band, which is associated with internal attention [35], and the \(\beta/\alpha\) ratio, which serves as a potential indicator of arousal [14], are sufficient to support the electroencephalographic analysis conducted in this research. In addition, the \(\alpha\) frequency band is considered to have the highest retest reliability and is a characteristic of the internal stability of the individual [36], so no other separate EEG bands (1-30 Hz) were visualized and further analyzed. To facilitate an intuitive comparison of the PSD across different brain ROIs before and after inhaling SEO or BEO, we averaged the PSD of three metrics (\(\alpha\)1, \(\alpha\)2, and \(\beta/\alpha\)) at each electrode in both the resting state (RS) group and the inhalation of SEO or BEO groups, and then computed the intragroup averages to generate topographic maps. A paired \(t\)-test (one-tailed) was conducted on the average PSD of the three metrics at each electrode between groups, with a significance level of \(\alpha\) = 0.05. Additionally, we plotted the spectrograms of the intersubject average PSD across different ROIs for all frequency points within the 8-30 Hz range (with a frequency resolution of 0.5 Hz). The PSD for each ROI was calculated as the average of all electrodes in that region. Paired \(t\)-tests (one-tailed) were also performed on the intersubject average PSD of each metric between the RS and SEO or BEO groups across different ROIs, with a significance level of \(\alpha\) = 0.05.