Emotions are a crucial aspect of daily life and play a vital role in shaping human inter-actions. The purpose of this paper is to introduce a novel approach to recognize human emotions through the use of electroencephalogram (EEG) signals. To recognize these signals for emotion prediction, we employ a paradigm of Reservoir Computing (RC), called Echo State Network (ESN). In our analysis, we focus on two specific classes of emotion recognition: H/L Arousal and H/L Valence. We suggest using the Deep ESN model in conjunction with the Welch Power Spectral Density (Wlech PSD) method for emotion classification and feature extraction. Furthermore, we feed the selected features to a grouped ESN for recognizing emotions. Our approach is validated on the well-known DEAP benchmark, which includes the EEG data from 32 participants. The proposed model achieved 89.32% accuracy for H/L Arousal and 91.21% accuracy for H/L Valence on the DEAP dataset. The obtained results demonstrate the effectiveness of our approach, which yields good performance compared to existing models of emotion analysis based on EEG.