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A significant number of fatal accidents are caused by drowsy drivers worldwide. Driver drowsiness detection based on electroencephalography (EEG) signals has high accuracy and is known as a reference method for evaluating drowsiness. Among brain waves, EEG alpha spindle activity is a silent feature of decreasing alertness levels. In this paper, based on the detection of EEG alpha spindles, a novel driver drowsiness detection method is presented. The EEG spindles were detected using Continuous Wavelet Transform (CWT) analysis and the Morlet function. To do so, the signal is divided into 30-s epochs, and the observer rating of drowsiness determines the drowsiness level in each epoch. Tests were conducted on 17 healthy males in a driving simulator with a monotonous driving scenario. The Convolutional Neural Network (CNN) is used for classifying EEG signals and automatically learns features of the early drowsy state. The subject-independent classification results for single-channel P4 show 94% accuracy.