Electrophysiological recordings are considered a reliable method of assessing a person's alertness. Sleep medicine is asked to offer objective methods to measure daytime alertness, tiredness and sleepiness. As EEG signals are non-stationary, the conventional method of frequency analysis is not highly successful in recognition of alertness level. In this paper, EEG signals have been analyzed using wavelet transform as well as discrete wavelet transform and classification using statistical classifiers such as euclidean and mahalanobis distance classifiers and a promising method SVM (Support Vector Machine). As a result of simulation, the average values of accuracies for the Linear Discriminant Analysis (LDA)-Quadratic, k-Nearest Neighbors (k-NN)-Euclidean, and Linear SVM were 48%, 34.2%, and 86%, respectively. The experimental results show that SVM classification method offer the better performance for reliable classification of the EEG signal in comparison with the other classification methods.