EEG signal-based sleep stage classification facilitates an initial diagnosis of sleep disorders. The aim of this study was to compare the efficiency of three methods for feature extraction: power spectral density (PSD), discrete wavelet transform (DWT) and empirical mode decomposition (EMD) in the automatic classification of sleep stages by an artificial neural network (ANN). 13650 30-second EEG epochs from the PhysioNet database, representing five sleep stages (W, N1-N3 and REM), were transformed into feature vectors using the aforementioned methods and principal component analysis (PCA). Three feed-forward ANNs with the same optimal structure (12 input neurons, 23 + 22 neurons in two hidden layers and 5 output neurons) were trained using three sets of features, obtained with one of the compared methods each. Calculating PSD from EEG epochs in frequency sub-bands corresponding to the brain waves (81.1% accuracy for the testing set, comparing with 74.2% for DWT and 57.6% for EMD) appeared to be the most effective feature extraction method in the analysed problem.