The diagnosis of sleep related disorders like sleep apnea, insomnia, restless legs syndrome, begins with grading sleep into stages to analyze the problem. The R&K rules recommend dividing the polysomnographic record of sleep consisting of EEG, EOG and EMG into 30 s epochs and classifying them as Stage 1, 2, 3, 4, Rapid Eye Movement (REM) and Wake state. In this paper, data from a single EEG electrode are decomposed into its wavelet coefficients (Daubechies wavelet from 2 to 6). Instead of using statistical parameters like entropy, energy, etc. of the coefficients as features, the coefficients are directly applied as input to a neural network for classification. Prior to training the neural network, the high dimensional input data are reduced to its principal components. The proposed method helps in isolating Stage 3 and 4, rather than identifying them as a combined Slow Wave Stage (SWS). Best results were obtained using Daubechies 2 wavelet, with an overall accuracy of 86%.