EEG signal processing is one of the hottest areas of research in digital signal processing applications and biomedical research. Analysis of EEG signals provides a crucial tool for diagnosis of neurobiological diseases. The problem of EEG signal classification into different sleep stages is primarily a pattern recognition problem using extracted features. Many methods of feature extraction have been applied to extract the relevant characteristics from a given EEG data. The EEG data was collected from publicly available source. The data consists of different age male & female recordings for a whole night of 8 hrs. The feature extraction was done by computing the Discrete Wavelet Transform and ANN using BP algorithm.The wavelet transform coefficients compress the number of data points into few features. The Approximation & Detailed coefficients obtained from Sub-band coding method provide important features of the EEG signals. In this project we have applied optimization techniques to reduce the computation complexity of the network without affecting the accuracy of the classification. Classification of the EEG data using neural network provides robust and improved Performance