The sleep stages provides the most basic evidence for diagnosing a variety of sleep diseases. for staging sleep by analysis of EEG(electroencephalogram), it is especially important to detect the characteristic waveforms from EEG. In this paper, sleep EEG signals were analyzed using Fourier transform and continuous wavelet transform as well as discrete wavelet transform. Proposeed system methods. Fourier and wavelet for detecting of important characteristic waves(hump, sleep spindles. K-complex, hill wave, ripple wave) in sleep EEG. Sleep EEG data were analysed using Daubechies wavelet transform method and FFT method. As a result of simulation, we suggest that our neural network system attain high performance in classification of characteristic waves.