In this experiment, we record the EEG data during the sleeping and the awakening for the drowsiness cognition. As is well known, analyzing the frequency components of the EEG is important for the sleeping. There are many studies to analyze the EEG frequency data for recognizing the sleeping quality, and so on. However, there is no established method for the analysis of the sleeping EEG. From these reason, we are going to apply the rhythmic component extraction (RCE), proposed by Tanaka et al., to extract the rhythmic component in the brain. RCE finds a component extracted by using a weighted sum of observed channel signals. The weights are optimized by maximizing the power in a certain frequency range of interest. In the experiment, the subjects lie back, relax in a chair, and sleep. We take the EEG recording at 30 channels. From the results, the EEG features, such as the alpha and the theta wave, are different between the sleeping and the waking. These rhythmic components are extracted by the Fourier transform and the RCE. By using the RCE, we confirmed the alpha wave and the theta wave when they are not extracted in a single channel signal. Furthermore, we confirmed the effective measurement locations by analyzing the RCE weights.