The analysis of Electroencephalogram (EEG) signals plays a very important role in the biomedical domain and has many applications. It is extensively used in the Brain-Computer Interface (BCI) system and can be used for disease diagnosis, disease treatment, etc. The two main technologies of EEG signal analysis is feature extraction and pattern recognition. The key features of EEG signals can be obtained through time-domain and frequency-domain analysis. The wavelet analysis is one kind of time-frequency analysis and has been considered very promising for data compression. The conventional method find wavelet synopsis to minimize the total mean squared error (L2). It cannot control the approximation error of each single data element in the data vector. Usually, the nonlinear classification algorithms perform better than the linears, also more time-consuming in the meantime. In this paper, one method is provided to realize the feature extraction and pattern recognition of EEG signals. The data compression algorithm Fixed-value Shift (F-Shift) proposed by Pang et al. takes a novel method to construct unrestricted Haar wavelet synopsis under uniform norm (L∞) error bound. In their algorithm, the maximum approximation error of each individual element can be bounded by an given error bound. We apply this method to EEG signal compression, thus the key features are obtained. Then a fast nonlinear classification algorithm, one Randomize Neural Network (RNN), is provided to identify different patterns of EEG signals. The experiments indicate that (1) the F-Shift algorithm can compress EEG signals effectively and obtain the key features at the same time and (2) the RNN can discriminate different patterns of EEG signals based on the extracted features.