A new quantitative analysis method to describe the dynamic variation of electroencephalogram (EEG) signals was proposed. Based on the Fourier transformation, the method is called Fourier multiresolution analysis (FMRA). FMRA decomposes the frequency domain with a binary system and can resolve EEG signals into the basic rhythms of the four waves to study the dynamic characteristics of EEG signal rhythms. FMRA has clear physical meaning, and can obtain more information than wavelet multiresolution analysis does. FMRA can extract perfectly the rhythmic characteristics of EEG signals in the time and frequency domains.