Electroencephalogram (EEG) provides important and unique information about the sleeping brain. Polysomnography was the major method of sleep analysis and the main diagnostic tool in sleep medicine. The standard interpretation of polysomnographic recordings describes their macrostructure in terms of sleep stages, delineated according to R&K scoring criteria. Several descriptors of sleep microstructure rely on the quantification of sleep spindles and slow wave activities, detection of arousals, etc. However, these descriptors are usually assessed by means of substantially different signal processing (or visual) methods. This hinders possibilities of combining their results into a coherent description of the sleep process. This study proposes a solution to these problems in terms of a framework based upon adaptive time-frequency approximations - a recent, advanced method of signal processing. The proposed approach provides compatibility with the visual EEG analysis and standard definitions of EEG structures and describes both the macro- and microstructure of sleep EEG. Adaptive time-frequency approximations of signals calculated by means of the matching pursuit (MP) algorithm allow for the discrimination between series of unrelated structures and oscillatory activity. The detection, parametrization, and description of all these features of sleep are based upon the same unifying approach