A system and method determines from EEG signals the lack of awareness and the depth of anesthesia of a patient to whom an anesthetic agent is being administered. In particular, a log-log representation of the EEG power spectrum is converted to two intersecting lines so that the intersection point and the relative slopes can be analyzed to determine a state of awareness of a patient. This system and method may also be used in an analysis of the brain function of a sleeping individual to distinguish between different levels of non-REM sleep, REM sleep, and awakeness.