Brainwave signals are analyzed in the nonlinear analysis field and are often studied by electroencephalography (EEG) using brain sensors. Although various frequency bands of brainwaves, such as α, β, and θ brainwaves, can be filtered out from multi-frequency brainwave signals, most modern medicine only interprets the meaning of the signals superficially and rarely conducts an in-depth quantitative analysis of brainwave data. In this study, we selected healthy adults to experimentally analyze their sleep in three stages: before sleep, during sleep, and awakening after sleep, and we observed the energy changes of the brainwaves in these three different periods. We used Welch’s method to quantify the EEG data for analysis. It is generally believed that the brainwave energy is lower when asleep than when awake. However, our experimental results show that not all brainwave energy is higher when awake than when asleep, that is, the brainwave energy in certain bands at the frontal cortex location Fz, the parietal cortex location Pz, and the central cortical location Cz is higher when asleep than when awake. In the future, this method may be extended by applying brain sensors to people with insomnia, Alzheimer’s disease, amnesia, anxiety, emotional disorders, and so forth.