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Non-Rapid Eye Movement Sleep is divided into four stages.
Stage 1 occurs when a person drifts in and out of sleep. It is considered the transition state between sleepfulness and wakefulness. The state of falling asleep is also called the hypnagogic state. During this stage, the brain occasionally produces "awake" waves, or alpha waves, which have a frequency of 8 - 13 cycles per second. Most of stage 1 brain waves, however, are theta waves, at 4-7 cycles per second. These brain waves are slower, but they have a high amplitude. For most healthy sleepers, this stage of sleep does not last long, only a few minutes.
Stage 2 of sleep has two unique patterns of brain waves. Sleep spindles (image above on left), in which the peaks of the waves get higher and higher in succession, are followed by K-complexes (image above on right), in which the peaks descend. During sleep spindles, the wave frequency is 12-14 cycles per second. Surprisingly, about 70% of sleepers awakened during stage 2 sleep will claim to have already been awake. (1)
Stage 3 and 4, often both considered "deep sleep," are characterized by delta brain waves, commonly called slow waves because of they have a very low frequency (.5-4 cycles per second). 20-50% of stage 3 sleep usually consists of delta waves. More than half of stage 4 sleep consists of delta waves. During this stage the rest of the brain waves are slow theta waves.
(1) Coren, Stanley. Sleep Thieves: an Eye-Opening Exploration into the Science & Mysteries of Sleep. New York: The Free Press, 1996. p. 31[an error occurred while processing this directive]