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How do brain waves during REM sleep resemble brain waves during wakefulness?

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During REM sleep, brain activity as measured by electroencephalography (EEG) exhibits patterns that are remarkably similar to those observed during wakefulness.12

While much of the sleep cycle is characterized by high-amplitude, low-frequency waves, REM sleep features low-amplitude, high-frequency beta waves, which are also present during periods of being awake. Because of this resemblance, REM sleep is frequently referred to as "paradoxical sleep". This state of brain activation is distinct from the patterns seen in NREM sleep, where brain activity is generally lower and dominated by slower frequencies.1345

The presence of these "activated" brain waves during REM sleep is closely associated with the occurrence of vivid, visual dreaming. Consequently, the electrical patterns recorded during this stage reflect a level of neural activity that can equal or even surpass that of an alert, waking person.24