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When someone sets an alarm clock, but wakes up just before it actually goes off.

Usually as a result of the brain anticipating that it will suddenly be awoken by a loud sound and therefore you awake without the need of the alarm.
"I don't know why I keep setting my alarm every morning, because I just end up waking up 10 minutes before it goes off".

"That's an Anticipation Awakening my good friend".
by Expanding The English Language December 05, 2010