All too often, I wake up about 30 minutes before when my alarm is set for, and feel relatively alert. On these occasions, I usually stay in bed and doze back to sleep again. Then, when my alarm does go off, I usually wake up feeling more tired than I did after doing so naturally.
Given a reasonable
period in which to rest, there are several sleep cycles through the night (or day, if you're nocturnal). At the end of these cycles, we normally wake up and adjust our position before falling asleep again - often never remembering in the morning that we had woken at all.
The instance when I wake up before the alarm is at the end of a sleep cycle. By the time the alarm wakes me I have entered another one, and emerging from this deeper state of restedness is why I feel less wide awake.
This alarm clock will have 2 variables:
1) The latest time at which one wishes to be woken (which roughly corresponds to the alarm time on a standard clock) e.g. 07:30
2) A time boundary e.g. 30 min
Using cut-down versions of equipment like that already used in scientific sleep studies, the alarm clock monitors the brain waves of its owner. When it detects the end of a sleep cycle, it determines whether the current time is within the boundary - so in the example given, this would be any time from 07:00. If it does the alarm is triggered, otherwise it remains silent. This means that the owner will be woken when they will feel most awake, rather than at a fixed time.
If the clock reaches the time set without the alarm being triggered, it activates regardless of the stage in the sleep cycle.