There's already an app for this
It's called 'Sleep Cycle' and it's on the iPhone. It works without an armband, I might add. I don't care what the lady in the video says, I would find an armband uncomfortable.
Did monitoring my sleep patterns help me to find out why I don't sleep well? No, I had already guessed the reasons, but it does help me to predict how tired - or awake - I will be during the day. It's a mildly useful app, but nothing to write home about.