Actually, after thinking about it, the midline signal is correct. Think about it, it swings high (positive) as the magnet approaches, then low (negative) as the magnet passes. At all other times, the magnet isn't affecting the coil, and thus the absence of a signal means a mid output. The overshoot and undeshoot might be explained by the weak effect of the magnet as it aligns with the coil around 180 degrees. The rest of the niose is probably inductive pickup caused by vibration or something. I'd just peak detect the signal, and call it a day.