As the world population is growing toward an aging society, elderly fall becomes a serious problem. Automatic fall detection and alert systems could shorten their waiting time after a fall and mitigate its physical and mental negative consequences. This work proposes a method that integrates a 3-axis accelerometer and a barometer on a wrist-worn device for the fall detection task. The method focuses on the use of noisy signals from a barometer in both pre-processing steps and feature extractions. A use of free falling events to address the lack of training data in a learning process is also explored. An evaluation using simulated falls and various activities shows a high classification performance except for a few false alarms occurring when sitting on the floor from a standing pose.