A method for removing motion artifacts from devices for sensing bodily parameters and apparatus and system for effecting same that includes analyzing segments of measured data representing bodily parameters and possibly noise from motion artifacts. Each data segment is frequency analyzed to determine up to three candidate peaks for further analysis. Up to three candidate frequencies may be filtered and various parameters associated with each candidate frequency are calculated. A pulse-estimate input may also be accepted from an external source. The best frequency, if one exists, is determined by arbitrating the candidate frequencies and the pulse-estimate input using the calculated parameters according to predefined criteria. If a best frequency is found, a pulse rate and SpO2 may be output. If a best frequency is not found, other, conventional techniques for calculating pulse rate and SpO2 may be used.