Running in circles: Describing running kinematics using Fourier series

We explore the use of Fourier series to describe the kinematics of human running. From a database of 285 trials of treadmill running, we drive a musculoskeletal model with 104 anatomical joint angles to obtain kinematics. Using FFT analysis, we determine a fundamental frequency for all independent joint angles and compute average step kinematics. Finally, we represent the average step kinematics using Fourier series with numbers of coefficient pairs ranging from one through ten. We find that five or fewer Fourier coefficient pairs provide an accurate (Pearson's correlation > 0.99 and root mean square difference < 0.5 degrees) representation for most joint angles. In conclusion, Fourier series appear to provide a compact and valid representation of running kinematics, thus enabling researchers to confidently use Fourier series in research of human running.