# Reference for the smoothing module¶

Trajectory smoothing routines. These are routines that are out of the Trajectory object because they precompute values that are dependent only on the smoothing method, and not on the trajectory itself, so they may be shared for processing a whole list of trajectories.

flowtracks.smoothing.savitzky_golay(trajs, fps, window_size, order)[source]

Smooth (and optionally differentiate) data with a Savitzky-Golay filter. The Savitzky-Golay filter removes high frequency noise from data. It has the advantage of preserving the original shape and features of the signal better than other types of filtering approaches, such as moving averages techniques.

Parameters

• trajs: a list of Trajectory objects
• window_size: int, the length of the window. Must be an odd integer number.
• fps: frames per second, used for calculating velocity and acceleration.
• order: int, the order of the polynomial used in the filtering. Must be less then window_size - 1.

Returns

• new_trajs: a list of Trajectory objects representing the smoothed trajectories. Trajectories shorter than the window size are discarded.

Notes

The Savitzky-Golay is a type of low-pass filter, particularly suited for smoothing noisy data. The main idea behind this approach is to make for each point a least-square fit with a polynomial of high order over a odd-sized window centered at the point.

References

 [1] Savitzky, M. J. E. Golay, Smoothing and Differentiation of

Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639.

 [2] Numerical Recipes 3rd Edition: The Art of Scientific Computing

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN-13: 9780521880688