5th Order Polynomial filtering and Force Plate Data Smoothing

[Brett Baxter]

Hi Guys,

Currently trying to filter laser speed gun data with respect to time at 100 Hz, I have a 5th order polynomial equation (1) but currently struggling to differentiate this to a 4th order.

(1) y = -0.0017x5 + 0.042x4 - 0.4432x3 + 2.4625x2 + 2.1189x + 10.315

Any help would be greatly appreciated.

Thank you.

[Allan Carman]

Re: 5th Order Polynomial filtering and Force Plate Data Smoothing

Brett,

As you are using a laser speed gun I will assume ‘y’ is equivalent to velocity and ‘x’ is time.
V = -0.0017t^5 + 0.042t^4 -0.4432t^3 + 2.4625t^2 + 2.1189t + 10.315

We can see that at t=0 velocity is 10.315 m/s

Differentiating wwt time gives:
dv/dt = acc(t) = -0.0085t^4 + 0.168t^3 -1.3296t^2 + 4.925t + 2.1189

We can see that at t=0 acceleration is positive and maximum velocity is reached when dv/dt = 0 which is approximately 10.25 secs

My experience with the stalker radar gun is that the velocity data is very noisy. With results being highly dependent on the filtering used, such that results cannot be compared between studies or test sessions unless they use similar filtering. Matt Cross (a former student at AUT) did some work on standardize filtering of raw velocity data for measuring athlete sprinting performance. Sprinting was commonly over 30 meters with variables of interest including peak acceleration, maximum velocity and power profile.

Matt Cross et al. (2015) International Journal of Sport Physiology and performance, 10, 695-702

hope this helps

Allan