Filter Angular Velocity. Calculate Angular Acceleration and Displacement
The collected angular velocity data were filtered using an algorithm to determine the optimum cutoff frequency for a 4th order digital Butterworth filter . Infinite impulse response (IIR) Butterworth filters are known to cause linear phase shifts in data. To overcome this, the data were first filtered using a 2nd order Butterworth filter. The data were then inverted and filtered again with the same filter. This resulted in a 4th order filter and removed the phase shift. After filtering, the angular velocity data were numerically integrated to obtain the angular displacement, and then numerically differentiated to obtain the angular acceleration.
Program, based on Yu et al., 1999, determining optimum cutoff frequency from kinematic data.
A semi-automated peak finding algorithm was created in MATLAB . The user designated the size of a boundary region within which the algorithm searched for either the maximum or minimum value. Using the plotted data, the user picked the approximate peak or valley they wished to find and that location would become the center of the boundary region the algorithm used to find the peak or valley. The valleys were subtracted from the peaks to obtain the overall angular excursion. All peaks and valleys were selected over the steady state portion of the data and the mean and standard deviation were reported for each animal.