Effect Of Noise And Filtering On Phase Plane Plots And Dimension For Simple Periodic Signals

We studied the effects of added noise and filtering on the calculated dimension and the phase plane plot of a simple periodic signal. Phase plane plots (PPP) of the unaltered sine wave were highly periodic with a calculated dimension of 1.0. However, the PPP lost all structure and appeared random with addition of as little as 5% noise to the signal. The dimension continued to remain at 1.0 even when 20% noise was added to the signal. However, dimension was significantly decreased by progressive smoothing. Filtering of noisy signals returned clear structure to the PPP. We conclude that phase plane plots are less robust than dimension calculations when analyzing a noisy signal, however appropriate filtering can return structure to the PPP. No one technique should be relied on exclusively to determine the presence of order in a biologic signal.