How can it be that my continuous relative phase exceeds 360 degrees?

Hello,

For my research project I have to investigate the synchronicity between rowers in terms of the continuous relative phase. When the CRP is calculated based on phaseangle2-phaseangle1, this results in wrapping of the data, as can be seen in the graph below. But when I use the function unwrap to solve this problem, the CRP shifts and even exceeds 360 degrees, while it should be around 0 degrees.

How do I fix this?

[Suuz HMS]

I think my question more specifically is, how can I use this CRP to get meaningful results for the mean and SD of the CRP? Since a discontinuous CRP will still result in unreliable values for the mean and SD, does anyone have tips on how I could do this?

[David Goodmanson]

You mention that the phase angle is phaseangle2 - phaseangle1. Could you expand on what the CRPs are measuring? For example, are each of these determined by setting angle=0 as when the oar is perpendicular to center line of the boat/shell, or some similar way? Is there a reference phase angle of some kind? Does each CRP correspond to a rower in the same boat, or are comparisons of different boats invoved? For rowers in the same boat, is <displacement from each other by a certain sample number> the quantity whose variation defines sigma?

Answer 1

[David Goodmanson]

Hello Suuz,

There is nothing inherently wrong with a phase angle of more than 360 degrees. In fact such a phase can be valuable. Given the mod 2pi ambiguity in the phase, you have two choices, which you showed above. You can either allow the phase be continuous, as in the lowest plot, or you can reset the phase to 0 every time it passes 360, and have discontinuous phase.

Sometimes one ends up taking the derivative of the phase, in which case the continuous function is obviously the choice. And the continuous function shows you a history, which is thrown away if you go to the discontinous version. If two cars are going head to head on the track, but one of them has been lapped twice, that is something you might want to know.

Also, it pays to remember that if you plug the continuous phase into a trig function, you get the same answer as you get from the discontinuous phase anyway.

[Suuz HMS]

Thank you for your answer! I do get your point, but in the end I will be using the mean and SD of the CRP to compare between different trials, so then the continuous option does not give reliable outcomes.

Could I use the reset/discontinuous option in this case? And what would be the best way to apply this?