Telling apart a right traveling non-periodic signal from a left-traveling non-periodic signal, with a background periodic signal
If you can sample at any point in time, this shouldn't be that difficult.  The first step is to collect as series of frames in time.
In each frame you should be able to find a best fit sinusoid, or set of harmonic sinusoids, to your periodic signal.  Since this signal is assumed to have the same parameters across time, except the phase values which would need to be time adjusted, you can find an &quot;average&quot; value across all your frames for the periodic signal.
Subtract the best fit periodic signal from your frames.  This should leave the other two behind.  From your drawing, it appears that you have regions where one hump will b e zero, and others where the other hump is zero.  Those are the locations to read your humps at.
For more accuracy, once you have your hump signals estimated, go back and subtract them from your frames.  This should leave the periodic signal behind.  Once again, find the best fit sinusoid assembly.  This time your results should be more accurate.
Rinse and repeat.