Assume an arbitrary (discrete) signal that is periodic and known over a whole period. I need a way to select a characteristic point along the signal such that I can always retrieve it even when the signal is phase shifted.
Candidates could be zero crossings or extrema or inflections... provided they exist and are unique or can be discriminated from others.
For example, the position of the maximum would work well for a triangle wave, a little less accurately for sinusoid and would raise an ambiguity for $\sin x+\frac13\sin 3x$ as this one has two maxima of equal height.
The method should be robust to noise and work for relatively smooth signals.
Do you know any general feature/formula having the desired properties ?