Actually, he has to provide the offset on one

Actually, no. Cross correlation can be used to determine the required offset.

From the Wikipedia page (my emphasis):

Explanation

For example, consider two real valued functions f and g that differ only by an unknown shift along the x-axis. One can use the cross-correlation to find how much g must be shifted along the x-axis to make it identical to f.

It's only an example and it doesn't work for the OP, only for theoretical functions. For actual signals you need to iterate the phase as you would in cross-correlation but then you have to standard-correlate the shifted version of f because f and g won't be identical. I've sketched what I mean as code in a reply to the OP. Just accept it, cross-correlation is a correlation where the second series is a derivation of the first using a MATHEMATICALLY SIMULATED SHIFT. Standard correlation uses two independently sourced series so if one is only theoretically or potentially a copy of the other shifted instead by say circuitry instead of maths you have to use standard correlation.

Update: although if in some weird situation, one mathematician supplies another with a mathematically shifted pair of identical sets without specifying the shift then the same technique of iterated correlation is required. Which reminds me, there is a factor not taken into account -- potential decay of one of the signals.

One world, one people

Sorry, but you are wrong. For a practical application of the process see http://blog.prosig.com/2001/06/06/correlation-example/

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