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Given $N$ functions $f_{i}(t)$, find an expression for the lag times $\tau_{ij}$ which maximise the sum of cross-correlations between the functions, i.e.

$\sum_{i = 1}^{N - 1}\sum_{j = i + 1}^{N}f_{i}(t)*f_{j}(t + \tau_{ij})$

Notes:

There are ${N \choose 2} = N(N - 1)/2$ terms in the summation, but there are only $N - 1$ independent lag times, because $\tau_{ij} + \tau_{jk} =\tau_{ik}$.

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    And your question is? – 2017-02-15
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    "Find an expression for the lag times which maximise the sum of cross-correlations between the functions." – 2017-02-15
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    You can compute the cross-correlation quickly using the fast Fourier transform algorithm and then loop over the correlations to find the biggest one. – 2017-02-15

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