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I'm actually trying to find some correlations between functions, and i was wondering if there is a function that quantifies the amount of time we need to shift a curve to have a high correlation with another one. I've made a higly professional scheme to explain what i mean :

enter image description here

Here for example, i would like a function that has a peak when x = length of the orange arrow because if we shift the red curve by this length, we get two perfectly aligned sine waves, that are moving exactly in the same direction.

It seems to be a mix between convolution and correlation:

  • Convolution because it gives you a function that reaches it's max when the energy is the highest possible (area under the product of the two functions), so you can detect some shift between two curves.
  • Correlation because it gives you an idea of how the two curves are moving together...

Have you an idea of what i'm looking for ?

Thank you for your help

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  • $\begingroup$ It looks like an optimization problem rather than a statistical analysis. Is finding the optimal shift by usual optimization methods an option? $\endgroup$
    – Romain Reboulleau
    Dec 12, 2018 at 19:50
  • $\begingroup$ Hi @RomainReboulleau, i'm intersted in any possible solution... but i thought that is was a very common problem, and that statistical tools or filters exist... $\endgroup$
    – Tbertin
    Dec 12, 2018 at 19:53
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    $\begingroup$ Cross-correlation function? Dynamic time warping? $\endgroup$
    – The Laconic
    Dec 12, 2018 at 20:38
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    $\begingroup$ The cross-correlation function is a convolution! $\endgroup$
    – whuber ♦
    Dec 12, 2018 at 21:10
  • $\begingroup$ @tbertin The standard approach would be to examine the cross correlation function and as whuber says, it is convolution. $\endgroup$
    – Glen_b
    Dec 13, 2018 at 1:48

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