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If you have 2 Lorentzian peaks that partially overlap and you have some frequency resolution df (your points in frequency space are separated by df) and both Lorentzian peaks have FWHM $\Gamma$ is there a critereon that says how large a frequency separation you need between the centres of the 2 Lorentzian peaks to distinguish them as 2 seperate peaks?

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    $\begingroup$ the answers are yes, but which answer depends on what you mean by distinguish. You can use something like a Rayleigh criterion hyperphysics.phy-astr.gsu.edu/hbase/phyopt/Raylei.html. You can also look at it as a statistical hypothesis test , where H0 is 1 peak as an example. They don’t give the same answers $\endgroup$ – Stanley Pawlukiewicz Jun 27 '18 at 13:56
  • $\begingroup$ Do you gave an example you could link where they look at it as a statistical hypothesis test? $\endgroup$ – SomeRandomPhysicist Jun 27 '18 at 13:58

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