# Is there a criterion that says at what point you can distinguish 2 partially overlapping Lorentzian peaks?

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?

• 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 – user28715 Jun 27 '18 at 13:56
• Do you gave an example you could link where they look at it as a statistical hypothesis test? – SomeRandomPhysicist Jun 27 '18 at 13:58