Fitting data with two peaks

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Niles Martinsen
Niles Martinsen on 4 Jun 2012
Edited: John Kelly on 2 Mar 2015
I have some data, which is not too different from the top graph in this picture: <>
In other words, there are two peaks that each represent a Lorentzian. I am not sure how to fit this in MatLAB. Is there a way to fit the data to one function consisting of two Lorentzians, or do I have to split the data set in two, one peak in each?
Ultimately I need to find the x-position of each peak.
Best, Niles.
  1 Comment
Enrique on 30 Jul 2014
Did you ever figure out how to do this and/or implement any of the solutions suggested below? I am trying to fit two Lorentzians to similar Raman data as yours (is yours a graphene Raman spectrum as well?). In the past I have done this using a single Lorentzian fitting function I found ( Lorentzian Function Fit lorentzfit), but have not tried to implement two Lorentzians. Any suggestion would help a lot.

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Answers (5)

Geoff on 4 Jun 2012
Define a function that accepts the parameters of the two lorenzian curves and computes the full curve.
I don't know how many parameters you need cos I'm no mathematician =) Let's say 2?
dualLorentz = @(x, a1, b1, a2, b2) = lorenz(x, a1, b1) + lorenz(x, a2, b2);
Then, define a function to generate that curve, subtract your actual dataset, square the result and sum it.... While you're at it, parameterise the whole thing (ie a vector p of [a1, b1, a2, b2])
objFn = @(p, x, y) sum( (y - dualLorentz(x, p(1), p(2), p(3), p(4))) .^ 2 );
Then chuck it at fsolve or fminsearch - assuming your dataset is in X and Y:
p0 = % some initial guess at a1, a2, b1, b2 : you can probably be very basic
p = fsolve( @(p) objFn(p, X, Y), p0 );

Ryan on 4 Jun 2012
Edited: John Kelly on 2 Mar 2015
You could get a close approximation of peak position with a cubic spline fit and local maxima. You could also try just smoothing the data first as well and then finding the maxima.
Cubic Spline:

Niles Martinsen
Niles Martinsen on 7 Jun 2012
If I use this approach, is there a way to obtain the errors on the fitted parameters?

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