Fitting data with two peaks

Hi

I have some data, which is not too different from the top graph in this picture: <http://www.aanda.org/index.php?option=com_image&format=raw&url=/articles/aa/full/2004/12/aa0526/img14.gif>

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.

[Enrique]

Niles,

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.

Thanks,

Enrique

Answer 1

[Geoff]

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 );

Answer 2

[Image Analyst]

Maybe try this:

http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

Answer 3

[Ryan]

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:

http://www.mathworks.com/help/curvefit/csaps.html

Answer 4

[Frederic Moisy]

Hi, you can try the Ezyfit toolbox:

http://www.mathworks.com/matlabcentral/fileexchange/10176-ezyfit-2-40

In particular, there is an example with two peaks (here fitted with the sum of 2 gaussian curves):

http://www.mathworks.com/matlabcentral/fileexchange/10176-ezyfit-2-40/content/ezyfit/demo/html/efdemo.html

Answer 5

[Niles Martinsen]

If I use this approach http://www.mathworks.se/support/solutions/en/data/1-GNRWCU/index.html, is there a way to obtain the errors on the fitted parameters?