I'm studying now the XRD profile analysis in order to get the dislocation densities by using the modified Warren-Averbach method.
As shown in the figure, double peaks appear on the graph.
The Lorentzian function used for fitting these data is:
Y=y0+(2/pi)*{A1*W1/[4*(x-xc1)^2+W1^2] + A2*W2/[4*(x-xc2)^2+W2^2]}
I want to know how to get the cosine fourier coefficient from this type of function.
If you want to know more details, I will reply.
For the Fourier transform of a Lorentzian see the Link given below. Since Fourier transformation is linear, you can just add the transforms of the two peaks, multiplied with the correct coefficient, and taking the shifts of the centers into account. Why do you aim at a cosine transform?
http://mathworld.wolfram.com/LorentzianFunction.html
Thank you for your answer.
I want to get the real part of the Fourier coefficient of XRD profile.
Well you can use exp(i a) = cos(a) + i sin(a) for that at the end. Note that you have a Fourier integral for the real line here, not a Fourier series, since there is no periodicity involved.
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