# Area under multiple peaks (Exponentially Modified Gaussians)

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FW on 3 Apr 2017
Edited: KSSV on 4 Apr 2017
Hello, I have numerical data from an instrument (time vs. absorbance) consisting of three overlapping peaks (attached Excel). Is there a way to numerically integrate this data from time t1(0.45 s) to t2 (2 s) to find the total area under the three peaks. Once the total area is estimated, I want to make a single exponentially modified Gaussian of the same area as the real data. Could anyone assist in the functions to be used for such a situation in MATLAB? Amplitude=A; mu= mean; lambda= variable (0.1 to 20); standard deviation =s; EMG=A*s*lambda*sqrt(pi/2)*exp(0.5*(s*lambda)^2-lambda.*(t-mu)).*erfc((1/sqrt(2))*(s*lambda-((t-mu)/s)))

KSSV on 3 Apr 2017
Edited: KSSV on 3 Apr 2017
t = num(:,1) ;
a = num(:,2) ;
idx = t>=0.45 & t <= 2 ;
ti = t(idx) ;
ai = a(idx) ;
Int = trapz(ti,ai) ;
area(ti,ai)

FW on 3 Apr 2017
Thanks you. Is it also possible to integrate the exponential modified Gaussian when the functional form is known?
Amplitude=A; mu= mean; lambda= variable (0.1 to 20); standard deviation =s; EMG=A*s*lambda*sqrt(pi/2)*exp(0.5*(s*lambda)^2-lambda.*(t-mu)).*erfc((1/sqrt(2))*(s*lambda-((t-mu)/s)))
Thanks once again.
KSSV on 4 Apr 2017