How to measure overlap area of peaks from different signals

Hi All, I wonder if there is a simple way to solve the following problem. There are two time-series signals S1 and S2 from two sensors and the signals were collected by the same frequency and time scale. If there are n peaks in S1 and m peaks in S2, how much area of peaks in S1 is overlapped with peaks in S2? Thanks in advance! Wenlong

[Sara]

Can you provide an example of your signal an indicate what you mean?

Answer 1

[Star Strider]

I’m not quite certain what you want, but if you want the total overlap of the peak areas, use trapz (or cumtrapz) and subtract:

% Create Data: 
pk = @(m,s,x) exp(-(x-m).^2./s);        % Create peaks with centre=m, width=s
x= linspace(0,20);
s1 = pk(5,2,x) + pk(11,3,x) + pk(17,2,x);
s2 = pk(7,2,x) + pk(12,2,x) + pk(15,2,x);

% Integrate, Then Subtract: 
Is1 = cumtrapz(x,s1);
Is2 = cumtrapz(x,s2);
Isd = Is1 - Is2;

figure(3)
plot(x,Isd)
grid

The final value of ‘Isd’ is the difference in the areas of the peaks between the two data vectors, ‘s1’ and ‘s2’.

Is this what you want to do?

[Image Analyst]

Apparently so since it was accepted. Thank goodness the signals were separate and we didn't have to get into mixture models http://en.wikipedia.org/wiki/Gaussian_mixture_model

[Star Strider]

Very much so!

And thanks!

[Wenlong]

Thanks! Star.

[Star Strider]

My pleasure!

Answer 2

[Salaheddin Hosseinzadeh]

Hi Wenlong,

You didn't explain the problem in detail, so you probably looking for an idea.

What I understood and I would do is:

1- Define what's the accepted signal level as a peak (you may wanna use FWHM or any preferred definition), lets call it "threshold".

2- peakAreaS1 = S1 > threshold;

3- peakAreaS3 = S2 > threshold;

4 - overlapedArea = peakAreaS1 & peakAreaS2;

Hopefully this is a good enough hint.

Good luck!

[Wenlong]

Thank you! Salaheddin, Your answer also helps.