Using trapz to calculate the area under part of the whole pulse where y is not zero

Hey,

I am trying to calculate the area under the pulse between the two specified minima shown in the picture from the whole pulse. I am wondering is it correct to use trapz here although one of the two specified points doesn't have y=0?

Thanks in advance!

Answer 1

[Robert Daly]

I would run traps on the peak data set between the two end points.

Then I would run traps using a line between the two endpoints to represent the baseline then subtract that from the first result.

peak.x = [1:10]

peak = struct with fields:
    x: [1 2 3 4 5 6 7 8 9 10]

peak.y = [2,3,6,20,25,26,20,5,2,1]

peak = struct with fields:
    x: [1 2 3 4 5 6 7 8 9 10]
    y: [2 3 6 20 25 26 20 5 2 1]

figure
plot(peak.x,peak.y)

baseline = interp1(peak.x([1,end]),peak.y([1,end]),peak.x) %interpolate a striaght line between the first and last data points in the peak

baseline = 1×10

2.0000 1.8889 1.7778 1.6667 1.5556 1.4444 1.3333 1.2222 1.1111 1.0000

hold on
plot(peak.x,baseline)

PeakArea = trapz(peak.x,peak.y) - trapz(peak.x,baseline)

PeakArea = 95

[Shaily_T]

Thanks! I am wondering mathematically does what you mentioned mean the area under the curve or just using the trapz(peak.x,peak.y)?

[Robert Daly]

trapz(peak.x,peak.y) 

will calculate the area under the curve between 0 and the curve.

It doesn't matter if the data doesn't start at zero it will still work (maybe this is what you were asking?). The results will be the area in yellow below.

trapz(peak.x,peak.y) - trapz(peak.x,baseline)

What my example will give you is the area in yellow below. This is commonly what gets done in chemistry for things like integrating peaks in chromatography (this is what I thought you were asking). It ignores the area in below the baseline.

[Chen Klein]

Hey, if my signal has also negative values, will it only calculate the area from the positive values to 0 (on Y-Axes) ? or it will calculate the whole area under the pulse as you showed here ?