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Integration and peak area measurment

The symbolic integration of functions and the calculation of definite integrals are topics that are introduced in elementary Calculus courses. The numerical integration of digitized signals finds application in analytical signal processing mainly as a method for measuring the areas under the curves of peak-type signals. Peak area measurements are very important in chromatography. Quantitation in chromatography is customarily carried out on the basis of peak area rather than peak height measurement. The reason for this is that peak area is less sensitive to the influence of peak broadening (dispersion) mechanisms. These broadening effects, which arise from many sources, cause chromatographic peaks to become shorter, broader, and more unsymmetrical, but have little effect on the total area under the peak. The peak area remains proportional to the total quantity of substance passing into the detector. Therefore peak area measurements are often found to be more reliable than peak height measurement. The simple numeric integration of a digital, e.g. by Simpson's rule, will convert a series of peaks into a series of steps, the height of each of which is proportional to the area under that peak. This is a commonly used method in proton NMR spectroscopy, where the area under each peak or multiplet is proportional to the number of equivalent hydrogens responsible for that peak. But this works well only if the peaks are well separated from each other (e.g. well resolved). In chromatographic analysis one often has the problem of measuring the the area under the curve of the peaks when they are not well resolved or are superimposed on a background. For example, Figure 15 shows a series of four computer-synthesized Gaussian peaks that all have the same height, width, and area, but the separation between the peaks on the right is insufficient to achieve complete resolution. The classical way to handle this problem is to draw two vertical lines from the left and right bounds of the peak down to the x-axis and then to measure the total area bounded by the signal curve, the x-axis (y=0 line), and the two vertical lines. This is often called the the perpendicular drop method, and it is an easy task for a computer, although very tedious to do by hand. The idea is illustrated for the second peak from the left in Figure 15. The left and right bounds of the peak are usually taken as the valleys (minima) between the peaks. Using this method it is possible to estimate the area of the second peak in this example to an accuracy of about 0.3% and the second and third peaks to an accuracy of better than 4%, despite the poor resolution.

Figure 15. Peak area measurement for overlapping peaks, using the perpendicular drop method.

SPECTRUM, the freeware signal-processing application that accompanies this tutorial, includes an integration function, as well as peak area measurement by perpendicular drop or tangent skim methods, with mouse-controlled setting of start and stop points.
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This page is maintained by Prof. Tom O'Haver , Department of Chemistry and Biochemistry, The University of Maryland at College Park. Comments, suggestions and questions should be directed to Prof. O'Haver at to2@umail.umd.edu.