# Integration

Integration in itself is a trivial task in FT-NMR: the spectrum is a discrete function, made of points, not of lines. Integration is simply performed by summing the height of each point within a portion of the spectrum. In this context, we'll call integral region the frequency range over which the integral is calculated. If we, instead, consider in a wider sense the task of integrating NMR peaks, it is indeed an arduous task that begins with sample preparation and acquisition of data on the spectrometer, and continues with baseline correction. This chapter only describes the final steps.

To define integral regions you pick the “Integrator”, from the “Tools” menu, which is a versatile tool capable of performing the following operations:

Operation --> | --> Effect |

selection | defines an integral region |

click into a region | deletes an integral region |

click outside, on a peak | creates a region comprising the peak |

double click into a region | opens the integration dialog |

When you create the first integral, it automatically takes the value of 1. All integrals are
referenced against it. With the double click you can choose any integral as the new reference integral
and assign to it any value, just 1.0, or another integer or non integer value. You do this into the Integration dialog, which also gives you the alternatives to display the absolute values or to calculate the current percentages.
The same dialog also lets you choose the number of significant digits with which integrals are shown.
In the case of 1D spectra, you can also adjust the integral(s), as explained here below. Remember: to open the dialog, it is necessary to select the integration tool and to double click inside a region.

When there are exactly three significant digits, decimal zeroes are not shown.

# Adjusting the 1D Integrals

The normal integral is the area between the spectral line and the x axis. Suppose to draw a straight line
from the first point of an integral region to the last one. iNMR calls “adjusted integral” the
area between this straight line and the spectral line. To adjust a 1D integral, double click into it and,
when the dialog appears, select the option “adjust”. With another click you can choose to adjust all
integrals __already__ created into the document. The value of an adjusted integral is displayed in parentheses.

To decrease the disturbance of noise, you can substitute the values of the two end-points with two averages.
An example clarifies this trick more than an abstract definition. Let's say you choose the value ‘10 points’
from the menu called ‘Calculate the adjustment from’. iNMR calculates the average among the leftmost
point in the integral region and the 4 points on its left; calculates the average among the rightmost
point in the integral region and the 4 points on its right (10 points in total).
When (ideally) drawing the straight line, the average values
are used instead of the actual values. The integral is then calculated as described above.

It's the user responsibility to check that there are no peaks confining with the integral region.
This is the obvious case in which adjusting is not advisable. It is advisable, instead,
when the peak of interest is on top of a much broader peak. Remember, however,
that approximating a broad peak to a straight line is cursory: more refined math treatments exist (not yet included into iNMR).
The purpose of adjustment is not to provide a quantitative treatment, but simply to provide a quick and sensible
solution. Other softwares permit the user to apply arbitrarily selected corrections to the integral.
That practice is an arbitrary one indeed, not allowed by iNMR.

# other commands

The ‘View’ menu contains three commands related to integrals which actually are self-explicative:

- ‘Integral Values’ shows/hides the integral regions and the numerical values.
- ‘Integral Curves’ shows/hides the graphic integrals over a 1D spectrum (see below for more controls to deal with them); today the curves aren't used anymore for themselves, more for showing them to colleagues and say: “Look how flat is my baseline!”.
- ‘Delete All Integrals’ removes the definitions of integral regions from the document.

As you may already know, you can move the 1D spectrum up and down or amplify/deamplify it with the arrow
keys
and the plus/minus keys, respectively.

If combined with the ‘Alt’ key,
the same keys reported above act on the integral curves.
The curves can also be dragged up and down with the mouse.

# Copying Integrals and their Regions

The command “Edit/Copy/Integrals” copies the list of integrals in a readable and printable form. If you paste the integrals into another spectrum, the effect is equivalent to creating new integral regions exactly at the same ppm coordinates. There are three cases in which it doesn't happen:

- When the receiving document already contains some integral regions. In this case, delete the latter with “View/Delete All Integrals”.
- When the sending and the receiving spectra have not the same number of dimensions.
- When the receiving spectrum is an extract.

The same command also creates a **table** in which an **array of spectra** (either mono-, bi- or three-dimensional) are integrated in the same regions. All you have to do is to define the inegration limits in a single spectrum of the series. With the Overlay Manager you then visualize all other spectra inside the same window. At this point The command “Edit/Copy/Integrals” will create the desired table into the clipboard. The integral values of each overlay are multiplied by the amplitude factor of that overlay (this factor is visible inside the overlay manager).

Sometimes an **array of 1D spectra** comes as a single file. The typical example is a **relaxation** study. To create the same table of integrals seen above,
extract any row (alt-click, then command File/Extract) and define 1D integrals regions therein. Return to the whole plot (command: File/Close Extract). If there are NO
2D integrals, the usual command Edit/Copy/Integrals will create the desired table, where the 1D integrals are calculated for all the experiments, into the specified intervals.