PROCESSING YOUR DATA
 
Fourier Transformation

The Fourier Transform (FT) is a mathematical procedure which analyzes an oscillating signal in terms of frequency, intensity, and decay constant. The transformed data are shown in a typical intensity/frequency graph, or spectrum. This procedure is applicable to a wide variety of physical problems, including several spectroscopic techniques.

The simulated FID below is clearly made up of one oscillating component, characterized by a frequency, initial intensity, and decay constant. To view its FT, move your mouse into and out of the figure area.
Note that the spectrum exhibits only one peak. Its chemical shift, or position along the x-axis, is characteristic of the frequency of the original signal.
 
The simulated FID below is of higher frequency than the one shown above. How will this affect the transformed data? Move your mouse over the image to see.
As in the example above, there is only only peak in the resulting spectrum. However, its chemical-shift, or frequency, position has changed. You can directly compare the two spectra below.
 
Real FID's are seldom composed of only one component. In fact, a typical 1H or 13C spectrum can easily contain dozens. As shown earlier, an NMR signal with two components looks like their sum. The signal below is the sum of the blue and yellow FID's above. What will its FT look like? Point to the figure to see.
Not surprisingly, the spectrum contains two peaks - one corresponding to the lower (originally blue) frequency, and one at the higher (originally yellow). Two other important features should be noted. The peaks are of roughly equal intensity, because the two components were equally weighted. Also, their widths are the same; this arises from the fact that the decay constants are identical. In a real spectrum, these two conditions rarely hold.
 
The simulated signal below also contains two slightly different frequencies, but one is ten times the intensity of the other. Because the second component is so small, its presence is not readily apparent in the FID. However, it is quite obvious in the resulting spectrum, as can be seen. This ability to highlight small components is one of the advantages of Fourier analysis.

Because NMR signals are directly proportional to the number of nuclei contributing to that signal, this spectrum may be interpreted to mean that the lower frequency peak represents ten times more atoms than the higher, provided that the spectrum was recorded quantitatively. This feature aids in interpretation of spectra and makes NMR a powerful tool for composition analysis.

Note also that the higher-frequency peak, while shorter, is the same width (measured at half-height) as the lower.
 
If, on the other hand, the two components are of equal intensity, but decay at different rates (a factor of four in this case), the FID is visibly distorted, with unusually high intensity at short times. Of course, if the faster-decaying component was much less intense, the effect would be harder to detect. The FT of this signal still reveals two slightly shifted peaks, but one is clearly much broader than the other.

While the heights of these two peaks differ drastically, the areas under the curves are the same. It is, frankly, unusual to see such a dramatic linewidth difference in a 1H or 13C spectrum, but even slight changes can create noticeable variations in peak height. For this reason, NMR peak areas, not heights, should always be used for comparisons.

Differences in linewidth within a spectrum are chemically and/or physically significant. If one peak, for example, is broader than the others, this suggests that the nuclei it represents may be bonded to certain types of atoms, such as nitrogen or a metal, or that their motion is restricted. In either case, such an observation can be helpful in interpretation. Linewidth measurements can also be used to investigate molecular dynamics, such as enzyme/substrate binding or viscosity.