PROCESSING YOUR DATA
 
Effect of exponential multiplication
Another approach to increasing S/N, and one that can be used after data is collected, is called apodization, or window processing. The most commonly used window is a decaying single-exponential curve. The magnitude of the decay constant determines how quickly the curve decays. In a properly recorded FID, the resonances due to the sample are found in the earlier parts of the signal. When you multiply the FID by a window function, you suppress the data at the end of the acquisition period, which is (or should be) essentially all noise.
A single exponential apodization function does not significantly affect the signal at short times, but it greatly reduces the noise at later times. To see the effect of multiplying an FID by a single exponential, move the mouse into and out of the area below. To compare the spectra of unapodized and apodized data, scroll down or click here.
The spectrum that results from an apodized FID is slightly broader than that from the original data, but the advantages of improved S/N may outweigh the slight increase in linewidth. To compare such spectra, move the mouse into and out of the area below.
When the new, apodized FID is transformed, there is an apparent improvement in S/N. There is also an increase in the width of the peaks in the spectrum. For this reason, decaying single-exponential apodization functions are sometimes called line-broadening functions.However, the slight line-broadening observed in the apodized spectrum is more than offset by the significant S/N enhancement.
 
Choice of line-broadening factor

If exponential multiplication is to be used, the line-broadening factor, which determines the sharpness of the decay, must be chosen carefully. This factor is given in units of Hz.

Apodization functions must be chosen carefully. If the decay is too severe, useful data will be lost, negating the signal-enhancement value of exponential multiplication. This also leads to severe line-broadening, and possibly, to peak overlap. To see the effect of a poorly chosen apodization function on the FID, move the mouse into and out of the image below. To compare the resulting spectra, scroll down or click here.
The quality of the over-apodized spectrum is obviously much poorer. Move the mouse over the figure area to observe this effect.
 
If, on the other hand, the apodization function is not strong enough, its effectiveness is lost, because noise reduction is not efficient. Move the mouse into and out of the image below to see this. To compare the resulting spectra, scroll down or click here.
The S/N of the under-apodized spectrum is clearly poorer when a weak window function is applied. Move the mouse over the figure area to observe this effect.
 
In most cases, the line-broadening function should follow the general shape of the FID, without cutting into the data. A ballpark figure to the line-broadening factor is usually the reciprocal of the data resolution (i.e., the value of the factor is the number of data points per Hz).