Apodization - application of a weighting, or "window", function to an FID

The time-domain signal (FID) of a lorentzian peak decays exponentially with time, due to relaxation.  The noise level is constant over the entire FID.  As a result, the signal-to-noise ratio (S/N) is greater at the beginning of the FID.  The S/N of the resulting spectrum can be improved by "weighting" the beginning of the FID more heavily than the end.   This is done by multiplying the FID by a decaying exponential function.

original FID		FT
exponential function
after apodization		FT

Of course, you don't get something for nothing - the improvement in S/N comes at the expense of resolution.  The ability to resolve closely-spaced peaks requires "watching" for long enough to allow their sinusoids to diverge, so the later data points are necessary for resolution.  Application of an exponential function broadens peaks and can obscure small splittings.

For example, the 2 sinusoids shown below differ by a few Hz.  

If only the first 100 data points are observed, they appear to be at identical frequencies, so would not be resolved.
They only begin to be distinguished at 250 points.

An exponential is the most common function in processing 1D spectra.  Other window functions are designed to enhance resolution, with some loss in S/N. 

original FID		FT
Lorent-Gauss resolution enhancement function
after apodization		FT

Applying a window function involves a trade-off between signal-to-noise and resolution, requiring an evaluation of the characteristics of the specific data and the information desired from it.

See also: Details of these and other window functions.

Last updated: 3/13/04