We can alter the FID at our advantage. It's enough to multiply the complex FID with a positive real function. Many functions have been proposed and it's difficult to find other common properties among them. Most have zero intensity at the end, but there are also exceptions. To do something useful with these functions you must be aware of your particular needs. Think in terms of: "What do I want to attenuate?". The name "Weighting" only describes the "how". A description of the "why?" would be: "Selective Attenuation". I have counted 4 things that can be attenuated.
After multiplication with a negative exponential (2 Hz) this spectrum becomes:
2) LORENTZIAN TAILS
The tails of NMR peaks are much larger than you may think. The components of a multiplet are often fused into a single group. In this case, the apparent distance of two positive Lorentzian curves is less than the actual distance. I can attenuate the tails and obtain a complete separation of the above signals with a positive exponential (1.6 Hz) and a gaussian (1.2 Hz).
3) DISPERSION TAILS
When a spectrum is in magnitude or power representation, you have a mix of absorption and dispersion curves. The latter contribute with large and nasty tails. I have attenuated them with a sine bell shifted by 6º.
4) TRUNCATION WIGGLES
This synthetic FID does not decay. I can attenuate the wiggles (without generating tails) with a cosine squared function.
Do you know about other things that can be selectively attenuated?