Monday, June 16, 2008

Size Does Not Matter

Zero-filling can't be dangerous. Here is the practical demonstration. I have created an artificial FID with 10 ideal signals (decaying exponentials).

All the signals have the same widths and all are truncated. If I apply zero-filling from the original 4096 points up to 32,000, the spectrum shows bad-looking wiggles.

If you only look at this picture, it seems that zero-filing is a cause of problems. It is true that, without zero-filling, there would be no wiggles. Let's try to FT the original 4096 points directly:

Hear: this spectrum is perfectly phased. When I have created the FID, the waves were all in phase. The experiment demonstrates that truncation causes an asymmetric shape change. Zero-filling, if applied to a truncated spectrum, restores the symmetry (beneficial effect) but at the cost of introducing wiggles (side effect).
black: truncated FID + FT
red: truncated FID + zero-filling + FT

Zero-filling is not responsible for the truncation. It has stressed in a special way a problem that was already there. If there is no truncation, a zero-filled spectrum can only look better than the original. If there is truncation you should resort to a longer acquisition time (if you can) or to Linear Prediction (in the remaining cases).
With today software you can monitor the effect of zero-filling on the fly (in 1D at least). It's enough to select a new value and the spectrum is instantaneously updated. If you see no difference, reselect the old value. I can see a severe effect when I truncate the spectrum, but when I increase the size it's hard to see any difference on the monitor. What I see is that, the bigger is the size, the slower is the computer. Just because I like to experiment with all the other real-time manipulations available (weighting, phase and baseline correction, etc..) I think it's better to zero-fill afterwards, after I have already decided/found the remaining processing parameters (but before performing peak-picking). This is the advantage of using a computer: you don't have to set the parameters in the order they are used by the program. You can set the parameters in any order at any time. It is necessary, of course, to reprocess the spectrum, but it usually takes less than 1 second. If it took 1 hour, than there would be an advantage in being an expert and knowing the optimal parameters in advance. But processing is thousands of times faster and the true advantage is when you don't take anything for granted but are curious enough to experiment.
An high number of points is required when you want to study the shape of the peaks or something related to it (for example, if you want to fit your spectrum with a simulation, for whichever reason) or when you want to measure coupling constants with accuracy. If I am aware of such a need before acquiring the spectrum, I don't rely on zero-filling but prolong the acquisition time.
Everybody can verify that extensive zero-filling has no visible effect on a properly acquired spectrum. Why, then, spending time with interactive optimization? Can't we adopt a rule and stick to it? Yes, it is known that the optimal zero-filling doubles the size of the FID. I remembered that the demonstration dated back to the early days of FT-NMR but could not find it again. The reference was kindly found by Mike:
JMR, 1973, 11, 9-19
This story will be the subject of my next post.


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