## Wednesday, December 01, 2010

### Routine Prediction

Not everybody remembers how easy it is and how effective it can be to add (or correct) a few points at the beginning of the FID. Two years ago I explained how Linear Prediction works and how we can extrapolate the FID in both directions. This time I will show a simple practical application.
I have observed that, in recent years, C-13 spectra acquired on Varian instruments require a much-larger-then-it-used-to-be phase correction. When I say correction, I mean first-order phase correction, because the zero-order correction is merely a different way of representing the same thing (a different perspective).
A large first-order phase correction can be substituted with linear prediction. I will show the advantage with a F-19 example, yet the concept is general.

The spectrum, after FT and before phase correction, looks well acquired. Now we apply the needed correction, which amounts to no less than 1073 degrees.

Have you noticed what happened to the baseline? It's all predictable. When you increase the phase correction, the baseline starts rolling. The higher the phase correction, the shorter the waves. With modern method for correcting the baseline we eliminate all the waves, yet there are two potential problems: 1) The common methods for automatic phase correction will have an hard time. 2) If you prefer manual phase correction, you need an expert eye to assess the symmetry of the peaks over such a rolling baseline. Anyway, just to show you that linear prediciton is not a necessity, here is the spectrum after applying standard baseline correction:

Now let's start from the FID again, this time applying linear prediction. one way to use it is to add the 3 missing points at the beginning. The result, after a mild phase correction (<10°) and before the baseline correction is:

The lesson is: by adding the missing points we correct the phase.
Alternatively we can both add the 3 missing points and recalculate the next 4 points. In this way the baseline improves a lot:

The lesson is: by recalculating the first few points of the FID we can correct the baseline of the frequency domain spectrum.