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  Adding or correcting data-points with Linear Prediction

The expression "Linear Prediction" identifies a principle and a technique which, although not essential for NMR, can be extremely useful in particular cases. The principle is that, just because the FID is the sum of regular (sinusoidal) waves, it is possible to extrapolate a fragment of a FID to reconstruct the whole or to prolong it forward and/or backward. LP can also be used to calculate the parameters (e.g. frequencies and intensities of all signals) that describe a spectrum. (iNMR does not implement this feature). FT has the advantage, over LP, of being much faster and stable and of being of more general applicability.

Normally you don't need to know anything about LP. If you want to use it as an alternative to zero-filling, it is enough to check the LP option inside the FT dialog. iNMR automatically sets all the parameters for you.

In rare cases you may want to use the “Linear Prediction” command. Its flexibility allows you to perform back- or forward prediction, to reconstruct portions of the FID (or interferogram in nD spectroscopy), to give an hint about the number of peaks contained into the spectrum. You can repeat LP how many times you want, yet only the final values are stored into the document. iNMR allows you to perform up to three LP runs with a single operations. Thanks to this mechanism, up to three runs per dimensions can be stored into each document. You must furnish the following parameters:

The stand-alone LP and the LP-filling, even when using the same algorithms, are not equivalent. When used in 2D (phase-sensitive) spectroscopy, stand-alone LP comes before shuffling (data-reduction), while LP-filling comes after. It's unlikely, yet possible, that the outcomes are different.

It is also important which phase-sensitive scheme is adopted. If the next FT is a real FT (when the TPPI scheme is in use), the Fast LP creates a counter-diagonal. In the other cases (Ruben-States and States-TPPI), signals near the diagonal are marred by noise produced by the LP. In most cases this is preferable to the counter-diagonal.


You can choose among 3 different algorithms to compute the LP coefficients. Singular Value Decomposition is probably the best compromise between speed and stability. Our implementation is optimized for today's CPUs. LP-filling follows the Fast algorithm by Cybenko, which is less stable. It has been optimized for the old G3 processor. The Zhu and Bax method is stable, but only for forward prediction.

See also

Forget What the Books Say

Phase Correction in 2D Spectroscopy

Solvent Suppression