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Forward Linear Prediction

Forward Linear Prediction

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Forward Linear Prediction (LN)

This is used to improve resolution in cases where the FID is badly truncated. This occurs most often in 2D data, where time constraints limit the number of slices which are acquired. Data which is truncated must be severely apodized to bring the end of the FID to zero to avoid truncation artifacts. This amounts to throwing away data which was acquired at great expense of time. As an alternative, we can use Linear Prediction to generate additional data points and then apply a window function which acts mostly upon these predicted points to bring the end of the FID to zero, preserving the real data points. The result is prevention of the broadening and loss of signal that would otherwise result, giving a net improvement in resolution and signal-to-noise.

Note that linear prediction is not included in NUTS Lite.

 

This FID has not decayed to zero, and must be apodized to prevent truncation artifacts, especially if zero-filling is desired.

 

The FID above has been apodized with cosine squared and zero-filled one time.

Note that we have thrown away good data.

 

The original FID has been opened and LN typed.

The first item, number of points for back prediction, is irrelevant for the present case of forward prediction.

The prediction is based here on the last 64 points of the FID. This parameter cannot exceed one half of the number of data points in the FID, 512 in this case. Using larger numbers will make the calculation slower.

The LN operation will double the data size to 1024.

 

This is the same FID as above after forward linear prediction to double the number of points and then application of a cosine squared window function.

Note that there is much less loss of the original data points (the first half of the FID).

 

This dual display plot shows the improvement in the resulting spectrum.

The top spectrum results from apodization and zero-filling.

The bottom spectrum results from linear prediction followed by the same apodization

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Last updated: 11/3/97.