Backward Linear Prediction to Correct for Receiver Saturation

If the receiver gain is set too high the initial portion of the FID is clipped and the NMR spectrum is distorted. In such cases the spectrum should be run again with an appropriate receiver gain setting. Sometimes however, this may not be convenient as the sample may have decomposed. One way to improve the quality of the data is to take a close look at the FID, discard the initial clipped points, use backward linear prediction to calculate the discarded points and then do the Fourier transform. An example of the improvement you can expect is shown in the figure below.

Backward Linear Prediction

Like forward linear prediction, backward linear prediction uses observed data to predict data which is unavailable. In the case of forward linear prediction, data is predicted at the end of the acquisition time in the observed domain (1D) or used to predict more slices in the indirect dimension of 2D datasets. Backward linear prediction, on the other hand, predicts missing or distorted data back to time zero (immediately after the observe pulse). The data immediately after the pulse may be unavailable or distorted due to a long receiver dead time, pulse breakthrough, or acoustic ringing. Backward linear prediction can recover broad features in a spectrum, solve baseline problems and recover phase information. It should be noted that if a broad signal has completely decayed before the collection of meaningful data, then backward linear prediction will not be able to predict the lost broad feature. An example of backward linear prediction to predict data lost during acoustic ringing is shown below.
Only the initial portion of the FID is shown.

Forward Linear Prediction in the Indirect Dimension of 2D Data

Forward linear prediction in 1D data is the calculation of new data points after the end of the acquisition time based on the observed data points. It can be used to artificially increase the acquisition time and thereby the spectral resolution. Forward linear prediction can also be used in the indirect dimension (F1) of 2D data to artificially increase the number of slices collected in the experiment and thereby improve the spectral resolution in the F1 domain. This represents a huge time saving as fewer slices need be acquired. The figure below shows the HMQC spectrum of 3-heptanone. The data in the top panel was collected with 256 slices in F1 and took 12.8 minutes to acquire. The data in the center panel was collected with 40 slices in F1 and took only 2.0 minutes to acquire. It has much lower resolution in F1 than the data in the top panel. The data in the bottom panel was produced from the same raw data as the spectrum in the center panel except forward linear prediction was applied in the F1 domain. It has comparable F1 resolution to that in the top panel but took less than 16% of the time to collect!

Forward Linear Prediction

The digital resolution in an NMR spectrum can be improved by zero filling the FID (i.e. adding zeros to the end of the FID before Fourier transformation). Forward linear prediction, on the other hand, can be used to improve both the digital and real resolution in a spectrum. Forward linear prediction uses the data collected in an FID to predict data after the receiver was turned off. Both processing techniques artificially increase the acquisition time, however it is only forward linear prediction which adds new information to the spectrum. In the figure below a truncated FID is transformed untreated, with zero filling and with forward linear prediction.