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.