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Monday, May 26, 2008

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.


Zhangzf said...

Dear Glenn,
Shall I throw away the first portion of FID distorded before back LP?
1.I have done the back LP with an FID:first,I throw away the several points of the FID,and then do BLP,FT.I try 5 and 30 points,and the results confuse me:the spectrum with 5 points has more terrible phase than that of 30.Why?
2. In a spectrum with several peaks,after back LP,the smaller peaks seem to disapear.So what are the factors determining this?

Glenn Facey said...


Thank you for the comment.

1. Look at the beginning of the FID and decide how many points are "bad".
2. Throw away the bad points. You should throw away an even number of points otherwise your spectrum may be reversed on its frequency axis.
3. Do the backward linear prediction.
4. Fourier transform.

I hope this helps.