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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.


Indranil Ghosh said...

Dear Glenn, thank you for your informative blog.

Say I have exactly 2 frequencies in my FID of a one-pulse experiment. Now a dead time introduces first order phase problem (since the frequencies are different, they acquire different phases at the end of the dead time, and the amount of phase acquired is directly proportional to the magnitude of the frequencies).
Say the lower frequency component acquire a phase of 15 degrees and the higher frequency component acquire a phase of 35 degrees (Ideally their phases should be 0 if the signal was acquired from t=0). Now if I perform linear prediction then my predicted phase factors are 15 and 35 degrees respectively (and not 0 degrees for both components, which misleads me!). If I use this predicted parameters to back predict my FID then I'm essentially predicting wrongly, isn't it?
I hope I could make my question clear. How exactly does backward LP take care of the first order phase problem?

Glenn Facey said...

Your question is clear. If you use backward linear prediction, both lines should ideally be in phase and require no correction if the pulse has zero width. If this is not the case, perhaps the dead time in your FID is not an exact multiple of the dwell time. In this case, the precision of the t=0 point would be quite low and the phases may not be correct. What is the frequency difference between the signals?

Also see these posts....


Indranil said...

Hi Glenn,

The previous comment was just a hypothetical situation. I am however looking for codes in C/C++/MATLAB that provides the predicted parameters and also does backward linear prediction if I give an FID (complex data vector) as input. I'd be grateful if you could provide with some sources of the same.

Glenn Facey said...

I have no expertise in computer code so not in a position to offer any advice.