Linear Prediction in 2D 

NMR SPECTROSCOPY
(Xwinnmr 3.5, on a PC with W2K)

on 

DPX 200, DPX 300, DRX 500

Department of Chemistry
University of Oslo
October 1997.
Version I

1997.  © F. Rise, B.J.Wik

Log in and start xwinnmr.  You should also know how to zero fill 2D spectra before using this manual.

		Linear prediction is a mathematical procedure where a missing part of a FID can be constructed.  Most linear prediction procedures are based on "singular value decomposition" (LPSVD), a digital processing technique which presupposes that the signal is composed of exponentially damped sinusoid curves.  The information (frequencies, phases, amplitudes) in the part of the FID (t2, F2 dimension) or INTERFEROGRAM (the "FID" in the t1, F1 dimension) that does exist is used to calculate the part(s) that is missing.  The calculated part is then added to the end of the original real existing FID/INTERFEROGRAM and the new combined "FID/INTERFEROGRAM" are then used in the Fourier transform process.  This is a much better way of processing half good data than simply zero filling the missing portion.  Linear prediction can be used forward in time (the last part of the FID is missing) or backwards in time (the first part of the FID is missing).  Linear prediction is extremely useful in 2D NMR as a way of reducing experiment time and/or improving the quality of already existing data sets.  In our laboratory the linear prediction is routinely used in for 2D spectra acquired at the DRX 500 instrument for the following types of 2D spectra: GS-HMQC, GS-HMBC, GS-COSY, COSY, TOCSY, NOESY, ROESY, COLOC and XHCORR (By Dirk Petersen for you). 
		Linear prediction is mostly used in 2D NMR in the t1, F1 dimension.  In the t2, F2 dimension it is fairly easy to acquire enough data points without adding to much time to the experiment.  In the t1, F1 dimension each addition of an increment adds a large amount of time to the experiment.  Why?  This is an excellent examination question.
		The number of points TD (time domain) in the t2 domain is usually 1024 (1k) or 2048 (2k).  In the t1 dimension the number of points in TD is usually a small number: 64 or 128 is often used.  This means that the digital resolution is bad (peaks are broad/long) in this dimension.  
		Linear prediction in the t1 dimension improves the resolution enormously on the F1 frequency axis.  In 2D 1H-13C spectra of the type XHCORR and COLOC spectra the 1H nuclei are on the F1 frequency axis.  In 2D 1H-13C (inverse spectra) e.g. HMQC, HMBC and HSQC the 13C nuclei are on the F1 frequency axis.  Linear prediction is therefore recommended on different nuclei depending upon what kind of experiment you are processing.  
		Linear prediction of uncomplete data is enabled by setting the ME_mod to LPfr (forward real) or LPfc (forward complex).  Use LPfc - as long as you use xfb to process, the computer changes to LPfr by itself if so needed.  
		To summarize:  Processing without LP is: baseline correction, window multiplication, Fourier transformation and phase correction.
		Processing with LP consists of: baseline correction, linear prediction, window multiplication, Fourier transformation and phase correction.  
		The processing parameter NCOEF represents the number of coefficients used for the LP-calculation.  NCOEF should be 2-3 times the number of peaks in the dimension(s) where LP is performed.  

		Linear Prediction for a 2D data set.

1.	Use search to find a 2D data set.  (Preferentially one with low quality, few increments). 

2.	Type wrd¿  this is the command for copying the dataset which is on screen to another disk 
	(home or other place) for permanent storage and at the same time change the ownership of 
	the files.  

Enter target data set NAME:				LINEARPRE2D¿		(use your own expname)
Enter target data set EXPNO:			1¿					(use the expno seen in the top part of the xwinnmr window).
Enter target data set PROCNO:			1¿					(use the procno seen in the top part of the xwinnmr window).
Enter target disk unit DU:					M:¿ 					(the dataset will go to your home directory on another computer for permanent storage use v if you not need a permanent copy)
Enter target user name USER:			user name¿ 	(your own uio user name)

3.	Perform the same procedure for LINEARPRE2D 2 1. 

4. 	Use search to find the LINEARPRE dataset which is now owned by you, then 
	append and apply expno1 procno 1 to the xwinnmr window and efp to Fourier transform 
	it.  You can not work properly with a dataset not owned or not processed by yourself.   If the 
	computer you are using does have another  plotter attached than the one used under acquisition use edo (edit output) to 
	select the new plotter.  The data set does regretfully remember the plotter name connected to the computer used to acquire 
	the spectrum.  

5.	apk the spectrum.  Expand a sensible part of the spectrum on the screen and look at the 
	form of the spectrum, especially at the baseline.

6.	Type re 2 1 to get the GS-HMBC spectrum on screen.  xfb it so that it is certain that you own 
	all of the dataset.  Type eda to see acquisition parameters.  Look for the parameter TD in both 
	F1 and F2 dimensions.    

6.	Type edp to see processing parameters.  Look for the parameter SI (size) in both dimensions. 
	SI in F1 is 64.  SI in F2 is 2048.  No zero filling is performed or other tricks is performed on 
	this data set.  (When SI=TD/2 no zero filling has taken place.)  

7. 	Use edc to increase the procno (processing numbers) to 2.  Change SI, Select SI (F1) to 256 
	and keep SI (F2) to 2048.  xfb the data set.  Observe any changes.  You have now zero filled 
	twice in the F1 dimension. 

8.	Use edc to increase the procno (processing numbers) to 3.  Click on ME_mod in the EDP 
	window for F1.  A list of options comes up, LPfr (forward real), LPfc (forward complex), 
	LPbr (backwards real), LPbc (backwards complex).  Since we are adding the missing end of 
	the FID LPfr and LPfc can be used.  Select LPfc to use both the imaginary (Im) and real part 
	(Re) of the FID in the calculations. 

9.	Find NCOEF (number of coefficients) for F1 in the edp window.  The number to be put in for 
	NCOEF must be larger than the number of resonances in the spectrum.  Select 32.  Select 
	LPBIN 256.  This means that linear prediction is performed from data point 65 to data point 
	256.  xfb.  Observe any changes.  

10. Use edc to increase the procno (processing numbers) to 4.  Change SI (F1)  to 1024.  
	  NCOEF to 100 and LPBIN to 1024.  xfb the data.  Observe any changes.  

11. 	A combination of linear prediction and zero filling is possible if LPBIN is set to a lower  
number than SI.  LPBIN at 512 means that 64 original data points are used, from 65 to 512 is linearly predicted and the last 512 points are zero filled.  

	Plot the same area for all processings to clearly observe the changes.  If the 1D 1H spectrum 
	does not appear on the F2 axis use edg and sub menues in edg to define it correctly.  If the 
	computer tells you that an unknown plotter is attached use edo to set correct plotter and printer.  
	Why are we predicting in the F1 dimension instead of the F2 dimension ?