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May 15, 2013, 5:34:47 AM5/15/13

to iNMR

The iNMR implementation of linear prediction has always been

confusing, probably because it's quite original.

Today I want to clarify a few simple points. Once you understand them,

there is nothing else to know.

* THEORY

Generally speaking, Linear Prediction (LP) represents an alternative

to Fourier Transform (FT). iNMR does not use LP in such a way, but as

an alternative to zero-filling (ZF) or as an alternative to baseline

correction. Each of the alternatives (LP and ZF) has its own virtues

and its defects. It's easy to choose the most appropriate. In normal

cases, where the signals have decayed by the end of the FID, zero-

filling is the only meaningful choice. In rare cases, when the signal

has been truncated either at the end or at the beginning, Linear

Prediction should be considered instead. You are free to use neither,

of course. While ZF can only be used to prolong the FID, LP can also

be used to recreate damaged or missing points at the start of it.

Prolonging the tail is called "Forward Linear Prediction". Adding

points before the beginning or correcting the first few points is

called "Backward Linear Prediction". The latter is an alternative to

baseline correction. Forward Prediction is relatively easier and more

frequently used. An example of Backward Prediction is described here:

http://www.inmr.net/articles/fluorine.html

* LINEAR PREDICTION DIALOG

The command is Process > Linear Prediction… If it is dimmed, use the

command File > Reload to make it active. Before opening the dialog,

you might want to change the scale unit to "points" (it's enough to

press "n"). In this way you can read the index of the first point of

the FID (usually zero) and the index of the last point. The latter can

also be calculated from the formula:

last index = number of points - 1 + first index

After you open the LP dialog, you must set 5 parameters.

1) First Predicted Point. If you are prolonging the FID, this must be

equal to the last index + 1.

2) Last Predicted Point. This must always be higher. Let's say, for

example, that the original FID goes from point 0 to point 1023. If you

want to add 1000 points to the tail, then set First Predicted Point =

1024 and Last Predicted Point = 2023. If, instead, you want to add 20

new points at the beginning, set First Predicted Point = -20 and Last

Predicted Point = -1.

3) Number of Signals (lines in the frequency domain spectrum). Can

only be estimated. After you eventually FT the FID, verify that your

guess was correct. If the result looks bad and the number of lines is

quite different from your initial guess, reload the spectrum and

attempt with a different value. The normal range is between 20 and

200. Avoid higher values in every way. The Fast algorithm is not

stable when the number of signals is higher than 24.

4) Points to Extrapolate From. This is not critical. Set between 10

and 100 times the number of signals.

5) Algorithm. Singular Value Decomposition is the best.

* A DECEPTIVE SHORTCUT

The FT dialog contains a check-box called "Use Linear

Prediction" (instead of Zero-Filling).

That's a shortcut useful in a single case only, that is in some HSQC

experiments. It's easy to understand why you shouldn't use it: you

can't set the parameters and you can't even read their values. There

is also another important reason. That checkbox will use the "Fast"

algorithm, which is not the best choice. The hidden parameters are:

First Predicted Point = last index + 1

Last Predicted Point = last index + the value selected in the FT size

menu (inside the FT dialog)

Number of Signals = 24 or FID size / 16 (the lesser of the two

values).

Points to Extrapolate From = FID size - Number of Signals - 1.

Algorithm = Fast Linear Prediction.

Having said this, only use that check box for HSQC experiments.

* WHAT ABOUT ZERO-FILLING ?

You never find the expression "zero-filling" in the iNMR interface.

When you open the FT dialog (command Process > Fourier Transform), you

see a value labelled "FID size" and a menu called "FT size". If the

latter is higher than the former, iNMR is going to apply zero-filling.

K is a shortened form for 1024. For example 32 K = 32768 complex

points.

* OPEN CONCLUSION

Though there's not too much to remember, and though it looks simple

and natural, I think that you should digest it all if you want to use

LP successfully. It's open for discussion.

confusing, probably because it's quite original.

Today I want to clarify a few simple points. Once you understand them,

there is nothing else to know.

* THEORY

Generally speaking, Linear Prediction (LP) represents an alternative

to Fourier Transform (FT). iNMR does not use LP in such a way, but as

an alternative to zero-filling (ZF) or as an alternative to baseline

correction. Each of the alternatives (LP and ZF) has its own virtues

and its defects. It's easy to choose the most appropriate. In normal

cases, where the signals have decayed by the end of the FID, zero-

filling is the only meaningful choice. In rare cases, when the signal

has been truncated either at the end or at the beginning, Linear

Prediction should be considered instead. You are free to use neither,

of course. While ZF can only be used to prolong the FID, LP can also

be used to recreate damaged or missing points at the start of it.

Prolonging the tail is called "Forward Linear Prediction". Adding

points before the beginning or correcting the first few points is

called "Backward Linear Prediction". The latter is an alternative to

baseline correction. Forward Prediction is relatively easier and more

frequently used. An example of Backward Prediction is described here:

http://www.inmr.net/articles/fluorine.html

* LINEAR PREDICTION DIALOG

The command is Process > Linear Prediction… If it is dimmed, use the

command File > Reload to make it active. Before opening the dialog,

you might want to change the scale unit to "points" (it's enough to

press "n"). In this way you can read the index of the first point of

the FID (usually zero) and the index of the last point. The latter can

also be calculated from the formula:

last index = number of points - 1 + first index

After you open the LP dialog, you must set 5 parameters.

1) First Predicted Point. If you are prolonging the FID, this must be

equal to the last index + 1.

2) Last Predicted Point. This must always be higher. Let's say, for

example, that the original FID goes from point 0 to point 1023. If you

want to add 1000 points to the tail, then set First Predicted Point =

1024 and Last Predicted Point = 2023. If, instead, you want to add 20

new points at the beginning, set First Predicted Point = -20 and Last

Predicted Point = -1.

3) Number of Signals (lines in the frequency domain spectrum). Can

only be estimated. After you eventually FT the FID, verify that your

guess was correct. If the result looks bad and the number of lines is

quite different from your initial guess, reload the spectrum and

attempt with a different value. The normal range is between 20 and

200. Avoid higher values in every way. The Fast algorithm is not

stable when the number of signals is higher than 24.

4) Points to Extrapolate From. This is not critical. Set between 10

and 100 times the number of signals.

5) Algorithm. Singular Value Decomposition is the best.

* A DECEPTIVE SHORTCUT

The FT dialog contains a check-box called "Use Linear

Prediction" (instead of Zero-Filling).

That's a shortcut useful in a single case only, that is in some HSQC

experiments. It's easy to understand why you shouldn't use it: you

can't set the parameters and you can't even read their values. There

is also another important reason. That checkbox will use the "Fast"

algorithm, which is not the best choice. The hidden parameters are:

First Predicted Point = last index + 1

Last Predicted Point = last index + the value selected in the FT size

menu (inside the FT dialog)

Number of Signals = 24 or FID size / 16 (the lesser of the two

values).

Points to Extrapolate From = FID size - Number of Signals - 1.

Algorithm = Fast Linear Prediction.

Having said this, only use that check box for HSQC experiments.

* WHAT ABOUT ZERO-FILLING ?

You never find the expression "zero-filling" in the iNMR interface.

When you open the FT dialog (command Process > Fourier Transform), you

see a value labelled "FID size" and a menu called "FT size". If the

latter is higher than the former, iNMR is going to apply zero-filling.

K is a shortened form for 1024. For example 32 K = 32768 complex

points.

* OPEN CONCLUSION

Though there's not too much to remember, and though it looks simple

and natural, I think that you should digest it all if you want to use

LP successfully. It's open for discussion.

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