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Window functions

Window functions

NUTS Help

Window functions

This section describes the apodization options provided by NUTS. 

See also: Introduction to apodization,  Reference deconvolution, Creating custom window functions, interactive application of window functions

Before applying a window function or doing an FT, the FID may need to be corrected for any offset from zero.

BC — Baseline Correction of the FID

If the data is time domain data (FID), this command averages the last 10% of the points of a complex FID set and then removes that DC offset from each FID. (A different DC offset between the 2 channels can result in a glitch in the center of the spectrum, see example.)

Note that this command acts differently if the current data is a spectrum, rather than an FID. 

BA — Baseline Average

This is an alternative to BC for removing DC offset between the real and imaginary halves of the data.  Instead of calculating the average of just the last 10% of the data (as BC does), BA calculates the average of all data points, then subtracts this average from each point.  This command only makes sense for FID data.


A quick way to see the shape of a chosen function is to open the FID to which it will be applied and execute the 21 command.  This sets the value of all data points to one.  Then apply the chosen function to see its shape.

Note that some apodization functions are dependent on time, so the total shape applied depends on the acquisition time of the FID.  By contrast, the sine functions (MS) apply one half of a sine wave over the entire FID, regardless of the acquisition time.

WV — Window View

This command allows interactive adjustment of parameters defining various window functions. The FID, the apodization function and the spectrum after apodization are shown simultaneously. Parameters can be adjusted and the new window function automatically applied, and the screen is updated. See details.

LB — Linebroadening

This parameter defines the decay of the exponential weighting function applied to the FID with the EM command, to enhance signal-to-noise. The value for the linebroadening (LB) must be set first. LB is set via a dialog box brought up by typing LB or selecting Conditions under the Process menu. The exponential multiplication is executed either by typing EM or by selecting it from the Window Functions menu within the Process menu.

EM — Exponential Multiplication

Applies an exponential weighting function to the FID to enhance signal-to-noise. The value for the linebroadening (LB) must be set first. LB is set via a dialog box brought up by typing LB or selecting Conditions under the Process menu. The exponential multiplication is executed either by typing EM or by selecting it from the Window Functions menu within the Process menu. Note the other available window functions which are listed in this menu.

The larger the value of LB, the faster the window function drops toward zero.  

         LB = 1

 

        LB = 3

GM — Gaussian Multiplication

Apodization function for Signal-to-Noise enhancement. This is similar to exponential multiplication (EM) but results in a Gaussian rather than Lorentzian lineshape. The amount of line broadening is set with LB.

The GM command uses the following equation:

G(t) = exp[-(PI*LB*time)^2 / (4*ln(2)) ]

Ref: equation [9], p543, in G.A.Pearson, "Optimization of Gaussian Resolution Enhancement", J.Mag.Res. 74, 541-545 (1987).

Do not confuse this with Lorentzian/Gaussian resolution enhancement.

As with EM, the larger the value of LB, the faster the window function drops toward zero.  

 

     LB = 1

 

        LB = 3

SG — Shifted Gaussian

Apodization function which is a gaussian shape centered at one-half the acquisition time.  The shape is determined by the value of LB.  Larger LB results in faster roll-off of the function.

        LB = 1

 

        LB = 3

IG — Incrementally Shifted Gaussian

This is a gaussian function for 2D data, in which the center of the gaussian is shifted based on the slice number.

LG — Lorentzian/Gaussian resolution enhancement

This command multiplies the FID by a function which combines a Lorentzian using a negative line broadening with a Gaussian. The composite function has the shape shown below. Two parameters must be specified before LG can be executed: LB (line broadening, the same parameter used by the EM command) and GF (Gaussian factor). LB must be negative for the Lorentzian/Gaussian function. If LB is set to a positive number, NUTS will use the negative of that value. GF is a number between 0 and 1 and defines where the maximum of the function will be, as a fraction of the acquisition time. (This is the same as the Bruker GB parameter). Reasonable starting values are LB = -1 and GF = .3, and then adjust empirically.

This command is also available from the Process menu under Window Functions.

Reference: A.G.Ferrige and J.C.Lindon, J. Magn. Reson., 37, 337 (1978).

GF — Gaussian Factor for LG command

This is one of the 2 required parameters for Lorentzian/Gaussian resolution enhancement. It must be a number between 0 and 1. (If its value is set outside these limits and the LG command is executed, NUTS will reset the GF value.) The GF value sets position of the maximum of the Gaussian function, expressed as a fraction of the acquisition time.

TF — TRAF resolution enhancement

Performed on a FID. The function has the shape shown below. The user must input a value for LB, which is an estimate of the natural linewidth. The TRAF function provides resolution enhancement with minimal loss of signal-to-noise.

Reference: D.D.Traficante and D.Ziessow, J. Magn. Reson., 66, 182-186, (1986).

JT — S-TRAF resolution enhancement

Performed on a FID.  The function has the shape below.  The user must input a value for LB, an estimate of the natural linewidth.  Shown below is LB = .3

MS — Multiply Sine

Multiply the reals and imaginaries by a window function which is the first half of a sine wave. Executing the command twice gives a sine squared window function.  These 2 figures show the shape of sine and sine squared functions.

    

The sine function may have a starting phase different from zero. This phase angle must be set with the S# command before MS is executed.  The next 2 figures show the shape of sine and sine squared functions with phase (S#) of 45.

 

The next 2 figures show the shape of cosine and cosine squared functions, which are sine functions with phase (S#) of 90.

This is also available from the Process/Window Functions menu. Note the other window functions which are available from this menu.

S# — Phase shift for sine multiplication

Used in conjunction with the Multiply Sine (MS) apodization function. The phase shift is entered in degrees. This can also be set within a macro, for example, for 2D processing.

The only valid values for S# are between 0 and 90, inclusive. Entering a value less than 0 or greater than 90 will cause NUTS to set the value to 0 or 90, respectively.

TM — Trapezoidal Multiplication

Multiplies FID by a trapezoidal shaped function defined by parameters T1 and T2. The first T1 number of points are scaled linearly from zero to one. The last T2 number of points are scaled linearly from one to zero to avoid truncation of the FID. Other points are unchanged. This command is available from the Process/Window Functions menu. Note the other available window functions which are listed in the menu, including sine multiplication (MS), Lorentzian/Gaussian (LG) and Traficante function (TF) for resolution enhancement.

 

T1 — Trapezoidal multiplication parameter

Defines the number of data points, starting from zero, to be scaled by the TM command.

T2 — Trapezoidal multiplication parameter

Defines the number of points at the end of an FID to be scaled by the TM command.

 

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Last updated: 3/13/04.