NMRPipe Processing Functions
GM: Lorentz-to-Gauss Window.

GM applies a Lorentz-to-Gauss window, which is a combination of an inverse exponential and a Gaussian. The purpose of the window is to replace the exponential decay of the original data with a Gaussian decay, so that the corresponding spectral lineshape will be more like a Gaussian rather than a Lorentzian. The exponential term is specified as a Lorentzian line sharpening in Hz. The Gaussian term is specified as a Gaussian line broadening in Hz, and a center position (location of the Gaussian maximum). The Gaussian center position is specified as a value ranging from 0.0 (Gaussian maximum at the first point of the FID) to 1.0 (Gaussian maximum at the last point of the FID). In a usual application, the Lorentzian line sharpening is chosen to match the intrinsic decay of the time-domain data, and the Gaussian broadening is chosen to provide a suitable degree of decay. In most cases, this means that the Gaussian broadening will be substantially larger than the Lorentzian sharpening.

In the following formula for GM, tSize is th number of time-domain points, which defines the length of the window function; GM[i] is the window function from i = 0 (first point) to i = tSize - 1 (last point); and sw is the sweep width in Hz.

          GM[i] = exp( e - g*g )

          e = PI*i*g1/sw
          g = 0.6*PI*g2*(g3*(tSize-1) - i)/sw

In addition to function-specific options, the GM window function provides the following features common to all NMRPipe window functions:

• Optional scaling of the first point of each FID.
• Automatic recording of window parameters and first point scaling in the data header during processing.
• Automatic adjustment of the default size of the window function to match the valid time-domain size recorded in the header.
• Optional extraction and use of window parameters recorded in the header, rather than from the command-line.
• An inverse mode, which divides by the window function and first point scale rather than multiplying by them.
• Options to adjust the size or starting point of the window function via command-line arguments.

GM OPTIONS

-g1 invExpHz
(Q1) Specifies the inverse exponential to apply in terms of a line sharpening in Hz. It is usually adjusted to match the natural linewidth. The default value is 0.0, which means no exponential term will be applied, and the window will be a pure Gaussian function.

-g2 gaussHz
(Q2) Specifies the Gaussian to apply in terms of a line broadening in Hz. It is usually adjusted to be larger (x 1.25 - 4.0) than the line sharpening specified by the -g1 option.

-g3 gCenter
(Q3) Specifies the position of the Gaussian function's maximum on the FID. It is specified as a value ranging from 0.0 (Gaussian maximum at the first point of the FID) to 1.0 (Gaussian maximum at the last point of the FID). It most applications, the default value of 0.0 is used.

GENERIC WINDOW OPTIONS

-size aSize
Specifies the number of points in the window function. The default value is the valid time-domain size recorded in the data header.

-start aStart
Specifies the starting point of the window function. The default value is 1, which means the window function starts at the first point of the FID. This option is intended for creation of composite windows by application of different functions to different regions of the FID.

-c fScale
Specifies the scaling applied to the first point of the FID, which influences the zero-order offset in the corresponding spectrum. The default value is 1.0, which means no first point adjustment is applied. A value of 0.5 is usually appropriate in cases where no substantial first-order phase correction will be applied.

-one
This flag influences the values used "outside" the window function, in cases where the window size is smaller than the actual number of data points. By default, data values outside the window region are multiplied by zero when the window is applied. However if the -one flag is used, data values outside the window region will be multiplied by 1.0 when the window is applied. This flag is intended to assist creation of composite windows by application of different functions to different regions of the FID.

-hdr
When this flag is used, default window parameters (Q1,Q2, and Q3) will be extracted from the data header, along with the first point scaling. This requires that all of these parameters have already been recorded, for instance during previous processing or format conversion (see EXAMPLES below). Additional command-line can be used to override values restored from the header. The window parameters stored in the data header can be viewed using the showhdr program, for example:

          showhdr -verb test.ft2

-inv
When this flag is used, the inverse (1/window) of the selected window and first point scale will be applied. This option is intended for removing a previously-applied window in inverse processing schemes. This option should generally only be used on window functions which have no values close or equal to zero. In cases where the window does have a zero value, the inverse window is also given as zero.

EXAMPLES

A typical usage of a Lorentz-to-Gauss window:

        nmrPipe -fn GM -g1 20 -g2 35

The following scheme shows window parameters (APOD, Q1, Q2, and Q3), first point scale (C1), and phasing (P0, P1) specified during conversion. The values are then extracted and used during processing by including the -hdr option with processing functions APOD and PS:

      #!/bin/csh

      bruk2pipe -in hsqcn.ser \
       -xN           2048    -yN         256   \
       -xT           1024    -yT         128   \
       -xMODE     Complex    -yMODE  Complex   \
       -xSW       9090.91    -ySW    2500.00   \
       -xOBS      600.138    -yOBS   60.8108   \
       -xCAR         4.73    -yCAR     118.0   \
       -xLAB           HN    -yLAB         N   \
       -xAPOD          GM    -yAPOD       GM   \
       -xQ1            20    -yQ1         10   \
       -xQ2            35    -yQ2         15   \
       -xQ3           0.0    -yQ3        0.0   \
       -xC1           0.5    -yC1        1.0   \
       -xP0           0.0    -yP0      -90.0   \
       -xP1           0.0    -yP1      180.0   \
       -ndim            2    -aq2D    States   \
       -out hsqcn.fid -verb -ov

      nmrPipe -in hsqcn.fid \
      | nmrPipe  -fn SOL                         \
      | nmrPipe  -fn APOD -hdr                   \
      | nmrPipe  -fn ZF -auto                    \
      | nmrPipe  -fn FT                          \
      | nmrPipe  -fn PS -p0 22 -p1 0.0 -di       \
      | nmrPipe  -fn EXT -left -sw -verb         \
      | nmrPipe  -fn TP                          \
      | nmrPipe  -fn APOD -hdr                   \
      | nmrPipe  -fn ZF -auto                    \
      | nmrPipe  -fn FT                          \
      | nmrPipe  -fn PS -hdr -di                 \
         -verb -ov -out test.ft2

HEADER VALUES

GM and the other nmrPipe window functions use the recorded time-domain size (NDAPOD) to establish their default length.

When the -hdr flag is used, default window parameters are extracted from header values NDAPODCODE, NDAPODQ1, NDAPODQ2, NDAPODQ3, and NDC1.

The header values NDAPODCODE, NDAPODQ1, NDAPODQ2, NDAPODQ3, and NDC1 are updated according to the values applied during processing.