When processing NMR data a window function, or apodisation, is typically applied to emphasise or deemphasise certain aspects of the spectrum. Numerous window functions are available each with their own benefits and drawbacks. A gaussian multiplication is often applied to 1D data to increase resolution at the expense of sensitivity.
Window functions are weighting schemes that are applied to the raw data, or FID, before fourier transformation. A gaussian multiplication emphasises points in the middle of the FID and demphasises those towards the end. Points in the middle are typically responsible for resolution in the spectrum, while those at the end contribute mostly noise. Points at the start define the intensity of the spectrum and are often dominated by large broad peaks.
The function used by the Bruker software to apply a gaussian multiplication (GM) is given by the equation below, where t is a point in the FID, LB is the exponential line broadening parameter, GB is the gaussian broadening, and AQ is the acquisition time or length of the FID.
LB is the same parameter used for an exponential multiplication, but when applying a gaussian negative values are used. LB takes values between zero and one and defines the fraction of the FID that is to be emphasised. The graph below shows example gaussian multiplications with different values of the LB and GB parameters. Notice that the first point is unchanged but all the following points, up until the fraction of the FID defined by GB, are scaled up. Points beyond the fraction defined by GB are scaled down. Also note that the later points are reduced but not scaled to zero. If the FID has not decayed completely at this point then fourier transformation will create sinc wiggles around large peaks. Complete decay of the FID is more likely with 1D data then multi-dimensional data which is why the gaussian multiplication is usually only used on 1D data.
The stackplot below shows an FID apodised with three different gaussian multiplications, all using GB=0.7. At the bottom in black is the unmodified data. The LB parameter was changed from -0.5 Hz for the red FID, to -1.0 Hz for the blue, and -1.5 Hz for the green. Note too, that the vertical scale was increased for the blue (x2) and green (x4) FIDs because of the intensity reduction caused by the apodisation. Notice how the intensity of the points towards the center of the FIDs increases relative to that of the starting points as the magnitude of the LB parameter is increased.
The stackplot below shows the fourier transformed spectra of the FIDs above. This spectrum was collected on a sample of nicotine in acetonitrile-d3 and shows the complicated upfield methylene multiplets. The unapodised spectrum is shown in black at the bottom and the line broadening parameter was changed from -0.5 Hz for the red spectrum, to -1.0 Hz for the blue, and finally to -1.5 Hz for the green. Again, the upper two spectra had to be scaled up because of the loss of sensitivity. The top, green spectrum shows baseline resolution of all the lines in three of the five multiplets, making analysis easier and measuring J-couplings more accurate, however, dips either side of the larger peaks are beginning to appear. These "wings" prevent accurate integrals from being calculated and so spectra apodised with a gaussian multiplication should not be used for integration.
Nicely demonstrated, Brendon. We often use 'extreme' anodizations when trying to pull out the smallest J values (~0.5 Hz or close to the magnet resolution). It helps to also do one zero fill before beginning. - Ted M.
ReplyDelete