NMR Processing: Convolution: Gaussian Multiplication

Function:
 

The figure shows the continuous example FID after gm with LB = -2.0, GB = 0.3 (upper) and LB = -0.5, GB = 0.3 (lower); these are datasets fid/102 and fid/103 in the download package. Note that Gaussian multiplication gm in TopSpin requires a negative value of LB!

Purpose:

• The objective is an increase in resolution at the expense of the signal-to-noise ratio.
• Another objective is to convert a Lorentzian lineshape to a Gaussian lineshape (for 2D NMR, particularly).

Examples/Exercises:
 

	Click on the figure to see how Gaussian and Lorentzian differ from each other: given the same area and the same full width at half height, the Gaussian peak is much higher and has significantly less excessive "wings". (Also note the optical illusion: the red arrow corresponding to the half width of the Lorentzian is NOT shorter than the black arrow of the Gaussian!)
	How do we go about selecting the proper parameters for gm? Here are two rules of thumb: (i) for LB, take the negative value of the natural line widths of the peaks; obviously, if the line widths differ widely, you won't find a solution that fits them all; (ii) for GB take the fraction of the FID where the signal drops into the noise. In general, you will need to fiddle with both parameters. Pearson reasonably argues that the rule of thumb for GB has shortcomings because according to this procedure it will depend on the number of scans. However, in practice it is a good starting point.
	Click on the figure to see the effect of gm with LB = -2 and GB = 0.2 applied to the synthetic dataset synth/111 in the download package. The decrease in signal-to-noise is notable, but the barely visable splittings are now resolved.
	Click on the figure to see the effect of changing the parameters for gm on the B-11 NMR spectrum of a boron cluster. The peaks at -6, -11 and -12.5 ppm (1 : 5 : 5) arise from the cluster compound, the rest are decomposition products. If you want to repeat the processing, here is the spectrum for download. A modest Gaussian multiplication, LB = -65, GB = 0.6, reveals additional peaks, the shoulder at -16 ppm in the original spectrum is now clearly resolved. If you make LB more negative, e.g. -130 Hz, the peaks will become even narrower, but they will show negative contributions at their wings. This will definitely falsify integration. If you increase GB, the signal-to-noise ratio will drop; in the worst case, you will only observe noise. Have a close look at the spectra treated by gm: the noise looks a little "funny" or strange, not completely random. Instead, there are little packages. An experienced NMR spectroscopist will recognize that you have used Gaussian multiplication, hence you better mention it in your experimental part or the figure legend ;-)

Literature:

• Pearson, J. Magn. Reson. 1987, 74, 541. doi:10.1016/0022-2364(87)90274-5
• Hoffman, Levy, Progr. NMR Spectrosc. 1991, 23, 211; doi:10.1016/0079-6565(91)80005-M
• Lindon, Ferrige, Progr. NMR Spectrosc. 1980, 14, 27; doi:10.1016/0079-6565(80)80002-1