Gaussian multiplication

Gaussian multiplication (Ernst, 1966 Marco and Wuethrich, 1976) has been used widely for resolution enhancement without significant loss of sensitivity in ID NMR spectra. There are two parameters altered by the... 

It is also possible to play other mathematical tricks with the FID. For example, we may want to make our signals appear sharper so we can see small couplings. In this case, we want our FID to continue for longer (an infinite FID has infinitely thin lines when Fourier transformed). To do this we use Gaussian multiplication . This works exactly the same way as exponential multiplication but uses a different mathematical function (Figure 4.2). 

It should be noted that Gaussian multiplication can severely distort peaks and also reduce signal-to-noise of the spectrum so it is not a good idea to do this if you have a very weak spectrum to start with. Spectrum 4.1 shows a real case where Gaussian multiplication has been able to resolve a triplet. Note that it is possible to just make out the triplet nature of the peak in the unmultiplied spectrum - Gaussian multiplication helps verify this and also allows us to measure the splitting pattern. 

Gaussian multiplication The application of a mathematical function to an FID to improve resolution (sharpen lines) at the expense of signal/noise. 

Figure 7.3.1.7 A 13C-decoupled HMQC spectrum of 54 mM chloroquine diphosphate in D2O acquired with an inverse detection microcoil probe. The 740-nl F0bs contained 40 nmol (13 jig) of chloroquine. The data, 32 transients per slice, 1024 x 128 (x2, hypercomplex) points, were acquired in 3.6h. The data were zero-filled to 256 points in the 13C dimension. A 40° shifted sinebell function was applied, followed by Gaussian multiplication prior to Fourier transformation...

FIGURE 45. 29Si spectra of HN(SiMe3)2 (at 71.55 MHz, 80% in CgDf, 10 mm sample tube, 2 K data points zero-filled to 8 K) acquired (a) with INEPT (16 transients) (b) the same as (a) after Gaussian multiplication (LB = —1 Hz, GB = 0.7) (c) with DEPT (16 transients) — note the effect of the longer sequence (d) with HEED-INEPT (64 transients, x = 35.7 ms, A = 19.06 ms, T = 0.3 s). Reproduced by permission of Academic Press from Reference 307... 

Answer Gaussian multiplication has been applied to the FID to improve the resolution. The line broadening (LB) was set to -1.0 Hz and the Gaussian maximum (GB) to 0.1. The resulting spectra have distorted lineshapes and intensities. If we attempt to enhance the resolution still further using a GB of 0.15 and an LB of -2.0 Hz, the spectrum becomes almost unrecognizable, as shown below. These parameters must be optimized for each spectrum, or even each signal. 

Gaussian multiplication is also an attractive alternative to increase sensitivity, with some concomitant alteration in line shape, as well as width. In this case... 

The multiplication here is a good approximation to exponential multiplication (for A = 2) and to Gaussian multiplication (for A 5= 3). For zero shift, the first data point will be nulled and hence dispersive contributions to the FID are eliminated. An advantage of this function over the commonly used real EM or GM is the fact that the sine functions decay to zero, eliminating truncation oscillations. 

Figure 3.37. The Lorentz-Gauss transformation ( Gaussian multiplication ) can be used to improve resolution, (a) Raw FID and spectrum following Fourier transformation and results after the L-G transformation with (b) lb = -IHz, gb = 0.2 and (c) lb =...

Gaussian multiplication, which has been used to improve resolution on the basis of lineshape modification ... 

Fig. 1. P-NMR spectrum of 50 mA/HjP 04 (40 atom % 0,27 atom % K)) in DjO, pD 1.8 at 81.0 MHz. Spectral parameters acquisition time 4.1 s, delay 1.0 s, spectra width 2 kHz, 70° pulse, line broadening 2.0 Hz, 1600 scans. The inset shows the expanded spectrum of the sharp peak, processed with Gaussian multiplication (LB = —2, GB= 0.2). Chemical shift 0.09 ppm downfield from 1 Af H3PO4.

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