Experimentally this is identical with the resolution test as described in Exp. 3.6. You have to set:

td	32 k
sw	1 ppm
o1	center of ODCB multiplet
p1	90° ¹H transmitter pulse
d1	1 s
rg	receiver gain for correct ADC input
ns	1

5. Processing

First transform the FID without any weighting function and observe the line-width of the eighth signal from the left, which should, after good shimming, be in the order of 0.1 Hz.

The theory of the “matched filter” for sensitivity enhancement requires multiplication of the original FID with a function having the same decay constant. This doubles the original line-width and yields the best signal-to-noise ratio without introducing too much distortion or reduction of fine structure. Thus, having measured a line-width of 0.07 Hz in this example, an exponential function with lb = 0.07 Hz was applied to the FID.

The application of Lorentz–Gaussian resolution enhancement requires enough data points to make the improvement visible; thus, zero-filling should be applied first. Adjust the data size si from 16 k to 32 k, which gives a zero-filling of 16 k data points. The Lorentz-Gauss function has two adjustable parameters, gb and lb (Bruker software). The first determines where the maximum of the function is and is given as a fraction of the FID length. Thus a gb of 0.33 puts the maximum of the window function at the end of the first third of the FID, reducing the initial fast-decaying components. The parameter lb is similar to the lb used in exponential weighting, but in some software packages it is applied with a negative sign for distinction. Especially for the Lorentz–Gauss function it is very advantageous to test the result interactively, which is possible in recent software packages. Thus one can, while observing a certain multiplet, make fine adjustments to both parameters to yield optimum results.

6. Result

The figure shows in a the left part of the AA′XX′ spectrum obtained on an ARX-200 spectrometer in a dual probe-head without digital filtering, and in b after application of exponential weighting with lb = 0.07 Hz. Note the improvement in signal-to-noise as judged from the baseline, but also the loss of resolution as seen best for the lines 5 and 6 from the left. In c the result of Lorentz–Gaussian multiplication is given with gb = 0.25 and lb = −0.06. Note the decrease in signal-to-noise, but the improved resolution for lines 5 and 6. Often the Lorentz–Gaussian filtering is excessively applied, leading to negative overshoots at the feet of the signals.