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Figure 3.34

Figure 3.34

natural decay of the FID signal is delayed and the peaks in the spectrum get sharper. This is especially useful for measuring coupling constants. Of course, "there is no free lunch," so you pay a price in poorer signal-to-noise ratio, but with some samples you have more signal than you could ever want. The naive approach would be to multiply the FID with an exponentially increasing function to "slow down" the natural decay of the FID. As with rabbit population and uncontrolled nuclear fission, exponential growth would be disastrous because the end of the FID (dominated by noise) would be huge and then would suddenly drop to zero. But we can rein it in by multiplying by a Gaussian function (the old statistical bell curve):

The first exponential is increasing if LB is made negative. The second one, the Gaussian term, reaches a maximum at time t = t, which can be set to any time during the FID. In Figure 3.34, the parameters for the Gaussian window are set to LB = — 1 Hz, with t adjusted to make the window reach a maximum at one fourth of the way through the FID. The first quarter of the FID is multiplied by an increasing function, slowing down the decay of the FID data, whereas the rest of the window function is decreasing, bringing the noise down.

A very simple window function for resolution enhancement is the sine bell (Fig. 3.34), which is just the function sin(x) for x = 0 to 180°. This function "grows" for the first half of the FID and then brings the signal smoothly to zero during the second half. We saw examples of this window in Chapter 2 (Figs. 2.9 and 2.10). We will see that the sine-bell family of

None Gaussian Sine-bell lb=1.0
0 0

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