Gaussian apodization

Figure 6 Simulated 2H (73.58 MHz) QCPMG spectra corresponding to a 3-by-2-site jump process using parameter set P2b in Table 1 and the single-frame set of Euler angles were69 (0.0,124.0, 0.0), (57.594, 55.006, 91.716), (302.406, 55.006, 268.206), (0.0, 124.0,180.0), (57.594, 55.006, 271.716), (302.406, 55.006, 88.206). The logarithm of the rate constants and k2 are indicated at each row and column of the spectra. All spectra were apodized by Gaussian line broadening of 50 Hz prior to Fourier transformation.

Figure 7 Simulated 2H (73.58 MHz) MAS spectra corresponding to a 3-by-2-site jump process the same parameter set as in Figure 6. The logarithm of the rate constants and k2 are indicated at each row and column of the spectra. All spectra were apodized by Gaussian line broadening of 50 Hz prior to Fourier transformation.

The use of certain apodization functions improves the frequency resolution we obtain in our Fourier-transformed spectrum, but caution should be exercised when employing this technique. The use of negative line broadening and shifted Gaussian or squared sine bells (with the maximum to the right of the start of the FID) can be used to resolve a small peak that formerly appeared as the shoulder of a larger peak, but supervisors and reviewers frown upon the excessive application of these methods the starting NMR spectroscopist would do well to exercise restraint in this area. 

Figure 5e shows the remarkable result that the Fourier transform of a Gaussian (time-domain signal) is also a Gaussian (frequency-domain signal). This property can be especially useful in manipulating spectral line shapes (see Apodization, below). 

We have described a procedure for assigning line positions that requires no operator intervention [8]. The data segment containing each line is moved to the Fourier domain and apodized with a Gaussian function. The line is zero-filled and inverse transformed to... 

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