Weighting functions resolution enhancement

Fig. 4.11 Illustration of the use of weighting functions to enhance the resolution in the spectrum. Note that the scales of the plots have been altered to make the relevant features clear. See text for details.

Heteronuclear-shift-correlation spectra, which are usually presented in the absolute-value mode, normally contain long dispersive tails that are suppressed by applying a Gaussian or sine-bell function in the F domain. In the El dimension, the choice of a weighting function is less critical. If a better signal-to-noise ratio is wanted, then an exponential broadening multiplication may be employed. If better resolution is needed, then a resolution-enhancing function can be used. 

Spectral Manipulation Techniques. Many sophisticated software packages are now available for the manipulation of digitized spectra with both dedicated spectrometer minicomputers, as well as larger main - frame machines. Application of various mathematical techniques to FT-IR spectra is usually driven by the large widths of many bands of interest. Fourier self - deconvolution of bands, sometimes referred to as "resolution enhancement", has been found to be a valuable aid in the determination of peak location, at the expense of exact peak shape, in FT-IR spectra. This technique involves the application of a suitable apodization weighting function to the cosine Fourier transform of an absorption spectrum, and then recomputing the "deconvolved" spectrum, in which the widths of the individual bands are now narrowed to an extent which depends on the nature of the apodization function applied. Such manipulation does not truly change the "resolution" of the spectrum, which is a consequence of instrumental parameters, but can provide improved visual presentations of the spectra for study. 

When resolution is a primary concern, as is almost always the case in H NMR, exponential weighting normally is not done. After viewing the spectrum, however, the operator may choose to use a resolution enhancement function. Such a function improves the... 

Figure 2-7 Weighting functions. (a) Sensitivity enhancement. (b) Resolution enhancement.

Many other weighting functions have been used for sensitivity enhancement and resolution enhancement. Perhaps the most popular are the sine bell are variants on it, which are illustrated in Fig. 4.13. 

The basic sine bell is just the first part of a sin 9 for 9 = 0 to 6 = tv, this is illustrated in the top left-hand plot of Fig. 4.13. In this form the function will give resolution enhancement rather like the combination of a rising exponential and a Gaussian function (compare Fig. 4.11 (j)). The weighting function is chosen so that the sine bell fits exactly across the acquisition time mathematically the required function is ... 

The sine bell can be modified by shifting it the left, as is shown in Fig. 4.13. The further the shift to the left the smaller the resolution enhancement effect will be, and in the limit that the shift is by tt/2 or 90° the function is simply a decaying one and so will broaden the lines. The shift is usually expressed in terms of a phase (p (in radians) the resulting weighting function is ... 

Explain why use of a sine bell weighting function shifted by 45° may enhance the resolution but use of a sine bell shifted by 90° does not. 

The group of weighting functions (Figures 8E-G) is used to provide resolution enhancement when the data must be displayed in AV mode. In addition, some 2D experiments such as HMBC produce FIDs which are echos, like the one shown in Figure 9G. Under these circumstances it is usually desirable to match the weighting function to the echo (by adjusting parameters which control the width and... 

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