Enhancement, resolution,

A more useful filter for resolution enhancement is the convolution difference filter, given by 

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. 

Although the appropriateness of the application of resolutionenhancing apodization is sometimes in doubt, the method does have a physical basis. By multiplying the digitized FID by a function that enhances the intensity of points that are collected later in the 

A single peak from an ordinary liquid chromatogram (a) is revealed as two closely separated peak.s by resolution enhancement (b). 

The reliability of any attempt at determination or characterization of lignin by NMR is dependent on fortuitous similarities in the various spin relaxation parameters. For example, values of T2(H) for lignins tend to be longer than those for cellulose or hemicellulose (Newman 1987, Tekely and Vignon 1987), but the differences are too small to be important for typical values of tp. Values of TI/((H) are sometimes indistinguishable for various components of a sample, and even when differences have been observed, the values are so long that the differences would have little effect on the results (Gerasimowicz et al. 1984, Haw et al. 1984, Maciel et al. 1985). 

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Rey, C., Renugopalakrishnan, V., Shimizu, M., Collins, B. and Glimcher, M.J. 1991 A resolution-enhanced Fourier transform spectroscopic study of the environment of the COj ion in the mineral phase of enamel during its formation and maturation. Calcified Tissue International 49 259-268. 

Bromba, M. U. A., and Ziegler, H., Variable Filter for Digital Smoothing and Resolution Enhancement of Noisy Spectra, Ana/. Chem. 56,1984, 2052-2058. 

Figure 2. Negative FAB mass spectra of maitotoxin. The numbers denote the mass number at the centroid of each peak. A A survey scan at a low resolution (R=300). B. Resolution enhanced spectrum (R=3000) for ion clusters at around m/z 3300. C. Resolution enhanced spectrum (R=3000) for ion clusters at around miz 3400.

The process of exponential multiplication just described produces a rapid decay of the FID and the production of broad lines suppressing the decay of the FID gives narrow lines and better resolution, with increased noise level. An alternative approach to resolution enhancement is to reduce the intensity of the earlier part of the FID. Ideally, we should use a function that reduces the early part of the FID, to give sharper lines, as well as reduces the tail of the FID, to give a better signal-to-noise ratio. 

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... 

What changes in the line shape of an NMR spectrum occur after resolution enhancement ... 

Another resolution-enhancement procedure used is convolution difference (Campbell et ai, 1973). This suppresses the ridges from the cross-peaks and weakens the peaks on the diagonal. Alternatively, we can use a shaping function that involves production of pseudoechoes. This makes the envelope of the time-domain signal symmetrical about its midpoint, so the dispersionmode contributions in both halves are equal and opposite in sign (Bax et ai, 1979,1981). Fourier transformation of the pseudoecho produces signals... 

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. 

F ure 10. solid-state NMR spectra of calcium pectate in the solid (A) and gel (B) forms. Inset resolution-enhanced spectra. The gel concentration was 290 g/1. 

Fig. 9. — (a) H-N.m.r. Spectrum (270 MHz, Resolution-enhanced) of Beef-lung Heparin in D20 (40%, w/v) at 90° (b) Computer-simulated Spectrum, with Calculated, Interproton Coupling-Constants (/, at 35°) for the Amino Sugar (A) and L-Iduronic acid (I) Residues.84... 

VCD and FTIR spectra should always be obtained on the same samples, the FTIR at higher resolution and optimized S/N to permit computation of deconvolved (resolution-enhanced) spectra (Kauppinen etal., 1981). VCD spectra of biomolecules are often normalized to the absorbance, since concentration and path lengths are rarely known to good accuracy. Because the absorbance coefficients for different molecules will vary, this is only an approximate correction for concentration variation. 

Schure, M.R. (1991). Resolution enhancement of chromatographic data. Considerations in achieving super-resolution with the constrained iterative relaxation method. J. Chromatogr. 550, 51. 

As with any separation technique, the desired goal is to maximize peak resolution at the fastest speed. Higher resolution in 2DLC is easier to achieve than when using onedimensional chromatography because selectivity differences between the two different columns can give a resolution enhancement. This is easily seen through the simplified resolution equation, discussed in Chapter 2,... 

FIGURE 2.2 Resolution may increase with increasing frequency. A two-line EPR absorption spectrum is given at three different microwave frequencies. The line splitting (and also the line position) is caused by an interaction that is linear in the frequency the linewidth is independent of the frequency. This is a theoretical limit of maximal resolution enhancement by frequency increase. In practical cases the enhancement is usually less in some cases there is no enhancement at all. 

DQ coherence between C (,-) and C m and then let the DQ coherence evolve under the influence of the heteronuclear I3C-15N dipole-dipole interaction [181, 182]. The virtue of this design is that it can be easily combined with other resolution enhancement technique such as INADEQUATE [183]. Alternatively, the magnetization of C (,) dephased under the 13C-15N dipolar coupling can be transferred to C (j) for another period of 13C-15N dipolar dephasing [183]. This idea can be combined with the NCOCA experiment so that the superior resolution provided by the C (,-)-N(j+i) correlation could be exploited. The overall efficiency, however, is relatively low due to the use of two polarization-transfer steps, viz. 15N —> 13C and 13C —> 13C [183]. In comparison with the techniques, the advan-... 

The presence of effective and legitimate legal, political and social mechanisms of conflict resolutions enhances the possibility of resolving conflict. 

By combining the quantitative approach [23] to extract cross-correlated relaxation with resolution enhancement methods using restricted coherence transfer in a so-called forward directed TOCSY [27], Richter et al. could determine the ribose sugar conformation for all but two residues in a uniformly 13C,15N labeled 25mer RNA [28] and compare them to 3J(H, H) values determined using a forward-directed HCC-TOCSY-CCH-E.COSY experiment [29]. 

Figure 10.1 shows a two-dimensional [15N, H]-TROSY correlation spectrum of the 15N,2H- labeled 110 kDa homo-octameric protein 7,8-dihydroneopterin aldolase from Staphylococcus aureus (DHNA) measured with the pulse sequence of Fig. 10.4 [13]. The gain in spectral resolution and sensitivity is readily apparent from comparison with the corresponding conventional experiment. The optimal sensitivity is achieved by adjusting the polarization transfer r in Fig. 10.4 (3 ms <2r<5.4 ms [3]). For an optimal suppression of the non-TROSY components, the so-called Clean TROSY might be used [19]. Similar signal and spectral resolution enhancements are achieved for 15N,2H-labeled or 13C,15N,2H-...

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