Convolution difference

Recent reports 54 seem to indicate that the resolution of the notoriously difficult solid-state spectra of coals may be enhanced by such techniques as double exponential multiplication and convolution difference. Differential relaxation behaviour as discussed in connection with intermolecular effects in carbohydrates and low temperature methods may further improve identification. 

Figure 1.36 Various selected apodization window functions (a) an unweighted FID (b) linear apodization (c) increasing exponential multiplication (d) trapezoidal multiplication (e) decreasing exponential multiplication (f) convolution differ-...

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... 

Chemical shifts (8) are given in p.p.m. downfield from sodium 4,4-dimethyl-4-silapentane-l-sulfonate the values in parentheses are coupling constants (Jia) in Hz. The numbering of the monosaccharide units in the reference compounds corresponds to that in the asialoglycan-Asn (see fundamental structure in Table II). Values from a convolution-difference spectrum. 

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

A detailed H study of P. aeruginosa cytochrome c-557 has been made (666) with the aid of the convolution difference technique. (585) A partial analysis has been reported and the structure of this cytochrome is shown to have many features in common with the mammalian cytochromes c despite having 20-25 fewer amino-acids. 

FIG. 13. (a) Aromatic carbon region in the convolution-difference natural abundance C spectra of myoglobins recorded at 15-18 MHz, under conditions of noise-modulated off-resonance decoupling and 32768 accumulations per spectrum. See ref. 683 for line assignments, (b) The eight titratable carbons of the histidine residues (plus C of Tyr-103, peak 27) of horse cyanoferrimyoglobin at 38°C. 

Figure 3.X The methyl region of a 270 MHz HNMR spectrum of human leukaemia lysozyme (5 mM, 55°C). The upper trace is the normal spectrum, the lower trace (a) is a convolution difference spectrum. Note the additional fine structure present in (a) which aids...

In the case of narrow unwanted signals a notch filter introduced by Marion et al. [80] and Cross [81] can be more efficient. These filters are based on convolution difference and usually employ a Gaussian function or sine-square function as a notch filter. 

Fig. 16. (A) The first increment of a NOESY spectrum of a 3 mM sample of a 26 amino acid peptide from the hepatitis B envelope protein recorded in 90% H2O at 273 K on a 500 MHz spectrometer. (B) Same as (A) but after applying the shifted time-domain convolution difference filter. (From Sodano and Delepierre with permission.)...

Figure 23. (A) Aromatic region of the convolution difference H-NMR spectrum at 360 MHz of a BPTl solution in HjO, pD = 7.8 = 26°. (B) Double-resonance irradiation at 7.07 ppm causes the collapse of a doublet at 7.33 ppm. (C) Irradiation at 7.33 ppm causes the collapse of a doublet at 7.07 ppm. The assignment of this AA BB spin system to residue 10 is from Reference 67. From [68].

Figure 17. Convolution difference C CP/MAS spectra of Powhatan 5 coal. The sharp peak at —2 ppm is due to an added external standard.

For Si work the glass in the probe area can be a nuisance, since it gives a broad resonance ca. 110 ppm to low frequency of the signal due to Me Si. This is only really a difficulty when compounds containing silicon tetrahedrally bonded to four oxygens are being studied, since otherwise chemical shifts are sufficiently removed from the problem area. Use of plastic NMR tubes (and even plastic probe components) can reduce or eliminate the problem. Convolution-difference methods are also applicable in some cases, but not when the sample itself contains silica-type materials—in such cases a blank run must be employed (14), which reduces spectrometer efficiency substantially. 

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