Gaussian deconvolution method

Figure 2.30 MAS NMR spectra of (A) TMPO and (B) TBPO adsorbed on fresh (MOR/F), regenerated (MOR/R), and various coked (MOR/C) samples. The dashed curves represent simulation of resonance peaks by Gaussian deconvolution method. Shaded peaks denote contributions from physisorbed adsorbates and the spinning sidebands are indicated by asterisks [75].

The two most common methods used to correct resolved peak profiles for the broadening imposed by the finite width of the X-ray beam in the diffractometer, are due to Jones (15) and Stokes (16). Both are essentially unfolding or deconvolution methods, but the Jones method defines specific functions for both the uncorrected and the instrumental broadening profile. If the uncorrected profile is Gaussian, then... 

In order to find out which of the Trp residues that is the most affected by the presence of calcofluor, two deconvolution methods were applied. In the first method, we fitted the spectra obtained as a sum of Gaussian bands. In the second one, we used the method described by Siano and Metzler (1969), and that was then applied by Burstein and Emelyanenko (1996) using a four parametric log-normal function (a skewed Gauss equation). The analysis were done at the three excitation wavelengths (295, 300 and 305 nm), although the results shown are those obtained at = 295 nm. 

Deconvolution methods can also be used to suppress residual water signals as demonstrated by Marion et Assuming that the latter are at the center of the spectral window, water is responsible for the low frequency component of the FID. A convolution of the time domain spectrum with a Gaussian or sine bell makes it possible to filter out the higher frequency and only retains the water component, which can later be subtracted from the original FID. This procedure can be fully automated and is quite appropriate for two- and three-dimensional experiments in the presence of water. The same year, Hoffman and Levy applied a computationally very demanding simulated annealing method to one-dimensional NMR spectra. 

When conventional methods of manual optimisation are no longer sufficient, it is possible to use deconvolution software or fuzzy logic to deconvolute unresolved peaks into Gaussian components for which the area can be easily measured (see Fig. 1.12). 

Two methods of deconvolution can be employed the standard deconvolution called DCV where the image Pc is convolved by the matrix M which describes the aperture transmission, the deconvolution called PSF to which we add a convolution of a gaussian of which the sigma is adapted to the spatial resolution (2.61 pixels SI in 40-75 keV energy band). This new convolution allows to obtain the most significant flux and to eliminate the high frequency noise [5]. 

FIGURE 11.7 (a) Affinity distributions obtained at different ionic strengths from experimental data for purified peat humic acid (PPHA) (b) deconvolution of the distribution obtained for PPHA with Gaussian functions. (Data from Milne. C.J. et al.. Environ. Sci. TechnoL, 37, 958-971, 2003 Reprinted from J. Colloid Interface Sci., 336, Orsetti, S. et al., Application of a constrained regularization method to extraction of affinity distributions Proton and metal binding to humic substances, 377-387. Copyright 2009, with permission from Elsevier.)... 

---