Gaussian multiplication, resolution

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... 

Gaussian multiplication The application of a mathematical function to an FID to improve resolution (sharpen lines) at the expense of signal/noise. 

Answer Gaussian multiplication has been applied to the FID to improve the resolution. The line broadening (LB) was set to -1.0 Hz and the Gaussian maximum (GB) to 0.1. The resulting spectra have distorted lineshapes and intensities. If we attempt to enhance the resolution still further using a GB of 0.15 and an LB of -2.0 Hz, the spectrum becomes almost unrecognizable, as shown below. These parameters must be optimized for each spectrum, or even each signal. 

Figure 3.37. The Lorentz-Gauss transformation ( Gaussian multiplication ) can be used to improve resolution, (a) Raw FID and spectrum following Fourier transformation and results after the L-G transformation with (b) lb = -IHz, gb = 0.2 and (c) lb =...

Gaussian multiplication, which has been used to improve resolution on the basis of lineshape modification ... 

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. 

Matched filter The multiplication of the free induction decay with a sensitivity enhancement function that matches exactly the decay of the raw signal. This results in enhancement of resolution, but broadens the Lorentzian line by a factor of 2 and a Gaussian line by a factor of 2.5. 

Diffusion and mass transfer effects cause the dimensions of the separated spots to increase in all directions as elution proceeds, in much the same way as concentration profiles become Gaussian in column separations (p. 86). Multiple path, molecular diffusion and mass transfer effects all contribute to spreading along the direction of flow but only the first two cause lateral spreading. Consequently, the initially circular spots become progressively elliptical in the direction of flow. Efficiency and resolution are thus impaired. Elution must be halted before the solvent front reaches the opposite edge of the plate as the distance it has moved must be measured in order to calculate the retardation factors (Rf values) of separated components (p. 86). 

To determine whether alternative ANN architectures can lead to improved resolution and successful agent detection, Radial Basis Function (RBF) networks [106] were considered for the same problem. RBFs are networks with one hidden layer associated with a specific, analytically known function. Each hidden layer node corresponds to a numerical evaluation of the chosen function at a set of parameters Gaussian waveforms are often the functions of choice in RBFs. The outputs of the nodes are multiplied by weights, summed, and added to a linear combination of the inputs, yielding the network outputs. The unknown parameters (multiplicative weights, means and spreads for the Gaussians, and coefficients for the linear combination of the inputs) are determined by training the RBF network to produce desired outputs for specific inputs. 

The high resolution solid-state H spectra, measured for different dried PVA films by combined rotation and multiple pulse spectroscopy (CRAMPS), are shown in Fig. 19.16. Here, a fully main-chain deuterated atactic PVA (A-PVA-resonance lines assignable to OH, CH and CH2 protons can be clearly observed, although the OH lines are rather broad and superposed on the neighboring CH lines. To discriminate well between the contributions of OH and CH protons, these superposed lines were resolved into their respective contributions, as shown in Fig. 19.16. In this analysis, each line was assumed as a Gaussian curve, and the validity of this assumption was confirmed by the good fitting for A-PVA-rf. ... 

The accuracy with which the mass of an ion can be determined is a combination of the ability to resolve one ion from another and how accurately the mass scale has been calibrated. There are multiple elemental compositions possible for any given nominal mass, e.g., (as noted above) there are three possible formulae, CO, Nj, and C2H4, at ndz 28, and the number increases rapidly as one moves up the mass scale. To obtain accurate measurements for each component of a set of isobaric ions, it is essential to resolve them from each other. As resolution increases and peaks become narrower, it becomes easier to be certain that an observed peak is a unique species and that the outline of the peak is Gaussian. Consequently, the center of gravity of the peak can be determined and the accurate mass of the ion calculated (Figure 3.3). 

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