Sampling, non-uniform

Because X-ray powder diffraction deals with solid samples, the analytical variables are different from those associated with the analysis of liquid or solution samples. Principle among these are particle size effects, uniform sample surface, crystallinity and X-ray absorption. Although particle size and a non-uniform sample surface are serious problems, their... 

Every brain biopsy specimen should be handled in such a way that if inflammation is found at surgery, it will be possible to culture the tissue for bacteria, mycobacteria, and fungi and to use special stains, immunostain-ing techniques, and electron microscopy. This author s experience has been that for organisms that grow in vitro, microbiologic culture is preferable to histochemi-cal stains, IHC, or polymerase chain reaction (PCR) assay if sampling of the lesion is uniform. Prior antibiotic treatment or non-uniform sampling of focal infection affects individual cases. 

The above formalism is quite general, and can be used to study the effects of doing transmission EXAFS on non-uniform samples and particles of all sorts. However, the mathematics quickly become forbidding if one looks at a realistic situation such as a particle illuminated by a Gaussian beam. Such situations require numerical methods. For a simple, analytically accessible example, imagine a uniform foil with a hole in it such that a fraction/of the beam goes through the hole. Then, we have... 

Rovnyak D, Frueh DP, Sastry M, Sun ZYJ, Stem AS, Hoch JC, Wagner G (2004) Accelerated acquisition of high resolution triple-resonance spectra using non-uniform sampling and maximum entropy reconstruction. J Magn Reson 170 15-21... 

Sun ZY, Hyberts SG, Rovnyak D, Park S, Stem AS, Hoch JC, Wagner G (2005) High-resolution aliphatic side-chain assignments in 3D HCcoNH experiments with joint H-C evolution and non-uniform sampling. J Biomol NMR 32 55-60... 

Mehdi M, Alan SS, Wolfgang B, Glenn FK, Jeffrey CH, (2010) A non-uniformly sampled 4D HCC(CO)NH-TOCS Y experiment processed using maximum entropy frn- rapid protein sidechain assignment J Magn Reson 204 160-164... 

Generalized Fourier Transform for Non-Uniform Sampled Data... 

Coupling between peak width and number of sampling points (i.e., experimental time) is the main reason for the use of non-uniform sampling in NMR. 

For non-uniform sampling the FT of sampling schedule (sometimes referred to as Point Spread Function, PSF) is not a simple train of delta pulses, but becomes a more complex function (see Sect. 4 and Fig. 6). This, in general, leads to three conclusions ... 

For arbitrary, non-uniform sampling it is no longer possible to obtain a spectrum that is equal to a spectrum of continuous signal, even if it is strictly band-limited. Spectral artifacts, depending on the sampling schedule, appear as part of Point Spread Function. 

Recently the method employing DNP for recording heteronuclear 2D NMR spectra of small drug-like molecules was proposed by Ludwig and coworkers [101]. This method ensures significant improvement in sensitivity due to the high spin polarization, but limits the number of points sampled in indirectly detected dimension, so the combination with the non-uniform sampling scheme was necessary. 

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