Pseudo-deconvolution

It is still possible to enhance the resolution also when the point-spread function is unknown. For instance, the resolution is improved by subtracting the second-derivative g x) from the measured signal g x). Thus the signal is restored by ag x) - (7 - a)g Xx) with 0 < a < 1. This llgorithm is called pseudo-deconvolution. Because the second-derivative of any bell-shaped peak is negative between the two inflection points (second-derivative is zero) and positive elsewhere, the subtraction makes the top higher and narrows the wings, which results in a better resolution (see Fig. 40.30). Pseudo-deconvolution methods can correct for sym-... 

There are, however, a number of methods [30] available for doing slit profile corrections in the spectral domain, Jones et al [31] have described a method based on slit pseudo-deconvolution. If the slit function is Igj (o)) and if the observed spectrum is obs then the true spectrum may be obtained from... 

The principle of image deconvolution is based on the same theory of the pseudo-WPOA but the procedure is different in the case of a defect stmcture. Replace in equation (5) with, which is the stmcture factor... 

If the ring electrode of the rotating ring-disc system monitors the flux of the oxidized or reduced components of the redox couple, then deconvolution of both Faradaic and pseudo-capacitive currents may be done [85]... 

One of the critical aspects of this approach is that two different experiments have to be performed between which the particular instrument conditions must be carefully kept constant in order not to affect the intensity ratios. This problem can be overcome by the enantiomer-labeled guest method [47]. It is based on the mass spectrometric examination of one enantiomer of the host with a pseudo-racemic mixture of the guest. In order to be able to detect both diastereomers separately, one enantiomer of the guest must be isotopically labeled, usually with deuterium. In the same experiment, both diastereotopic complexes are formed and their intensities can be compared directly. However, the stereochemical effect might additionally be superimposed by an unknown isotope effect. A way to separate stereochemical and isotope effects is to perform the same experiment with the second host enantiomer [4B]. In one experiment both stereochemical and isotope effects disfavor the same complex and thus work in the same direction. In the other experiment, they partly cancel each other. If both experiments have been performed, one can use the two experimental values for the intensity ratios of both diastero-meric complexes to deconvolute both effects [49]. 

The experiments described above produce accurate decay constants only when sir is negligible. The apparent kinetic parameters that are obtained when this is not the case involve all of the k and W values simultaneously. It is not possible under these circumstances to obtain the actual decay constants from these experiments. Experimental methods have been developed, however, that allow extraction of the individual k and W values in the presence of slr. One method applies to the regime where sir is dominant, that is, W > k, whereas the other is applicable when W < k. The latter method has been applied to biopolymer ODMR and involves deconvolution of phosphorescence decays measured during continuous microwave saturation of pairs of triplet sublevels. Microwave saturation creates a pseudo-two-level system whose decays are easily deconvoluted and are amenable to analysis. The analytical development of the microwave-saturated phosphorescence decay method is rather lengthy, so it is not discussed in this chapter. Detailed descriptions of the method may be found elsewhere. 

FIGURE 7.2 A representative multiplexed DTIMS gating sequence. The ion beam is modulated using a pseudo-random sequence (PRS) derived from a Simplex matrix, which is applied to the BNG. This is mathematically expressed as a multiplication of the original ion mobility spectra (4 ) by the Simplex matrix (S ,). The multiplexed spectrum (T)) is collected at the detector. The deconvoluted data (ip) is recovered by multiplication of the multiplexed spectrum (Tj) with the inverse of the Simplex matrix (S ). 

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