Deconvolution of experimental

The accuracy of peak deconvolution programs can be tested with synthetically overlapping peaks 43,58). Another procedure is useful for checking deconvolution of experimental peaks a gas chromatograph is... 

Fig. 17 Deconvolution of experimental IR spectra in the CO stretching region (symbols) into three Lorentzian components (lines 1,2, and i) for (a) Cr (ID/S948-500 and (b) Crai)/ S948-800. The spectra predicted by the deconvoluted components is also shown...

Mannschreck, A. Kiessl, L. Enantiomerization during HPLC on an optically active sorbent. Deconvolution of experimental chromatograms. Chromatographia 1989, 28 (5-6), 263-266. 

The procedure for deconvolution of experimental spectra is, therefore, as follows ... 

In order to extract the contributions and dynamics of the ketyl radical and fluoranil anion from the TR spectra obtained with the 416 nm probe wavelength, a deconvolution of the Raman bands were done using a fitting procedure employing a Lorentzian lineshape for the Raman bands of the two intermediates. Figure 3.20 shows a comparison of the best-fit (lines) to the experimental TR spectra (dots) in the left-side spectra and the deconvolution extracted from this best fit for the ketyl radical spectra... 

There is significant debate about the relative merits of frequency and time domain. In principle, they are related via the Fourier transformation and have been experimentally verified to be equivalent [9], For some applications, frequency domain instrumentation is easier to implement since ultrashort light pulses are not required, nor is deconvolution of the instrument response function, however, signal to noise ratio has recently been shown to be theoretically higher for time domain. The key advantage of time domain is that multiple decay components can, at least in principle, be extracted with ease from the decay profile by fitting with a multiexponential function, using relatively simple mathematical methods. 

Fig. 6. NMR lineshape for glow discharge deposited a-Si H film grown at 25°C. The top curve is the experimental data and the middle and bottom curves are the deconvolution of the data into broad and narrow components (Reprinted with permission from Reimer et al., 1981a, Pergamon Press, pic).

Thermochemical data obtained from experiments in which only a fast heat deposition is detected is more reliable than those in which two or more heat depositions are observed. This is due in part to the necessity for deconvolution of the experimental data. With conventional transducers and low pulses energies,... 

Wilson-Lingardso, L., Davis, P.W., Ecker, D.J., Hebert, N., Acevedo, O., Sprankle, K., Brennan, T., Schwarcz, L., Freier, S.M., and Wyatt, J.R., Deconvolution of combinatorial libraries for drug discovery experimental comparison of pooling strategies, J. Med. Chem., 1996, 39, 2720-2726. 

Such a treatment, within its mechanistic restrictions, is general across the full range of experimental techniques. This convolution-deconvolution approach is the basis of the E G G Condecon system. 

Figure 4. Deconvolution of the denaturational endotherm for native CBHI at pH 4.80. Circles represent experimental values for differential heat capacity the solid curves represent the overall best fit model and the two sequential component transitions that contribute to the overall fit (See text).

In addition to offering a comparison between theoretical and experimental values, Table 8.2 also indicates that there may be a significant difference between the 0 values that have been independently obtained by the deconvolution of Cp measurements and from magnetic measurements. There is also a significant spread between the 0 values obtained by using different methods to extract the magnetic... 

In principle we could deconvolute the experimental spectrum with the instrumental lineshape, if that were known, to recover the true spectrum. In our example we have some good experimental evidence as to the form of the instrumental lineshape since the acetone signal is (apart from small carbon-13 satellites) a singlet, its experimental shape is just the instrumental lineshape convoluted by a Lorentzian of width l/(7rr2 ), where is the spin-spin relaxation time of the acetone protons. How can we use this experimental evidence to correct the imperfect experimental spectrum The simplest way to deconvolute one function fi uj) by another f2 ( ) is to Fourier transform the ratio of their inverse Fourier transforms ... 

Natural minerals may contain simultaneously up to 20-25 luminescence centers, which are characterized by strongly different emission intensities. Usually one or two centers dominate, while others are not detectable by steady-state spectroscopy. In certain cases deconvolution of the liuninescence spectra may be useful, especially in the case of broad emission bands. It was demonstrated that for deconvolution of luminescence bands into individual components, spectra have to be plotted as a function of energy. This conversion needs the transposition of the y-axis by a factor A /hc (Townsend and Rawlands 2000). The intensity is then expressed in arbitrary imits. Deconvolution is made with a least squares fitting algorithm that minimizes the difference between the experimental spectrum and the sum of the Gaussian curves. Based on the presumed band numbers and wavelengths, iterative calculations give the band positions that correspond to the best fit between the spectrum and the sum of calculated bands. The usual procedure is to start with one or... 

Recent work on a production basis involving 5-fim spectra of 12CD3F has verified line-center frequency stability under deconvolution. Large numbers of experimental records of 12CD3F, simultaneously recorded with CO in the sample, were calibrated before and after deconvolution (point-simultaneous methods, Jansson algorithm). No systematic differences were detected in comparisons of the before and after frequencies of nonblended absorption lines. That is, the variance was consistent with the optomechanical precision of the spectrometer and the mean deviation summed to approximately zero, validating the frequency calibration of the deconvolved data. 

Figure 11.26—Example of spectrum deconvolution. The experimental spectrum (uppermost curve) is treated in order to obtain the spectra of the five individual components. This method assumes that the spectra of the individual components are known.

Before comparing with experiment, however, the theoretical results at an energy of 40 meV (equivalent to room temperature) were convoluted with the energy resolution function of the detector used for the measurement. This procedure was adopted because deconvolution of the experimental data was found to be numerically unstable. The convoluted theoretical data were then normalized to the experimental data at zero Doppler shift to yield the results shown. The agreement between the convoluted theoretical results and experiment is extraordinarily good, extending as it does over more than three orders of magnitude. These results also reveal... 

Figure 7 Deconvolution of an absorption spectrum of CV in ethanol at 295 K to four Gaussians. The solid line represents an experimental spectrum. The broken lines show two calculated spectrums, each of which is composed of two Gaussians. The dotted line, which is totally hidden under the solid line, is the sum of the two calculated spectrums. (From Refs. 1, 20.)...

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