Deconvolution of spectra

Figure 4. 187-MHz CRAMPS spectra ofMCB silica gel (A) evacuated at 100 °C and (B) evacuated at 500 °C. Plot C is a deconvolution of spectrum A, and plot D is a computer simulation based on C.

Figure 1. Point-by-point Pt NMR spectra of 2.5 nm sample at T" = 80K A, As-received catalyst B, electrochemically cleaned C, sintered to nominally larger Pt size by extensive potential cycling and D, layer-model deconvolution of spectrum B. (Reprinted with permission from Copyright 1999 Am. Chem. Soc.)...

Fig. 3. FTIR spectra of CO adsorbed at -196 C and a CO pressure of 4 mbar (a) Y-AI2Q3, (b) 3% AI2O3/ Y-A12Q5- The dashed line shows the deconvolution of spectrum (b) into its components. Inset portion of spectrum (b) magnified 10 times...

Fig.4 Typical point-by-point 1 Pt NMR spectra showing electrochemical cleaning, sintering by potential cycling, and a layer-model analysis of the 2.5-nm sample (a) as-received catalyst (b) electrochemically cleaned in 0.5 M H2SO4 by holding electrode potential at 0.45 V versus reversible hydrogen electrode (RHE) (c) cleaned by extensive potential cycling and (d) layer-model deconvolution of spectrum (b). The solid line in (b) is the result of the simulation.

Most EDS systems are controlled by minicomputers or microcomputers and are easy to use for the basic operations of spectrum collection and peak identification, even for the computer illiterate. However, the use of advanced analysis techniques, including deconvolution of overlapped peaks, background subtraction, and quantitative analysis will require some extra training, which usually is provided at installation or available at special schools. 

Fig. 17 FTIR absorbance spectrum of two-phonon processes in single crystalline a- Sg in the range 550-1000 cm, after [109], The strong bands in the range 800-950 cm result from combinations of components of the stretching vibrations. The insert shows a numerical deconvolution of the prominent spectral feature between 750-950 cm ...

The behavior of D2 in the Raman experiments is strongly correlated with the Q4 chemical shift, 6, in the NMR spectra. 6 equals about -110 to -111 ppm when D2 is absent or when it exhibits low relative intensities comparable to those in conventional vitreous silica, for example the 50 and 1050°C sample spectra and the rehydrated 600°C sample spectrum. From the regression equation cited above -110 to -111 ppm corresponds to - 147 to 149°, values quite close to the average in conventional v-Si02, 151° (4 ). The average 64 is shifted downfield to about -107 ppm in the 600°C sample in which D2 is observed to be quite intense. Deconvolution of this peak reveals two Q4 resonances at -110 and -105 ppm. -105 ppm corresponds to - 138°, which is very near the equilibrium 4> calculated for the isolated cyclic trisiloxane molecule, HgSi303, ( = 136.7°) (46). The positions of the Q2 and Q3 resonances, however, appear to be totally unaffected by the presence or absence of D2 (as shown in the 600°C CP MASS sample spectrum). 

Because online separations provide such a wealth of information about target proteins, interpretation becomes of critical importance in order to make full use of the data. The first step in any analysis of LC-MS data involves integration and deconvolution of sample spectra to determine protein mass and intensity. In manual analysis (Hamler et al., 2004), users identify protein umbrellas, create a total ion chromatogram (TIC), integrate the protein peak, and deconvolute the resulting spectrum. Deconvolution of ESI spectra employs a maximum entropy deconvolution algorithm often referred to as MaxEnt (Ferrige et al., 1991). MaxEnt calculates... 

Fig. 20 Deconvolution of the transient spectrum obtained upon the application of a 25-ps laser pulse to a solution of [hexamethylbenzene, NO+] charge-transfer complex showing the Wheland intermediate (430 nm) and the hexamethylbenzene cation radical (495 nm). Courtesy of S.M. Hubig and J.K. Kochi, unpublished results.

As we optimized Tethering we used a variety of mass spectrometers. In our experience, the sensitivity and high resolution of TOP analyzers has provided the most rapid and accurate analyses of intact proteins. An example of an ESI-TOF data set from a standard experiment is illustrated in Fig. 9.2. Figure 9.2A is the deconvoluted mass spectrum of a Cys-mutant target protein after equilibration... 

Figure 2. Computer deconvolutions of the absorption and MCD spectra of ZnTPP in BuCl containing CCl at 79 K. The starred band represents part of the spectrum of unoxidized ZnTPP.

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... 

The actual deconvolution of a data set is formally straightforward. Let dik)(x) be the kth iterative estimate of the actual spectrum o(x), where x is nominally time viewed as a sequence-ordering variable. Further, let i(x) be the actual observed spectrum that has been instrumentally convolved with the observing system response function s(x). The observed data set i(x) is assumed to be related to o(x) by the convolution integral equation... 

Fig. 1 Deconvolution of simulated noiseless data using the Jansson weighting scheme. Trace (a) is the original spectrum o x trace (b) the convolved spectrum i x). Traces (c) and (d) are the power and phase spectra of o(x), traces (e) and (f) the power and phase spectra of i(x), traces (g) and (h) the power and phase spectra of the error spectrum E(jc). Traces (i)-(m) are the deconvolution result, the power and phase spectra of the deconvolution result, and the power and phase spectra of the error spectrum, respectively, after 10 iterations with r(jjjax = 1.0. Traces (n)-(r) are the same results after 20 additional iterations with r ax= 2.0. Traces (s)-(w) are the same results after 20 additional iterations with r(3.5. Traces (x)-(bb) are the same results after 20 additional iterations with r( Jax= 5.0.

We conclude this chapter by presenting several examples of deconvolution of real data. Most of these examples represent deconvolutions of data that were used as part of a spectral analysis rather than generated as deconvolution examples or tests. The examples include high-resolution grating spectra, tunable-diode-laser (TDL) spectra, a Fourier transform infrared spectrum (FTIR), laser Raman spectra, and a high-resolution y-ray spectrum. 

Fig. 24 Tunable-diode-laser spectrum of RQ0 of v9 of ethane. Trace (a) is the average of 250,000 scans and exhibits linewidths of 0.0022 cm-1 (the Doppler width is 0.0018 cm-1). Trace (b) results from the deconvolution of the data in trace (a) using a gaussian with a FWHM of 0.0022 cm-1 as a response function. Trace (c) is the Q branch calculated using a model that includes torsional splitting effects Av = 1.95 mk. Trace (c) is calculated for Av = 0.00075 cm-1, which is less than one-half the 300 K Doppler width.

Fig. 26 Fourier transform spectrum of v2 of ammonia. Trace (a) is a section of the infrared absorption spectrum of ammonia recorded on a Digilab Fourier transform spectrometer at a nominal resolution of 0.125 cm-1. In this section of the spectrum near 848 cm-1 the sidelobes of the sine response function partially cancel, but the spectrum exhibits negative absorption and some sidelobes. Trace (b) is the same section of the ammonia spectrum using triangular apodiza-tion to produce a sine-squared transfer function. Trace (c) is the deconvolution of the sine-squared data using a Jansson-type weight constraint.

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