Peak Gaussian

The result is a series of Gaussian "peaks" in co-spaee, eentered at ... 

Distribution Coefficients. Gel-permeation stationary-phase chromatography normally exhibits symmetrical (Gaussian) peaks because the partitioning of the solute between mobile and stationary phases is linear. Criteria more sophisticated than those represented in Figure 8 are seldom used (34). 

FIG. 16"31 Properties of a Gaussian peak. is the peak height tfn, the peak apex time <3, the... 

Resolution The chromatographic separation of two components, A and B, under trace conditions with small feed injections can be characterized in terms of the resolution, R,. For nearly Gaussian peaks ... 

FIG. 16-32 Exponentially modified Gaussian peak with Xq/Gq = 1.5. The graph also shows the definition of the peak asymmetry factor at 10 percent of peak height. 

FIGURE 2.13 From measurements of the retention volume, Vr, and the peak width at half peak height, Wr, of a gaussian peak, an estimate of column efficiency N and relative efficiency, HETP, may be calculated. The last figure is for very well packed columns close to 2 X dp. [Reproduced from Sofer and Hagel (1997), with permission.]... 

Tangents Method. The tangents on either side of the peak are drawn through the inflection points until the baseline. For an ideal Gaussian peak the resulting base line interval Wi, is equal to 4or. Equation (1) becomes with the width (Wb) ... 

Most GPC columns are provided with vendor estimates of the plate count of the column and a chromatogram of a series of test peaks. These plate count estimates are usually obtained using small molecule analytes that elute at the total permeation volume (Vp) of the column. The Gaussian peak shape model... 

Plate number N (as for Gaussian peaks) Resolution factor R ... 

Figure 5-21. N(ls) core level spectra of the iiniim model compound PC20X adsorbed on ITO. The upper curve corresponds to a thick film, the central curve to an intermediate thick film, and the lower curve to an ultra thin Him, essentially a mono-layer in thickness. The bold solid lines are the filled curves and the thin solid and dolled lines are the Gaussian peak components lor physisorbed and chemisorbed PC20X, respectively.

Double-click the SMAC-icon (Fig. 5.1) on your desktop that features three Gaussian peaks the main menu screen appears. (See Fig. 5.2.) The full-screen background of this and all screens that follow is light blue and contains about a dozen renditions, in a range of sizes, of the initials SMAC the coordinates of which change with every call. 

In the simplest approach T is the full width of the peak (measured in radians) subtended by the half maximum intensity (FWHM) corrected for the instrumental broadening. The correction for instrumental broadening is very important and can be omitted only if the instrumental broadening is much less than the FWHM of the studied diffraction profile, which is always the case in presence of small nanoclusters. The integral breadth can be used in order to evaluate the crystallite size. In the case of Gaussian peak shape, it is ... 

Use of densitometric detection provides an insight into the concentration profiles of chromatographic bands, thus furnishing an indispensable prerequisite, needed for proper assessment of the retention mechanisms in the preparative adsorption TLC. Figure 2.4 shows three types of the band eoncentration profiles. The Gaussian peak (a) in this figure represents the linear isotherm of adsorption of a given species, peak... 

Fig. 40.12. (a) FT (real coefficients) of a Gaussian peak located in the origin of the measurements (256 data points). Solid line w A = 20 dashed line wVi = 5 and corresponding maximal frequencies, (b) FT (real and imaginary coefficients) of the same peak shifted by 50 data points. 

Fig. 40.22. Distortion (hJhn) of a Gaussian peak for various window sizes (indicated within parentheses). (a) Moving average, (b) Polynomial smoothing.

The effect of a 5-point, 17-point and 25-point quadratic smoothing of a Gaussian peak with 0.3% noise is shown in Fig. 40.22b. Peaks are distorted as... 

Fig. 40.26. Effect of exponential smoothing (A. = 0.6) on a Gaussian peak (wi/, = 6 data points) (solid line original data bold line smoothed data).

Table 40.3. As one can see, the filter introduces a slower response to stepwise changes of the signal, as if it were measured with an instrument with a large response time. Because fluctuations are smoothed, the standard deviation of the signal is decreased, in this example from 2.58 to 1.95. A Gaussian peak is broadened and becomes asymmetric by exponential smoothing (Fig. 40.26).

Back-transform F(v) by which the undamaged signal jc) is estimated. The effect of deconvolution applied on a noise-free Gaussian peak is shown in... 

Fig. 40.32. Deconvolution (result in solid line) of a Gaussian peak (dashed line) for peak broadening ((M i/,)prf/(H vi)G = 1). (a) Without noise, (b) With coloured noise (A((0,1%), Tx = 1.5) inverse filter in combination with a low-pass filter, (c) With coloured noise (A (0,1 %), Ta = 1.5) inverse filter without low-pass filter.

C.R. Mittermayr, S.G. Nikolov, H. Mutter and M. Grasserbauer, Wavelet denoising of Gaussian peaks a comparative study. Chemom. Intell. Lab. Syst., 34 (1996) 187-202. 

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