Gaussian curves linear combination

Additional information can be obtained by XPS (X-ray Photoelectron Spectroscopy). Figure 14.7 shows the N(ls) core level spectra of samples, degassed at 973 K and 1123 K. The most important assignments are presented in table 14.2. The band fitting was based on a 10/90 linear combination of Lorentzian and Gaussian curves. 

Any linear combination of quantities each of which is distributed according to the Gaussian curve is itself distributed according to the Gaussian curve (law of addition). Thus if 2 = + 0 2 + 0 3 + + where... 

This computational approach of finding the optimal alignment for the Kalman filter resolution of the overlapped shifted spectra by the simulated annealing algorithm has been tested on simulated overlapped spectra obtained by linear combination of Gaussian-Lorentzian curves, synthetically generated using the mathematical model described by Eqn. (9)... 

Figures. Synthetic Gaussian-Lorentaan curves. The values of the Gaussian-Lorentzian factor b in the Eqn.(9) were 0.3, 0.5, 0.7 for the curves 1, 2, and 3, rei )ectively. The FWHM of curves IB and 2B were doubled with respect to 1A and 2A. The peak maxima coordinates Xq were 150, 200, 250 for the curves 1, 2, and 3. ( — ) are the linear combination (unitary coefficients) of the three curves. (From Fresenius J Anal. Chan(1993) 345 490, with permission).

Often, it is found that certain data profiles are best described by non-linear bases. A typical example is curves from e.g. infrared spectroscopy [20] which are well described by a linear combination of Lorentzian peaks. Sometimes it is also possible to use Gaussian peaks. The Lorentzian peak function is written as... 

Curve Fit is a function used to decompose the area of heavily overlapping bands into constituent components. The implemented procedure is based on the least-squares minimization algorithm. Each band is characterized by the parameters band position, intensity, and width. Furthermore, the type of the band shape is taken into account, whereby you can choose a Gaussian or Lorentzian function or a linear combination of both. 

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