Peak fitting algorithm

The amount of tebuconazole residue is calculated by using a least-squares fitting algorithm to generate the best line which can be used to calculate the corresponding concentration for a given peak area or peak height. Calculate the slope and the intercept of the standard calibration curve. 

The tools we created in Chapter 3, Physical/Chemical Models, form the core of the fitting algorithms of this chapter. The model defines a mathematical function, either explicitly (e.g. first order kinetics) or implicitly (e.g. complex equilibria), which in turn is quantitatively described by one or several parameters. In many instances the function is based on such a physical model, e.g. the law of mass action. In other instances an empirical function is chosen because it is convenient (e.g. polynomials of any degree) or because it is a reasonable approximation (e.g. Gaussian functions and their linear combinations are used to represent spectral peaks). 

FIGURE I I The ApexTrack integration algorithm and its ability to easily identify and quantitate shoulders.These shoulder peaks may be quantitated using simple dropped perpendicular lines or through Gaussian peak fitting. 

S-FIT An S-FIT approximation is a mathematical algorithm for guessing at which cells in a DNA-content histogram are actually in the S phase of the cell cycle. The S-FIT algorithm bases this guess on the shape of the DNA histogram in the middle region between the G0/G1 and the G2/M peaks. 

Figure 6 Results of a peak picking algorithm. At x = 80, the first derivative spectrum crosses zero and the second derivative is negative. A 9-point cubic least-squares fit is applied about this point to derive the coefficients of the cubic model. The peak position (dytdx = 0) is calculated as occurring at x = 80.3...

The combined (in quadrature) relative systematic uncertainty bounds for E and V have been determined to be 0.070. This relative systematic uncertainty is within the boundary condition established within the NUREG. It should be stressed that the areas evaluated represent only a portion of the analytical evaluation performed by the current "state-of-the-art software systems. Peak search and complex spectral fitting algorithms have not been addressed directly to date in this evaluation. An attempt will be made to address some of these items in a later section through evaluation of samples containing added isotopes of known quantity. 

Detailed spectra were processed with CasaXPS software (V2.3.12, Casa Software Ltd., UK). An iterated Shirley-Sherwood background subtraction was applied before peak fitting using a linear-least-squares algorithm. Minor charging was observed and corrected by referencing the aliphatic carbon to 285.0 eV. Details on the curve-fitting parameters, whieh have been measured on reference compounds, have been pubUshed elsewhere [10, 11],... 

Fig. 3. XPS spectra of sol-gel-derived Z1O2 thin films (a) XPS Zr 3d spectrum and (b) XPS O Is spectrum. Solid lines are the observed XPS spectra and dashed lines are for Zr 3d and O Is sp>ectra, which have two Gaussian peaks fitted by the nonlinear least-squares algorithm (Shimizu et al., 2009).

In both of the peak width algorithms, it is necessary to estimate the height of the peak at a position which, more likely than not, is between two channels. A full Gaussian fitting over the peak region would provide this information but a simpler, and sufficiently accurate, approach can be used. The channel contents in a Gaussian peak should be related by the equation ... 

The infrared spectrum of each sample was analyzed with a Fourier transform infrared (FTIR) microspectroscopy (IRT-5000-16/FTIR-6200, Jasco Co., Tokyo, Japan) equipvped with a mercury cadmium telluride (MCT) detector via a transmission technique (Gao Lin, 2010 Lin et al., 2006, 2010). All the FTIR spectra were obtained at a 4 cmi resolution and at 100 scans. The components and relative compositions of each sample were estimated quantitatively within the 1740-1600 cm-i region of FTIR spectra by a curve-fitting algorithm with a Gaussian-Lorenzian function (Cheng et al., 2008 Hu et al., 2002). The best curvefitting procedure was performed by iterative fits toward a minimum standard error. The relative composition of the component was computed to be the fractional area of the corresponding peak, divided by the sum of the area for all the peaks. 

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