Mathematical Model of Signal Generation

In an ideal case, the signal y A = f(zA), as shown in Fig. 3.6, is determined only by the analyte A (or the phenomenon of interest), namely both the position, zA = /(A), and intensity, yA = f(xA). But in real samples, matrix constituents are present which can principally interfere with the analyte signal. In structure analysis the same holds for the neighboring relationships (the environment of the species A of interest). Therefore, signal parameters are additionally influenced by the matrix (or the neighborhood , respectively), namely the species B,C.N, and follow then the complex relationships zA = /(A N), yA = /(xa xb,Xc.xN). Additionally, influencing factors a,b.m, background, y0, and noise (random deviations eA) may become relevant and have to be considered. 

The signal position is given by a characteristic value zA0 which is determining for the species A according to evaluation rules for identification and qualitative analysis see Sect. 2.4, Eq. (2.18a-c). Additional changes in position such as  

The real signal position and structure then is given by 

The signal intensity is influenced by the entire matrix (Q = A,B,C.N) with preference of A. In ideal case, yA would be only caused by xA  

The factors SA represent the cross sensitivities (partial sensitivities according to Kaiser [1972]) characterizing how the signal y(zA) is influenced by the species i  

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