Gaussian, exponentially modified

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. 

Due to the possible change in retention time and peak profile that may take place during day-to-day operation, it is necessary to measure peak characteristics every day to verify the status of the method validation. A blank sample should be evaluated for an analysis run, where the resolution is determined. For asymmetric peaks, the Gaussian equation cannot be used, so the modified equation, using an exponentially modified Gaussian (EMG) method has been proposed [21]. 

Another approach is the characterization of peaks with a well-defined model with limited parameters. Many models are proposed, some representative examples will be deaaib i. Wefl known is the Exponentially Modified Gaussian (EMG) peak, i.e. a Gaussian convoluted with an exponential decay function. Already a few decades ago it was recognized that an instrumental contribution such as an amplifier acting as a first-order low pass system with a time constant, will exponentially modify the... 

Exponentially modified Gaussian (EMG) Spectroscopy Gaussian, amplitude and area... 

Peaks departing from Gaussians are often described by exponentially modified Gaussian (EMG) functions, a combination (via a convolution operation) of a Gaussian and an exponential function [27,28]. Other empirical functions have been used as well [29]. None of the above functions has a very sound theoretical footing, but they are nonetheless important for descriptive purposes. 

With all these precautions and when using modern columns, it clearly appears that peaks are not Gaussian, but systematically skewed. New computing facilities allow one to analyze more precisely such peaks by various functions. The best results seems to be obtained by exponentially modified gaussian (EMG) functions [4], which are the convolution of a Gaussian dispersion and an exponential decay. In that case, two parameters define the shape of the peak a and t, which allow quantitative mapping of BB characteris-... 

Lan and Jorgensen [8] gave a detailed discussion of the exponential-Gaussian hybrid function, which describes asymmetric peaks better than the exponentially modified Gaussian. The proposal does not seem to have advantages when applied to the situations considered in this book. 

Table 4.1 Statistical Parameters of the Zone Profiles Simulated by MC Technique and of the MC Profiles Fitted by the Exponentially Modified Gaussian...

Foley, J. P., Dorsey, J. G. A review of the exponentially modified Gaussian (EMG) function Evaluation and subsequent calculation of universal data, J. Chromatogr. Sci, 1984, 22, 40-46. 

One empirical model that is widely used for the evaluation of band asymmetry is the exponentially modified Gaussian (EMG) fimction [111-113]. It is the convolution of the unit area Gaussian function and of an exponential decay of unit area. By definition, the convolution of two functions and (f) is the following function... 

Figure 6.18 Comparison of the exponentially modified Gaussian (EMG) and the Gaussian profile. Dimensionless plot of Cj versus Solid tine Gaussian profile with N = 5000. Dotted line EMG function with N = 5000 and r/tj = 0.02. Reprinted bp permission of Kluwer Academic Publishing, from S. Golshan-Shirazi and G. Guiochon, NATO ASI Series C, vol 383, 61 (Fig. 7), with kind permission of Springer Science and Business Media.

In our work 10) we used the Gaussian function to simulate column broadening in step (3), but obviously any function could be used, for example the currently favored exponentially modified Gaussian 8,11). 

---