Curve fitting to asymmetrical chromatograms by the extended Kalman filter in frequency domain

Felinger, Attila; Pap, Tamás L.; Inczédy, J.

doi:10.1016/0039-9140(94)80081-2

Cited by 16 publications

(5 citation statements)

References 13 publications

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“…22 Many problems associated with the EMG model in the time domain can be addressed in the frequency domain. 24 Diffusion acts as a filter that cuts high frequencies, hence signals with different peak shapes affect the calculations in the frequency domain, based on their frequency components.…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

“…For example, peak tailing underestimates the diffusion coefficient, while sample overload and slow migration in highly concentrated samples lead to overestimation . Many problems associated with the EMG model in the time domain can be addressed in the frequency domain …”

Section: Simulation Results and Discussionmentioning

confidence: 99%

“…23 Many problems associated with the EMG model in the time domain can be addressed in the frequency domain. 24 The Fourier computation assumes that the signal is periodic in the time frame in respect to the captured profile. A signal profile that starts at zero and decays again to zero within the time window meets the periodic requirement.…”

Section: ■ Simulation Results and Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Accurate Determination of the Diffusion Coefficient of Proteins by Fourier Analysis with Whole Column Imaging Detection

Zarabadi

Pawliszyn

2015

Anal. Chem.

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Section: Simulation Results and Discussionmentioning

confidence: 99%

Section: Simulation Results and Discussionmentioning

confidence: 99%

Section: ■ Simulation Results and Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Accurate Determination of the Diffusion Coefficient of Proteins by Fourier Analysis with Whole Column Imaging Detection

Zarabadi

Pawliszyn

2015

Anal. Chem.

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“…One of the most popular models used for asymmetric peaks is the exponentially modified Gaussian function (EMG). [5][6][7][8][9][10][11][12] Application of the EMG peak model yields a new set of CFOMs: the retention time (t G ); the standard deviation, (s G ), of the associated parent Gaussian peak from which the skewed EMG peak is derived; the exponential modifier (t); the fundamental ratio (t/s G ), which characterizes peak asymmetry; the number of theoretical plates of a given asymmetric chromatographic system (N SYS ); the maximum efficiency a given system could achieve (N MAX ), if all sources of asymmetry were eliminated; the relative system efficiency (RSE), which demonstrates dramatically how peak asymmetry drastically reduces chromatographic efficiency; and the relative plate loss (RPL).…”

Section: Introductionmentioning

confidence: 99%

Determination of chromatographic peak parameters by non-linear curve fitting using statistical moments

Pápai

Pap

2002

Analyst

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There are many methods (manual, computer), which make possible the detailed analysis of chromatographic peak shape. Curve fitting seems to be one of the successful applications of the evaluation of chromatographic signals. In this case, a mathematical function is fitted to the digitized measuring points. Chromatographic elution curves are generally asymmetric, so it is necessary to find the best mathematical function, which corresponds perfectly to the signal form, and then to determine the parameters of the found equation. In this work a modified mathematical function is presented and used for curve fitting, in which the starting parameters are calculated from the statistical moments (retention time, variance, skewness, excess) of the peak shape. The fitting process gives a more accurate and rapid determination of peak shape characteristics, noise filtering and correction of baseline. The suggested modified Gaussian function, the simulated chromatographic peak shapes, the application of the function to the description of real signals and the parameters obtained by the fitting process will be demonstrated.

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“…The fitting and resolution of peaks is of great importance in the field of analytical chemistry. In the literature, there are a number of reports where numerical methods are used to describe individual peaks and to achieve the deconvolution of overlapped peaks in a chromatogram. − The most simple chromatographic models predict Gaussian elution profiles. However, in practice, skewed peaks with low efficiencies may be obtained, and, in such cases, the assumption of a Gaussian model yields large errors. , The reasons for the deviation from the ideal behavior are diverse, but the main explanation is the slow mass transfer of the solutes between stationary and mobile phases and, to a lesser extent, extracolumn effects.…”

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confidence: 99%

A Model for the Description, Simulation, and Deconvolution of Skewed Chromatographic Peaks

1997

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A family of models is proposed for the description of skewed chromatographic peaks, based on the modification of the standard deviation of a pure Gaussian peak, by the use of a polynomial function, h(t) = He-(1/2)([ t - t R ]/[ s 0 + s 1 ( t - t R )+ s 2 ( t - t R )2+...])2 , where H and t R are the height and time at the peak maximum, respectively. The model has demonstrated a high flexibility with peaks of a wide range of asymmetry and can be used to accurately predict the profile of asymmetrical peaks, using the values of efficiency and asymmetry factor measured on experimental chromatograms. This possibility permits the simulation of chromatograms and the optimization of the separation of mixtures of compounds producing skewed peaks, where both the position and peak shape are considered. A first-degree polynomial was adequate for peaks of moderate asymmetry, but higher degree polynomials were preferable for peaks showing a high asymmetry, including those with negative skewness. The proposed models can be employed in the resolution of overlapped peaks in binary and ternary mixtures of compounds, or to improve the accuracy in the evaluation of peak shape parameters. The results obtained with the proposed models were comparable or even superior to those achieved with the exponentially modified Gaussian model.

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Curve fitting to asymmetrical chromatograms by the extended Kalman filter in frequency domain

Cited by 16 publications

References 13 publications

Accurate Determination of the Diffusion Coefficient of Proteins by Fourier Analysis with Whole Column Imaging Detection

Accurate Determination of the Diffusion Coefficient of Proteins by Fourier Analysis with Whole Column Imaging Detection

Determination of chromatographic peak parameters by non-linear curve fitting using statistical moments

A Model for the Description, Simulation, and Deconvolution of Skewed Chromatographic Peaks

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