Smoothing of chromatographic signals by their approximation in the basis of Chebyshev-Hermite functions

Abstract

The paper deals with assessing the scope of the approximation algorithm for smoothing chromatographic signals. The algorithm is based on Chebyshev-Hermite functions. For approximation, an algorithm is used that implies the calculation of the shift and scale factors for the basis functions, as well as the division of the signal into fragments. The smoothing error of the model signal is considered when it is approximated in the selected basis in comparison with the digital moving average filter. The error of smoothing the derivative of the signal and the position on the derivative of extremums is also investigated, a comparison is made, as in the previous case, with a digital moving average filter. As part of an experimental study, the nine most characteristic chromatographic peaks extracted from real chromatograms are processed in the work. To assess the quality of smoothing, the standard deviation of the noise and the residual are compared, and the distribution law of the residual is determined. According to the results of the study, restrictions are set on the maximum allowable value of the asymmetry coefficient of the processed chromatographic peaks. Thanks to the use of the chosen approximation approach, it is possible to solve the problem of smoothing chromatographic signals without attenuating the useful component. The computer algebra system Wolfram Mathematica 11.3 was used for calculations and graphical presentation of the simulation results.