Optimization of parameters of linear smoothing applied to chromatographic peaks

This paper presents an analysis of the errors in integrating chromatographic peaks in the case of using linear methods of smoothing a signal with non-negative weights and additive uncorrelated noise. Smoothing methods based on a moving weighted average are analyzed: arithmetic moving average, Savitsky-Golay method, exponentially weighted moving average, multiple smoothing, Gaussian smoothing, median smoothing. Criteria for optimizing the chromatographic peak smoothing procedure are considered. It is stated that the parameters of the peak can be divided into two groups: basic and validation. There are three basic parameters: retention, area and height. It is shown that there is an optimal linear filter that minimizes the relative error in calculating the height and peak area. In the case of a Gaussian peak and a Gaussian filter, the optimal smoothing results are obtained when the width of the Gaussian filter is equal to the width of the Gaussian of the original peak, regardless of the noise level.