Non-parametric linear regression of discrete Fourier transform convoluted chromatographic peak responses in non-ideal conditions

This manuscript discusses the application of chemometrics to the handling of HPLC response data using a model mixture containing ascorbic acid, paracetamol and guaiphenesin. Derivative treatment of chromatographic response data followed by convolution of the resulting derivative curves using 8-points sin xi polynomials (discrete Fourier functions) was found beneficial in eliminating different types of interferences. This was successfully applied to handle some of the most common chromatographic problems and non-ideal conditions, namely: very low analyte concentrations, overlapping chromatographic peaks and baseline drift. For example, a significant change in the correlation coefficient of guaiphenesin, in case of baseline drift, went from 0.9978 to 0.9998 on applying normal conventional peak area and first derivative under Fourier functions methods, respectively. It also compares the application of Theilʹs method, a non-parametric regression method, in handling the response data, with the least squares parametric regression method, which is considered the de facto standard method used for regression. Theilʹs method was found to be superior to the method of least squares as it assumes that errors could occur in both x- and y-directions and they might not be normally distributed. In addition, it could effectively circumvent any outlier data points.