Resolving of Overlapping Asymmetrical Chromatographic Peaks by Using Wavelet-Transform and Gram-Charlier Peak Model

The paper describes a method for resolving overlapping asymmetric peaks that make up a chromatogram. The presented method uses the Gram-Charlier model in the form of the first three terms of the Gram-Charlier series as a basis. Using the wavelet transform, the parameters of this model are determined, which is used to describe a single or overlapping chromatographic peak. Hermitian wavelets of the first four orders are used in the computation of the wavelet transform. To speed up the computation of multiple wavelet transforms, the possibility of coding a signal using the Chebyshev-Hermite functions is considered in order to further restore the set of wavelet transforms simultaneously. According to the presented method, the parameters of the peaks are determined by analytical expressions without using the numerical approximation of the chromatogram by the peak model, which avoids the disadvantages of the numerical approach. The resulting method is used to resolve overlapping asymmetric peaks. The advantage of the method over others is shown by calculating the area of each of the resolved peaks.