A 2nd-order spline wavelet convolution method in resolving overlapped peaks is developed. It determines the number of peaks, peak positions and width through wavelet's convolution, then uses spline function to construct the resoluter, which is used to resolve overlapped peaks. Theoretical proof is given, and the selections of wavelets and parameters are discussed. It is proven that baseline separation can be achieved after processed, the relative errors of peak position and area are less than 0.2% and 4.0% respectively. It can be directly applied to seriously overlapped signals, noisy signals and multi-component signals, and the results are satisfactory. It is a novel effective method for resolution.
A new method based on the combining of the wavelet theory with the fractal theory and named wavelet fractal peak position method (WFPPM) is introduced to ex-tract the number of the components and the relevant peak positions from overlapping signals in chemistry. The over-lapping signal is first transformed into continuous wavelet transform value of time domain in certain dilation range via continuous wavelet transform (CWT), and then changed into capacity dimensions (Dc). The number of the components and the relevant positions of overlapping peaks can be iden-tified easily according to the change of Dc. An investigation concerning the influence of different dilation ranges on the peak positions extracted by WFPPM is also provided. Stud-ies show that the WFPPM is an efficient tool for extracting the peak positions and identifying the number of peaks from unresolved signals, even when this kind of overlapping is significantly serious. Relative errors of less than 1.0% in peak positions are found when WFPPM is used in the pro- cessing of the cadmium(Ⅱ)-indium(Ⅲ) mixture system. The analytical results demonstrate that the desired peak positions can be extracted conveniently, accurately and rapidly from an unresolved signal via WFPPM. Tremendous developing and applications based on currently reported WFPPM in extracting overlapping signals would be expected in the near future.
QIU Jianding1,2, ZOU Xiaoyong1, LIANG Ruping1,2, MO Jinyuan1 & CAI Peixiang1 1. School of Chemistry and Chemical Engineering, Zhongshan Univer-sity, Guangzhou 510275, China
