Wavelet fractal character of overlapping signal

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 extract the number of the components and the relevant peak positions from overlapping signals in chemistry. The overlapping 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 identified 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. Studies show that WFPPM is and efficient tool for extracting the peak positions and identifying the number of peaks from unresolved signals, even wht\en this kind of overlapping is significantly serious. Relative errors of less than 1.0% in peak are found when WFPPM is used in the processing 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 and unresolved signal via WFPPM. Tremendous developing and applications based on currently reported WFPPM in extracting overlapping signals would be expected in the near futrue.