Wavelet Transform For The Resolution Study Of Overlapping Chemical Signals

On the basis of the development and process of application of wavelet transform (WT) in chemistry, a detailed investigation of resolving and quantifying the overlapped chemical signals by using wavelet transform (WT) was carried out, and the relevant theory was also provided. The innovative research work mainly focused on the four aspects as follows: 1. Using the special wavelets, which included Marr, Haar and DOG for the continuous wavelet transform (CWT) and biorthogonal wavelet for the discrete wavelet transform (DWT), the peak positions of the component's responses, described by Gaussian, Lorentzian and sech2-function, could be determined via WT from the overlapped signals. The corresponding theoretical bases were also presented in this work. According to the validation of synthetic and real data, the results manifested that (1) the CWT and DWT could both be employed to find the peak positions of the components from the unresolved signals under the suitable dilations or the appropriate resolutions. Hence, the WT could be used to perform the qualitative analysis. (2) For CWT, the different wavelets did not exert the effect on the determination of the peak positions. (3) In term of extracting the peak positions, the CWT had some superior aspects as compared with the DWT, such as simplicity, refined dilations and straightforward application to very noisy signals, so the application of CWT would be very promising. 2. Depending on the linear property of WT, a new method to construct the suitable baseline for quantitative analysis of the overlapped square wave voltammogram (SWV) of two components in WT domain was proposed. (1) The relative satisfactory results of evaluating the peak height could be achieved by using the graphical measures established on this appropriate baseline in the case of different dilations or resolutions, degrees of separation and parameters of the peak (peak width and peak height). Since the proposed measure yielded the least absolute values of systematic errors as compared with other measures, it could be applied to performing the quantitative analysis straightforward for the overlapped SWV without separating each component. (2) The comparison of quantification between the different wavelets was conducted, and demonstrated that Marr, Haar, DOG and biorthogonal wavelet could be used for quantitative analysis and results had little correlation with the wavelets. 3. Using Marr wavelet, the essence of CWT of the signal was discussed. (1) Combining the definition of CWT and the derivative property of convolution, we constructed a general method to calculate the approximate derivative of signal through CWT by using the first and second derivative of Gaussian function, Haar, and the first derivative of three-order-Spline function as wavelets. As compared with the other approaches of calculating derivative, which include the numerical differentiation, polynomial filters, Fourier transform, and the recently proposed DWT method, fast calculation and simple mathematical operation were remarkable advantages of CWT method. For the signal corrupted by severe noise (Signal-to-Noise Ratio = 5), the satisfactory results could also obtained via CWT method through appropriately adjusting the dilations. (2) The improved DWT method after updating the original one was able to cope with the limitations. (3) The limit of resolution enhancement obtained by using CWT method (the first and second derivative of Gaussian function, Haar, and the first derivative of three-order-Spline function as wavelets) and the improved DWT method (Haar and the first derivative of three-order-Spline function as wavelets) was also analyzed from the theoretical angle. 4. (1) An algorithm, cross-iterative algorithm of continuous wavelet transform and original signal (CIACWTOS), based on finding the peak positions by using the Marr wavelet through the CWT, was established on to locate the refined peak positions. (2) On the basis of CIACWTOS, a new method, flip shift subtraction method (FSSM), was proposed to separate the overlapped SWV of the two components. Depending on the validation of simulated signals and real data, the results showed that FSSM was a simple method, and could be utilized to separate the two peaks efficiently. Meanwhile, the introduced errors of FSSM were relatively small.