| Chemical signals are always multicomponent systems since measurements related to the chemical composition of a substance are very complex. As a consequence, resolving or recovering overlapped bands into the contributions from individual components has become a crucial problem encountered in analyzing many kinds of chemical spectra and in data processing. In general, the pure component spectrum recovered and resolved from mixtures should resort to mathematical resolution rather than chemical separation and instruments. The methods for resolving overlapped bands can be classed into two groups:signal processing, such as high order derivatives, wavelet transform, Fourier self-deconvolution; and non-linear optimization, such as curve fitting, multivariate calibration, genetics algorithms. Signal processing technique possesses the advantage of good resolution, yet the parameters related to each component should resort to other methods to calculate. Non-linear optimization method has the advantages of good configuration and parameter optimization, however, it requires a mathematical model, in particular, the optimized results strongly depend on the assumption of the initial values. So as for this problem and the problems in Oscillographic frequency spectra analysis, some new methods are proposed in this thesis, for instance, nested genetic algorithms, some methods based on wavelet transform and wavelet frequency spectrum analysis of oscillograms. In addition, the electrochemical behaviors of some anticancer drugs are investigated to attempt to explain their antioxidation.The thesis comprises two parts of six chapters, in which the following work has been done: 1. A nested genetic algorithm, including a genetic parameter level and a genetic implemented level, was proposed and applied for resolving simulated overlapped spectra for the first time. By the genetic parameter level, parameters of genetic algorithms were optimized. Moreover, the number of overlapped peaks was detected simultaneously. Then parameters of individual peaks in multiplets were computed with the genetic implemented level. It is obvious that not only the number of overlapped peaks can be detected by itself but also the optimization results do not heavily depend on the assumptions about the system. Consequently, the very good results can be achieved when the number of the components is not too many and the signal-to-noise ratio is not to low. Nevertheless, despite the genetic algorithm could approach the globally optimal solution irrespective of diverse starting conditions, it is always prone to converge to a least solution due to its random genetic parameters. Based on this, wavelet transform-based genetic algorithms are presented to resolving overlapping bands for the first time. Here, wavelet transform was used to denoise, to deduct the background as well as to provide the initial parameters for genetic algorithms, then genetic algorithms are employed to optimize the parameters of unresolved bands. There is no doubt that reliable initial values can facilitate the convergence and good optimized results. 2. Curve fitting using wavelet transform for peak finding and signal-to-noise ratio enhancement was proposed for the first time, in which wavelet transform was performed prior to curve fitting to enhance noise level for subsequent fitting and to determine peak number and corresponding parameters. Accordingly, the fitted conditions can be improved to the point that very accurate results could be acquired even for the overlapped bands with higher noise level. 3. Wavelet transform-based Fourier self-deconvolution was proposed and applied to resolving electrochemical signal. Wavelet transform was used to decompose signals into components with different frequency, then an appropriate approximation served as a line shape function for deconvolution as well as wavelet function was used as apodization function. Hence, the procedure of Fourier self-deconvolution is simplified and the resolution enhancement factor is enhanced significa...
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