Spectra Analysis Using Wavelet Transform And Kalman Filter

Wavelet transform (WT) and Kalman filter are very important in Chemometrics. WT becomes more and more popular in spectra analysis because it has some particular advantages in signal processing. Kalman filter, an optimal self-adaptive filter, has been usually used in spectra de-noise. In this thesis, the application of wavelet transform and Kalman filter to analyze spectra, especially the overlapped spectra, are systematically discussed.According to the specialty of WT, not only continuous wavelet transform(CWT) and discrete wavelet transform(DWT), but also stationary wavelet transform(SWT) can be used to calculate derivative in spectra analysis. In contrast to CWT, SWT has less calculation in derivative, thereby it suits for engineering calculation; In contrast to DWT, SWT is better because SWT retains the same data points in the transform. Therefore, SWT is an efficient tool in spectra analysis.The simple principle to choose the optimal wavelet function in derivative is discussed. The result indicates that the optimal wavelet function can be chosen based on the signal SNR. Two methods, both derivative and multiresolution analysis by WT, can enhance the SNR and resolution of signal. Comparatively, the derivative by WT is more effective in improving the SNR and the multiresolution analysis by WT does better in improving the resolution. The results offer a reference for the parameter choice of WT in engineering.A novel derivative algorithm based on Kalman filter is proposed for resolving the overlapped peaks in spectra. The algorithm overcomes the disadvantage that the noise...