A Study on Wavelet-based Identification of Nonstationary Systems

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1. We developed a method for estimating the dead time of transfer function model by taking the wavelet transform of finite-data input/output correlation function of linear systems, and reconsidered the method from the viewpoint of frequency domain.2. We developed a method of estimating the frequency response of transfer function model by taking the wavelet transforms of finite-data input/output correlation functions of linear systems, and of estimating the time-varying rational parts of transfer functions by the least squares method in the frequency domain.3. We. extended the methods proposed here to the 2-input/2-output linear feedback systems, and applied them to the control system of water-tube drum boiler in the power station. This demonstrates the feasibility and effectiveness of our methods.4. We investigated the normalization of spectrum based on the, wavelet transform (frequency-dependent short-time Fourier transform) of correlation function.5. We analyzed the relation between the wavelet transform of the correlatin function and the power spectrum under a general assumption. As a result, we showed theoretically these close relation by using the multiplication of the exponential function and the even function including the Gabor function as an analyzing wavelet.6. The method developed for the transfer function estimation is based on the Blackman-Tukey method, called the indirect method. We proposed another method for the transfer function estimation by directly taking the wavelet transforms of input/output data of linear systems called the direct method.7. As the applications of the wavelet transform, we developed a new method of blind source separation in convoluted mixture of sound signals, and we analyzed the extraordinary sounds of bike.