Research On Wavelet Theory For Signal Analysis And Integrated Wavelet Analyzer

Wavelet analysis is a new discipline developed from engineering, physics and pure mathematics during last thirty years, whose remarkable characteristics include the property of time-frequency localization and the"zoom-in"property. Therefore, it is very suitable for nonlinear and non-stationary signals analysis, and has been widely applied to many different fields. At present, wavelet analysis is still a hot theme all over the world, and a great many new methods and theories emerge in endlessly. However, the development of wavelet analyzers greatly lags behind the evolution of wavelet theories. Hence, on the above situation, this thesis systematically researches various wavelet analysis methods in theory and application, and some innovative achievements are obtained. Based on the above theoretical achievements, the integrated wavelet analyzer is developed with virtual instrument technology and integrated instrument technology, so as to provide a valuable analysis tool for feature extraction of complex signals in mechanical engineering.Firstly, the present research status of non-stationary signals analysis methods, wavelet theories and wavelet analysis instruments (software) is summarized, and the values of this thesis are presented. Subsequently, the classical wavelet theories are systematically reviewed, which refer to continuous wavelet transform, dyadic wavelet transform, discrete wavelet transform, wavelet frames, multiresolution analysis, orthogonal wavelet bases, biorthogonal wavelet bases, wavelet packet, wavelet pursuit and the second generation wavelet transform et al..Research on the implementation algorithms of various wavelet transforms has important significance for the development of wavelet analysis instrument. Firstly, two algorithms for implementing dyadic wavelet transform, i.e.àtrous algorithm and direct algorithm of wavelet transform, are introduced. Then, the problems in Mallat algorithm are indicated, and an improved Mallat algorithm is elaborated. Finally, after the review of the current algorithms for continuous wavelet transform, a new fast algorithm for implementing continuous wavelet transform by band-pass filtering is proposed, and its performance is analyzed. Experimental results show that this proposed algorithm has a higher performance than current algorithms.Signal denoising is one of the most significant applications of wavelet analysis, thus the denoising methods in wavelet domain are systematically studied. Four main wavelet denoising method, i.e. denoising method based on time-frequency filtering, denoising method based on modulus maxima of wavelet coefficients, denoising method based on spatial correlation and denoising method based on thresholding, are introduced, and their characteristics are discussed. A new denoising method based on dyadic wavelet transform is proposed by combining the modulus maxima denoising method with the thresholding denoising method. Compared with the denoising method based on soft thresholding, has the lower bound of denoising error of the proposed method are smaller, so it has a higher denoising performance the thresholding denoising method. Furthermore, since this method reconstructs the denoised signal with modulus maxima of wavelet coefficients, the denoised result well reserve the singularities of the original signal. The denoising performance of the proposed has been proved by simulation experiments and engineering applications.Instantaneous frequency and instantaneous amplitude can be calculated by the wavelet ridge, therefore wavelet ridge has high application value in engineering. An improved ridge algorithm which changes the iteration threshold adaptively at the divergence points is brought forward to solve the problem of iterative divergence that exists in the wavelet ridge iterative extraction algorithm. Its antinoise performance and the characteristic of extracting the wavelet ridge for the multi-component signal are investigated. This improved ridge algorithm is applied to the fault diagnosis of rotating machinery, and the analysis results are exciting. For multi-component signals, a new multi wavelet ridge extraction method based on reassigned algorithm and singular value decomposition is proposed. It has excellent antinoise performance and can be effectively applied for mechanical fault diagnosis.Expansive discrete wavelet transform is an important development of wavelet analysis theory. Framelet transform, which has been studied by many famous scientists in recent years, is also a kind of expansive discrete wavelet transform. First, some contents concerning framelet are reviewed, and several kinds of typical expansive discrete wavelet transforms. Then, the higher density discrete wavelet transform is primarily studied, its least asymmetric wavelets are constructed, and the properties of its combined filter bank are researched. Furthermore, this paper proves that the wavelet frame of the higher density discrete wavelet transform is a tight frame for L2(R), the corresponding frame decomposition and reconstruction algorithm is proposed. In order to improve the sampling density for the time-frequency plane, a higher density dyadic wavelet transform is innovatively proposed, and its fast decomposition and reconstruction algorithm is given. Simulation and application results show that the proposed new wavelet transform has quite high denoising performance.The development of wavelet analyzer is one of the main targets of this thesis. Virtual instrument technology and integrated instrument technology are researched. And then integrated wavelet analyzer is successfully developed, which is based on Qin's model, integrated measurement system and the above theoretical achievements. This instrument has both the virtues of virtual instrument and the virtues of traditional hardware instrument, and has powerful abilities for signal analysis, thereby it is suitable for analyzing complex signals in scientific experiments and engineering. A large number of simulation experiments and practical engineering applications are implemented with this instrument, in order to validate the correctness and stability of its functions.Summarization of the thesis and expectations of the next research aspects are in the end of the thesis.