The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the fam...The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the family of periodic trigonometric spline wavelets is dense in L2([0,2π]).展开更多
A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite elem...A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.展开更多
B-Spline wavelet-BEM numerical algorithm is presented. To avoid to treating singular integrals in wavelet-BEM, a method of putting source points out of the domain is used and discussed. Meanwhile, two higher effective...B-Spline wavelet-BEM numerical algorithm is presented. To avoid to treating singular integrals in wavelet-BEM, a method of putting source points out of the domain is used and discussed. Meanwhile, two higher effective numerical quadrature formulae are suggested. Finally, an example in mechanics is given and numerical results show that this method is effective. In addition, this method can be extended to manipulate problems, especially, with singularity.展开更多
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is ort...Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.展开更多
A new method of determination for roxithromycin tablets by non-aqueous capillary electrophoresis (NACE) with square-wave amperometric detection was carried out. Several parameters affecting the NACE-AD determination ...A new method of determination for roxithromycin tablets by non-aqueous capillary electrophoresis (NACE) with square-wave amperometric detection was carried out. Several parameters affecting the NACE-AD determination were studied. The data was modified by spline wavelet least square (SWLS). The method is simple, rapid and highly reliable for routine analysis.展开更多
Spline wavelet and orthogonal wavelet are two widely used wavelet methods. In this paper, comparison of these two methods has been made, including their algorithm, properties and results of signal processing in analyt...Spline wavelet and orthogonal wavelet are two widely used wavelet methods. In this paper, comparison of these two methods has been made, including their algorithm, properties and results of signal processing in analytical chemistry signals. It is found that spline wavelet is more effective than orthogonal wavelet in processing high noise signals. The curves obtained from spline wavelet are closer to the theoretical ones than those obtained from orthogonal wavelet and the errors of spline wavelet are smaller than those of orthogonal wavelet.展开更多
Fault diagnosis of rolling element bearings requires efficient signal processing techniques. For this purpose, the performances of envelope detection with fast Fourier transform （FFT） and continuous wavelet transfo...Fault diagnosis of rolling element bearings requires efficient signal processing techniques. For this purpose, the performances of envelope detection with fast Fourier transform （FFT） and continuous wavelet transform （CWT） of vibration signals produced from a bearing with defects on inner race and rolling element, have been examined at low signal to noise ratio. Both simulated and experimental signals from identical bearings have been considered for the purpose of analysis. The bearings have been modeled as spring-mass-dashpot systems and the simulated signals have been obtained considering transfer functions for the bearing systems subjected to impulsive loads due to the defects. Frequency B spline wavelets have been applied for CWT and a discussion on wavelet selection has been presented for better effectiveness. Results show that use of CWT with the proposed wavelets overcomes the short coming of FFT while processing a noisy vibration signals for defect detection of bearings.展开更多
基金This work is pastially supported by NNSFCthe Foundation of Zhongshan University Advanced Reseasch Centre
文摘The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the family of periodic trigonometric spline wavelets is dense in L2([0,2π]).
基金supported by the National Natural Science Foundation of China (Nos. 50805028 and 50875195)the Open Foundation of the State Key Laboratory of Structural Analysis for In-dustrial Equipment (No. GZ0815)
文摘A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.
文摘B-Spline wavelet-BEM numerical algorithm is presented. To avoid to treating singular integrals in wavelet-BEM, a method of putting source points out of the domain is used and discussed. Meanwhile, two higher effective numerical quadrature formulae are suggested. Finally, an example in mechanics is given and numerical results show that this method is effective. In addition, this method can be extended to manipulate problems, especially, with singularity.
基金theNationalNaturalScienceFoundationofChina (No .50 40 90 0 8)
文摘Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.
基金This work was supported by the National Natural Science Foundation of China and Guang Dong Provincial Natural Science Foundation(29675033 and 20175037 001237)
文摘A new method of determination for roxithromycin tablets by non-aqueous capillary electrophoresis (NACE) with square-wave amperometric detection was carried out. Several parameters affecting the NACE-AD determination were studied. The data was modified by spline wavelet least square (SWLS). The method is simple, rapid and highly reliable for routine analysis.
基金Project supported by the National Natural Science Foundation of China (No. 29675033)Natural Science Foundation of Guangdong Province (No. 960006)
文摘Spline wavelet and orthogonal wavelet are two widely used wavelet methods. In this paper, comparison of these two methods has been made, including their algorithm, properties and results of signal processing in analytical chemistry signals. It is found that spline wavelet is more effective than orthogonal wavelet in processing high noise signals. The curves obtained from spline wavelet are closer to the theoretical ones than those obtained from orthogonal wavelet and the errors of spline wavelet are smaller than those of orthogonal wavelet.
文摘Fault diagnosis of rolling element bearings requires efficient signal processing techniques. For this purpose, the performances of envelope detection with fast Fourier transform （FFT） and continuous wavelet transform （CWT） of vibration signals produced from a bearing with defects on inner race and rolling element, have been examined at low signal to noise ratio. Both simulated and experimental signals from identical bearings have been considered for the purpose of analysis. The bearings have been modeled as spring-mass-dashpot systems and the simulated signals have been obtained considering transfer functions for the bearing systems subjected to impulsive loads due to the defects. Frequency B spline wavelets have been applied for CWT and a discussion on wavelet selection has been presented for better effectiveness. Results show that use of CWT with the proposed wavelets overcomes the short coming of FFT while processing a noisy vibration signals for defect detection of bearings.
