We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider t...We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.展开更多
Based on the brief introduction of the principles of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of view of perfect reconstruction of signals and emphasizes that design...Based on the brief introduction of the principles of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of view of perfect reconstruction of signals and emphasizes that designing wavelet bases which are used to decompose the signal into a two-band form is equivalent to designing a two-band filter bank with perfect or nearly perfect property. The generating algorithm corresponding to Daubechies bases and some simulated results are also given in the paper.展开更多
When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We us...When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We use a method called symmetric extension to solve the problem. We only consider the case of the two-band filter banks, and the results can be applied to M-band filter banks. There are only two types of symmetric extension in analysis phrase, namely the whole-sample symmetry (WS), the half-sample symmetry (HS), while there are four types of symmetric extension in synthesis phrase, namely the WS, HS, the whole-sample anti-symmetry (WA), and the half-sample anti-symmetry (HA) respectively. We can select the exact type according to the image length and the filter length, and we will show how to do these. The image can be perfectly reconstructed without any edge effects in this way. Finally, simulation results are reported. Key words edge effect - image compression - wavelet - biorthogonal bases - symmetric extension CLC number TP 37 Foundation item: Supported by the National 863 Project (20021111901010)Biography: Yu Sheng-sheng (1944-), male, Professor, research direction: multimedia information processing, SAN.展开更多
The BER performance for an optimal circular 16-QAM constellation is theoretically derived and applied in wavelet based OFDM system in additive white Gaussian noise channel. Signal point constellations have been discus...The BER performance for an optimal circular 16-QAM constellation is theoretically derived and applied in wavelet based OFDM system in additive white Gaussian noise channel. Signal point constellations have been discussed in much literature. An optimal circular 16-QAM is developed. The calculation of the BER is based on the four types of the decision boundaries. Each decision boundary is determined based on the space distance d following the pdf Gaussian distribution with respect to the in-phase and quadrature components nI and nQ with the assumption that they are statistically independent to each other. The BER analysis for other circular M-ary QAM is also analyzed. The system is then applied to wavelet based OFDM. The wavelet transform is considered because it offers a better spectral containment feature compared to conventional OFDM using Fourier transform. The circular schemes are slightly better than the square schemes in most SNR values. All simulation results have met the theoretical calculations. When applying to wavelet based OFDM, the circular modulation scheme has also performed slightly less errors as compared to the square modulation scheme.展开更多
In the fifties. Calderon established a formal relation between svmbol and kernel distribu-tion, but it is difficult to establish an intrinsic relation. The Calderon-Zygmund (C-Z) school studiedrhe C-Z operators, and H...In the fifties. Calderon established a formal relation between svmbol and kernel distribu-tion, but it is difficult to establish an intrinsic relation. The Calderon-Zygmund (C-Z) school studiedrhe C-Z operators, and Hormander. Kohn and Nirenberg, et al. studied the symbolic operators. Herewe apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases.to characterize both symbolic operators spaces OpS~m and kernel distributions spaces with other spacescomposed of some ahnost diagonal matrices. then get an isometric between OpS~m and kernel distri-bution spaces展开更多
This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kern...This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.展开更多
In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ ...In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ are two compactly supported vectors of functions in the Sobolev space (H μ(? s )) r for some μ > 0. We provide a characterization for the sequences {ψ jk l : l = 1,...,r, j ε ?, k ε ? s } and $ \tilde \psi _{jk}^\ell :\ell = 1,...,r,j \in \mathbb{Z},k \in \mathbb{Z}^s $ to form two Riesz sequences for L 2(? s ), where ψ jk l = m j/2ψ l (M j ·?k) and $ \tilde \psi _{jk}^\ell = m^{{j \mathord{\left/ {\vphantom {j 2}} \right. \kern-0em} 2}} \tilde \psi ^\ell (M^j \cdot - k) $ , M is an s × s integer matrix such that lim n→∞ M ?n = 0 and m = |detM|. Furthermore, let ? = (?1,...,? r ) T and $ \tilde \phi = (\tilde \phi ^1 ,...,\tilde \phi ^r )^T $ be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, $ \tilde a $ and M, where a and $ \tilde a $ are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr ) T and $ \tilde \psi ^\nu = (\tilde \psi ^{\nu 1} ,...,\tilde \psi ^{\nu r} )^T $ , ν = 1,..., m ? 1 such that two sequences {ψ jk νl : ν = 1,..., m ? 1, l = 1,...,r, j ε ?, k ε ? s } and { $ \tilde \psi _{jk}^\nu $ : ν=1,...,m?1,?=1,...,r, j ∈ ?, k ∈ ? s } form two Riesz multiwavelet bases for L 2(? s ). The bracket product [f, g] of two vectors of functions f, g in (L 2(? s )) r is an indispensable tool for our characterization.展开更多
A novel method of synthesizing seismic wave using wavelet reconstruction is proposed and compared with the traditional method of using theory of Fourier transform. By adjusting the frequency band energy and taking it ...A novel method of synthesizing seismic wave using wavelet reconstruction is proposed and compared with the traditional method of using theory of Fourier transform. By adjusting the frequency band energy and taking it as criterion, the formula of synthesizing seismic wave is deduced. Using the design parameters specified in Chinese Seismic Design Code for buildings, seismic waves are synthesized. Moreover, the method of selecting wavelet bases in synthesizing seismic wave and the influence of the damping ratio on synthesizing results are analyzed. The results show that the synthesis seismic waves using wavelet bases can represent the characteristics of the seismic wave as well as the ground characteristic period, and have good time-frequency non-stationary.展开更多
Two kinds of wavelet-based elements have been constructed to analyze the stability of plates and shells and the static displacement of 3D elastic problems.The scaling functions of B-spline wavelet on the interval（BSW...Two kinds of wavelet-based elements have been constructed to analyze the stability of plates and shells and the static displacement of 3D elastic problems.The scaling functions of B-spline wavelet on the interval（BSWI） are employed as interpolating functions to construct plate and shell elements for stability analysis and 3D elastic elements for static mechanics analysis.The main advantages of BSWI scaling functions are the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis.The performances of the present elements are demonstrated by typical numerical examples.展开更多
A method of fairing B spline surfaces by wavelet decomposition is investigated. The wavelet decomposition and reconstruction of quasi uniform bicubic B spline surfaces are described in detail. A method is introduce...A method of fairing B spline surfaces by wavelet decomposition is investigated. The wavelet decomposition and reconstruction of quasi uniform bicubic B spline surfaces are described in detail. A method is introduced to approximate a B spline surface by a quasi uniform one. An error control approach for wavelet based fairing is suggested. Samples are given to show the feasibility of the algorithms presented in this paper. The practice showed that the wavelet based fairing is better than energy based one in case where the number of vertices of the B spline surface is greater than 1000. The quantitative variance of the approximation error in accordance with the change of decomposition levels needs to be further explored.展开更多
This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying...This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.展开更多
Based on the scale function representation for a function in L2(R), a new wavelet transform based adaptive system identification scheme is proposed. It can reduce the amount of computation by exploiting the decimation...Based on the scale function representation for a function in L2(R), a new wavelet transform based adaptive system identification scheme is proposed. It can reduce the amount of computation by exploiting the decimation properties and keep the advantage of quasi-orthogonal transform of the discrete wavelet, transform (DWT). The issue has been supported by computer simulations.展开更多
Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the re...Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the results vary greatly. To overcome this problem and to improve the accuracy and efficiency, a new method denoted by Natural-based Wavelet Method is introduced and extended. It can be proved that the proposed method in fact is a special class of discrete wavelet. At first, two numerical examples are designed to show the capacity of the novel method. Second, this method is applied to a precipitation series. According to wavelet analysis and short-range precipitation prediction, this precipitation exists a faintly increasing trend. Through the analysis, the studied precipitation has two major periods: 11 and 41 years. The results validate that the Natural-based Wavelet Method used in application of multi-complicated observed data is suitable. It is easy to write the source code of the proposed method. When new information appears, new information can be easily added into the original sequence, this is another advantage of the proposed method.展开更多
In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study h...In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.展开更多
Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller b...Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.展开更多
We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous...We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous experiments were done on typical images to calculate (using Matlab) the entropy before and after wavelet transform. It was verified that, to obtain minimal entropy, a three-layer decomposition should be adopted rather than higher orders. The result achieved by using biorthogonal wavelet decomposition is better than that of the orthogonal wavelet decomposition. The results are not directly proportional to the vanishing moment, however.展开更多
The thesis introduces various characteristic wavelet bases used in non-stationary machinery equipment diagnosis, then discusses genetic wavelets and harmonic wavelets and their practical application respectively in fa...The thesis introduces various characteristic wavelet bases used in non-stationary machinery equipment diagnosis, then discusses genetic wavelets and harmonic wavelets and their practical application respectively in fault diagnosis of an internal combustion engine and in orbits extracting (analysis) of rotating machinery.展开更多
文摘We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.
文摘Based on the brief introduction of the principles of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of view of perfect reconstruction of signals and emphasizes that designing wavelet bases which are used to decompose the signal into a two-band form is equivalent to designing a two-band filter bank with perfect or nearly perfect property. The generating algorithm corresponding to Daubechies bases and some simulated results are also given in the paper.
文摘When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We use a method called symmetric extension to solve the problem. We only consider the case of the two-band filter banks, and the results can be applied to M-band filter banks. There are only two types of symmetric extension in analysis phrase, namely the whole-sample symmetry (WS), the half-sample symmetry (HS), while there are four types of symmetric extension in synthesis phrase, namely the WS, HS, the whole-sample anti-symmetry (WA), and the half-sample anti-symmetry (HA) respectively. We can select the exact type according to the image length and the filter length, and we will show how to do these. The image can be perfectly reconstructed without any edge effects in this way. Finally, simulation results are reported. Key words edge effect - image compression - wavelet - biorthogonal bases - symmetric extension CLC number TP 37 Foundation item: Supported by the National 863 Project (20021111901010)Biography: Yu Sheng-sheng (1944-), male, Professor, research direction: multimedia information processing, SAN.
文摘The BER performance for an optimal circular 16-QAM constellation is theoretically derived and applied in wavelet based OFDM system in additive white Gaussian noise channel. Signal point constellations have been discussed in much literature. An optimal circular 16-QAM is developed. The calculation of the BER is based on the four types of the decision boundaries. Each decision boundary is determined based on the space distance d following the pdf Gaussian distribution with respect to the in-phase and quadrature components nI and nQ with the assumption that they are statistically independent to each other. The BER analysis for other circular M-ary QAM is also analyzed. The system is then applied to wavelet based OFDM. The wavelet transform is considered because it offers a better spectral containment feature compared to conventional OFDM using Fourier transform. The circular schemes are slightly better than the square schemes in most SNR values. All simulation results have met the theoretical calculations. When applying to wavelet based OFDM, the circular modulation scheme has also performed slightly less errors as compared to the square modulation scheme.
基金Supported by a foundation from the Education Ministry of China for young scholars back from abroad
文摘In the fifties. Calderon established a formal relation between svmbol and kernel distribu-tion, but it is difficult to establish an intrinsic relation. The Calderon-Zygmund (C-Z) school studiedrhe C-Z operators, and Hormander. Kohn and Nirenberg, et al. studied the symbolic operators. Herewe apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases.to characterize both symbolic operators spaces OpS~m and kernel distributions spaces with other spacescomposed of some ahnost diagonal matrices. then get an isometric between OpS~m and kernel distri-bution spaces
基金Project supported by the National Natural Science Foundation of China (No. 10001027).
文摘This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.
基金supported by National Natural Science Foundation of China (Grant Nos. 10771190, 10471123)
文摘In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ are two compactly supported vectors of functions in the Sobolev space (H μ(? s )) r for some μ > 0. We provide a characterization for the sequences {ψ jk l : l = 1,...,r, j ε ?, k ε ? s } and $ \tilde \psi _{jk}^\ell :\ell = 1,...,r,j \in \mathbb{Z},k \in \mathbb{Z}^s $ to form two Riesz sequences for L 2(? s ), where ψ jk l = m j/2ψ l (M j ·?k) and $ \tilde \psi _{jk}^\ell = m^{{j \mathord{\left/ {\vphantom {j 2}} \right. \kern-0em} 2}} \tilde \psi ^\ell (M^j \cdot - k) $ , M is an s × s integer matrix such that lim n→∞ M ?n = 0 and m = |detM|. Furthermore, let ? = (?1,...,? r ) T and $ \tilde \phi = (\tilde \phi ^1 ,...,\tilde \phi ^r )^T $ be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, $ \tilde a $ and M, where a and $ \tilde a $ are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr ) T and $ \tilde \psi ^\nu = (\tilde \psi ^{\nu 1} ,...,\tilde \psi ^{\nu r} )^T $ , ν = 1,..., m ? 1 such that two sequences {ψ jk νl : ν = 1,..., m ? 1, l = 1,...,r, j ε ?, k ε ? s } and { $ \tilde \psi _{jk}^\nu $ : ν=1,...,m?1,?=1,...,r, j ∈ ?, k ∈ ? s } form two Riesz multiwavelet bases for L 2(? s ). The bracket product [f, g] of two vectors of functions f, g in (L 2(? s )) r is an indispensable tool for our characterization.
基金'Qing Lan' Talent Engineering Funds by Lanzhou Jiaotong University (QL-05-08A).
文摘A novel method of synthesizing seismic wave using wavelet reconstruction is proposed and compared with the traditional method of using theory of Fourier transform. By adjusting the frequency band energy and taking it as criterion, the formula of synthesizing seismic wave is deduced. Using the design parameters specified in Chinese Seismic Design Code for buildings, seismic waves are synthesized. Moreover, the method of selecting wavelet bases in synthesizing seismic wave and the influence of the damping ratio on synthesizing results are analyzed. The results show that the synthesis seismic waves using wavelet bases can represent the characteristics of the seismic wave as well as the ground characteristic period, and have good time-frequency non-stationary.
基金supported by the National Natural Science Foundation of China (No. 50805028)the Key Project of Chinese Ministry of Education (No. 210170)+1 种基金Guangxi key Technologies R & D Program of China (Nos. 1099022-1 and 0900705 003)supported in part by the Excellent Talents in Guangxi Higher Education Institutions of China
文摘Two kinds of wavelet-based elements have been constructed to analyze the stability of plates and shells and the static displacement of 3D elastic problems.The scaling functions of B-spline wavelet on the interval（BSWI） are employed as interpolating functions to construct plate and shell elements for stability analysis and 3D elastic elements for static mechanics analysis.The main advantages of BSWI scaling functions are the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis.The performances of the present elements are demonstrated by typical numerical examples.
文摘A method of fairing B spline surfaces by wavelet decomposition is investigated. The wavelet decomposition and reconstruction of quasi uniform bicubic B spline surfaces are described in detail. A method is introduced to approximate a B spline surface by a quasi uniform one. An error control approach for wavelet based fairing is suggested. Samples are given to show the feasibility of the algorithms presented in this paper. The practice showed that the wavelet based fairing is better than energy based one in case where the number of vertices of the B spline surface is greater than 1000. The quantitative variance of the approximation error in accordance with the change of decomposition levels needs to be further explored.
文摘This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.
基金Supported by the National Natural Science Foundation of China,no.69672039
文摘Based on the scale function representation for a function in L2(R), a new wavelet transform based adaptive system identification scheme is proposed. It can reduce the amount of computation by exploiting the decimation properties and keep the advantage of quasi-orthogonal transform of the discrete wavelet, transform (DWT). The issue has been supported by computer simulations.
基金Sponsored by the National Natural Science Foundation of China(Grant Nos.11461026,11361024,51378206 and 11661036)the Provincial Natural Science Foundation(Grant No.2017BAB201009)
文摘Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the results vary greatly. To overcome this problem and to improve the accuracy and efficiency, a new method denoted by Natural-based Wavelet Method is introduced and extended. It can be proved that the proposed method in fact is a special class of discrete wavelet. At first, two numerical examples are designed to show the capacity of the novel method. Second, this method is applied to a precipitation series. According to wavelet analysis and short-range precipitation prediction, this precipitation exists a faintly increasing trend. Through the analysis, the studied precipitation has two major periods: 11 and 41 years. The results validate that the Natural-based Wavelet Method used in application of multi-complicated observed data is suitable. It is easy to write the source code of the proposed method. When new information appears, new information can be easily added into the original sequence, this is another advantage of the proposed method.
文摘In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.
基金This project is supported by National Natural Science Foundation of China (No.50205050).
文摘Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.
基金the Natural Science Foundation of China (No. 60472037).
文摘We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous experiments were done on typical images to calculate (using Matlab) the entropy before and after wavelet transform. It was verified that, to obtain minimal entropy, a three-layer decomposition should be adopted rather than higher orders. The result achieved by using biorthogonal wavelet decomposition is better than that of the orthogonal wavelet decomposition. The results are not directly proportional to the vanishing moment, however.
基金National Natural Science Foundation of China !59775023 Natural Science Research Foundation of Shaanxi Province ! 97G14
文摘The thesis introduces various characteristic wavelet bases used in non-stationary machinery equipment diagnosis, then discusses genetic wavelets and harmonic wavelets and their practical application respectively in fault diagnosis of an internal combustion engine and in orbits extracting (analysis) of rotating machinery.
