信号小波理论与一体化小波分析仪的研究
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摘要
小波分析是近三十年从工程、物理及纯数学发展起来的一门新兴学科,其最大优点是具有“时频局部化”和“数学显微镜”性质,因此它非常适合于非线性、非平稳信号的分析,并已在许多领域得到广泛应用。目前,小波分析仍是国际研究的热点,各种新方法和新理论层出不穷,但小波分析仪器的发展却相对滞后。基于以上背景,本文系统地进行了多种小波分析方法的理论与应用研究,取得了一些创新性研究成果;然后基于以上理论成果,利用虚拟仪器技术和一体化仪器技术研制成功一体化小波变换分析仪,从而为机械工程领域中复杂信号的特征提取提供了一个有用的分析工具。
本文首先综述了非平稳信号分析方法、小波理论与小波分析仪器及软件的研究现状,并指出了本文研究的意义。然后系统地回顾了经典的小波理论,包括连续小波变换、二进小波变换、离散小波变换、小波框架、多分辨分析、正交小波基、双正交小波基、小波包、小波追踪、二代小波变换,等。
研究小波变换的实现算法对于小波分析仪器的开发具有重要的意义。首先介绍了实现二进小波变换的两种算法:多孔算法和小波变换直接算法;然后分析了Mallat算法中存在的问题,并详细介绍了一种改进的Mallat算法;最后,在对已有连续小波变换实现算法回顾的基础上,提出了一种利用带通滤波实现连续小波变换的快速算法,分析了其性能,并用实例验证了它的优越性。
信号降噪是小波分析的一个重要应用,于是本文对信号的小波域降噪方法进行了系统的研究。介绍了四种主要的小波降噪算法:时频滤波降噪、小波系数模极大值降噪、空域相关降噪和阈值降噪,并讨论了它们的特点。通过结合阈值降噪与模极大值降噪两种方法,提出了一种新的二进小波降噪方法,该方法可以改进阈值降噪法的误差下界,因此它具有更高的降噪性能。此外,由于该方法是通过小波系数模极大值来重建信号,因而其降噪结果更好地保留了信号中的奇异性。通过仿真试验和工程实例验证了本文所提方法的降噪性能。
利用小波脊线可以度量信号的瞬时频率和瞬时幅值,因而它在工程中具有很高的应用价值。针对小波脊线迭代提取算法中存在的迭代发散问题,提出一种在发散点处自适应改变迭代阈值的改进脊算法,并分析了它的抗噪特性和在提取多分量信号小波脊线中的特性,然后将新算法用于旋转机械故障诊断,取得了较好的分析效果。对于多分量信号,本文提出了一种基于重分配算法和奇异值分解的多脊提取方法,它也具有很好的抗噪性能,并能有效地用于机械系统的故障诊断。
膨胀离散小波变换是小波分析理论的一个重要发展,目前研究最多的框架波变换也是属于膨胀离散小波变换。本文首先回顾了框架波理论的相关内容,介绍了几种典型的膨胀离散小波变换;然后重点研究了高密度离散小波变换,构造了它的最小不对称小波,分析了所用滤波器组的性质,证明了它的小波框架是L2 (R)空间上的紧框架,并提出了高密度离散小波变换的框架分解与重构算法。为了进一步提高对时频面的采样密度,还创新性地提出了高密度二进小波变换,同时给出了它的快速分解与重构算法。仿真实验和实际应用的结果都表明本文提出的小波变换具有很高的降噪性能。
开发小波分析仪器是本文研究的主要目标之一。本文对虚拟仪器技术和一体化仪器技术进行了研究,并基于秦氏模型、一体化测试系统与前面的理论研究成果,研制成功了一体化小波变换分析仪。该仪器兼具虚拟仪器和传统硬件化仪器的优点,并具有强大的信号分析能力,适合于科学实验和工程中的复杂信号分析。本文还通过大量的仿真实验和实际工程应用,对仪器功能的正确性和稳定性进行了验证。
文章最后对本文工作进行了总结,并展望了下一步的研究方向。
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.
本文首先综述了非平稳信号分析方法、小波理论与小波分析仪器及软件的研究现状,并指出了本文研究的意义。然后系统地回顾了经典的小波理论,包括连续小波变换、二进小波变换、离散小波变换、小波框架、多分辨分析、正交小波基、双正交小波基、小波包、小波追踪、二代小波变换,等。
研究小波变换的实现算法对于小波分析仪器的开发具有重要的意义。首先介绍了实现二进小波变换的两种算法:多孔算法和小波变换直接算法;然后分析了Mallat算法中存在的问题,并详细介绍了一种改进的Mallat算法;最后,在对已有连续小波变换实现算法回顾的基础上,提出了一种利用带通滤波实现连续小波变换的快速算法,分析了其性能,并用实例验证了它的优越性。
信号降噪是小波分析的一个重要应用,于是本文对信号的小波域降噪方法进行了系统的研究。介绍了四种主要的小波降噪算法:时频滤波降噪、小波系数模极大值降噪、空域相关降噪和阈值降噪,并讨论了它们的特点。通过结合阈值降噪与模极大值降噪两种方法,提出了一种新的二进小波降噪方法,该方法可以改进阈值降噪法的误差下界,因此它具有更高的降噪性能。此外,由于该方法是通过小波系数模极大值来重建信号,因而其降噪结果更好地保留了信号中的奇异性。通过仿真试验和工程实例验证了本文所提方法的降噪性能。
利用小波脊线可以度量信号的瞬时频率和瞬时幅值,因而它在工程中具有很高的应用价值。针对小波脊线迭代提取算法中存在的迭代发散问题,提出一种在发散点处自适应改变迭代阈值的改进脊算法,并分析了它的抗噪特性和在提取多分量信号小波脊线中的特性,然后将新算法用于旋转机械故障诊断,取得了较好的分析效果。对于多分量信号,本文提出了一种基于重分配算法和奇异值分解的多脊提取方法,它也具有很好的抗噪性能,并能有效地用于机械系统的故障诊断。
膨胀离散小波变换是小波分析理论的一个重要发展,目前研究最多的框架波变换也是属于膨胀离散小波变换。本文首先回顾了框架波理论的相关内容,介绍了几种典型的膨胀离散小波变换;然后重点研究了高密度离散小波变换,构造了它的最小不对称小波,分析了所用滤波器组的性质,证明了它的小波框架是L2 (R)空间上的紧框架,并提出了高密度离散小波变换的框架分解与重构算法。为了进一步提高对时频面的采样密度,还创新性地提出了高密度二进小波变换,同时给出了它的快速分解与重构算法。仿真实验和实际应用的结果都表明本文提出的小波变换具有很高的降噪性能。
开发小波分析仪器是本文研究的主要目标之一。本文对虚拟仪器技术和一体化仪器技术进行了研究,并基于秦氏模型、一体化测试系统与前面的理论研究成果,研制成功了一体化小波变换分析仪。该仪器兼具虚拟仪器和传统硬件化仪器的优点,并具有强大的信号分析能力,适合于科学实验和工程中的复杂信号分析。本文还通过大量的仿真实验和实际工程应用,对仪器功能的正确性和稳定性进行了验证。
文章最后对本文工作进行了总结,并展望了下一步的研究方向。
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.
引文
[1]秦树人,季忠,尹爱军,秦毅,段虎明,毛永芳.工程信号处理[M].北京:高等教育出版社, 2008.
[2]邹红星,周小波,李延达.时频分析:回溯与前瞻[J].电子学报, 2000, 28(9): 78-84.
[3]张贤达.现代信号处理[M]. 2版.北京:清华大学出版社, 2002.
[4]张贤达,保铮.非平稳信号分析与处理[M].北京:国防工业出版社, 1998.
[5]纪跃波.多分辨时频分析理论与多功能时频分析系统的研究[D].重庆:重庆大学博士学位论文, 2002.
[6] L. Cohen著.时频分析:理论与应用[M].白居宪译.西安:西安交通大学出版社, 1998.
[7] D. Gabor. Theory of communication[J]. J. IEE, 1946, 93: 429-457.
[8] E.P. Wigner. On the quantum correction for thermodynamic equilibrium[J]. Physical Review, 1932, 40: 749-759.
[9] J. Ville. Theorie et applications de la notion de dignal analytique[J]. Cables et Transmission, 1948, 2A: 61-74.
[10] L. Cohen. Generalized phase-space distribution functions[J]. J. Math. Phys., 1966, 7: 781-786.
[11] I.H. Choi, J.W. Williams. Improved time-frequency representation of multicomponent signals using exponential[J]. IEEE Trans. Acoust, Speech, Signal Processing, 1989, 37: 862-871.
[12] J. Jeong, J.W. Williams. Kernel design for reduced interference distributions[J]. IEEE Trans. Signal Processing, 1992, 40: 402-412.
[13] J.W. Williams, J. Jeong. New time-frequency distributions: theory and application[J]. In: Proc. IEEE ICASSP-89, 1989: 1243-1247.
[14] Y. Zhao, Y. Atlas, R. Marks. The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals[J]. IEEE Trans. Acoust., Speech, Signal Processing, 1990, 38: 1084-1091.
[15] F. Auger, P. Flandrin. Improving the readability of time-frequency and time-scale representations by the reassignment method[J]. IEEE Trans. Signal Processing, 1995, 43:1068-1089.
[16] L. Cohen T.E. Posch. Positive time-frequency distribution functions[J]. IEEE Trans. Acoust, Speech, Signal Processing, 1985, 33: 31-38.
[17] C. John, T. Daniel. Radon transformation of time-frequency distributions for analysis of multicomponent signals[J]. IEEE Trans. Signal Processing, 1994,42: 3166-3177.
[18] V. Namias. The fractional order Fourier Transform and its application to quantum mechanics[J].J. Inst. Math. Applicat., 1980, 25: 241-265.
[19] A. Grossmann, J. Morlet. Decomposition of hardy function into square integrable wavelet of constant shape[J]. SIAM J. of Math. Anal., 1984, 15(4): 723-736.
[20] C.K. Chui. An introduction to wavelets[M]. New York: Academic Press, 1992.
[21] I. Daubechies. Ten lectures on wavelets[M]. Philadelphia: SIAM, l992.
[22] N.E. Huang, Z. Shen, S.R. Long, et al. The empirical mode decomposition and the Hilbert Spectrum for nonlinear and non-stationary time series analysis[J]. Proc. R. Soc. Lond. A, 1998, 454:903-995.
[23]钟佑明.希尔伯特-黄变换局瞬信号分析理论的研究[D].重庆:重庆大学博士学位论文, 2002.
[24]钟佑明,秦树人,汤宝平.一种振动信号新变换法的研究[J].振动工程学报, 2002, 15(2): 233-238.
[25]钟佑明,秦树人.希尔伯特-黄变换的统一理论依据研究[J].振动与冲击, 2006, 25(3): 40-43.
[26]李天云,赵妍,李楠,等.基于HHT的电能质量检测新方法[J].中国电机工程学报, 2005, 25(17): 52-56.
[27]于德介,杨宇,程军圣.一种基于EMD和SVM的齿轮故障诊断方法[J].机械工程学报, 2005, 41(1): 140-144.
[28] D.J. Yu, J.S. Cheng, Y. Yang. Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings[J]. Mechanical Systems and Signal processing, 2005, 19(2): 259-270.
[29]徐冠雷,王孝通,徐孝刚,朱涛.基于限邻域经验模式分解的多波段图像融合[J].红外与毫米波学报, 2006, 25(3): 225-228.
[30]程军圣,于德介,杨宇.基于支持矢量回归机的Hilbert-Huang变换端点效应问题的处理方法[J].机械工程学报, 2006, 42(4): 23-31.
[31] Y. Qin, S.R. Qin, Y.F. Mao. Fast implemention of orthogonal empirical mode decomposition and its application into harmonic detection[J]. Chinese Journal of Mechanical Engineering, 2008, 21(2): 93-98.
[32]赵进平.异常事件对EMD方法的影响及其解决方法研究[J].青岛海洋大学学报, 2001, 31(6): 805-814.
[33] J.S. Cheng, D.J. Yu, Y. Yang. Research on the intrinsic mode function (IMF) criterion in EMD method[J]. Mechanical Systems and Signal processing, 2006, 20(4): 817-824.
[34] S.R. Qin, Y.M. Zhong. A new envelope algorithm of Hilbert-Huang transform[J]. Mechanical Systems and Signal processing, 2006, 20(8): 1941-1952.
[35] Q.H. Chen, N.E. Huang, S. Riemenschneider, Y.S. Xu. A B-spline approach for empirical mode decompositions[J]. Advances in Computational Mathematics, 2006, 24: 171-195.
[36] A. Potamianos, P. Maragos. A comparison of the energy operator and the Hilbert transform approach to signal and speech demodulation[J]. Signal Processing, 1994, 37(1): 95-120.
[37] P. Maragos, J.F. Kaiser, T.F. Quatieri. On amplitude and frequency demodulation using energy operator[J]. IEEE Transacitons on Signal Processing, 1993, 41(4): 1532-1550.
[38] A.C. Bovik, P. Maragos, T.F. Quatieri. AM–FM energy detection and separation in noise using multiband energy operators[J]. IEEE Transacitons on Signal Processing, 1993, 41(12): 3245-3265.
[39] B. Santhanam, P. Maragos. Multicomponent AM–FM demodulation via periodicity-based algebraic separation and energy-based demodulation[J]. IEEE Transacitons on Communications, 2000, 48(3): 473-490.
[40] F. Gianfelici, G. Biagetti, P. Crippa, et al. Multicomponent AM-FM representations: an asymptotically exact approach[J]. IEEE Transactions on Audio, Speech, and Language Processing, 2007, 15(3): 823-837.
[41] Y. Qin, S.R. Qin, Y.F. Mao. Research on iterated Hilbert transform and its application in mechanical fault diagnosis[J]. Mechanical Systems and Signal processing, 2008, 22(8): 1967-1980.
[42]李建平.小波分析与信号处理——理论、应用与软件实现[M].重庆:重庆出版社, 1997.
[43] Y. Meyer. Principe d’incertitude, bases hilbertiennes et algebras d’operateurs[C]. France:, Seminaire Bourbaki, 1986.
[44] G. Battle. A block spin construction of ondelettes, Part 1: Lemarie function[J]. Commun. Math. Phys., 1987, 110: 601-615.
[45] P.G. Lemarie. Ondelletes a localization exponentlelles[J]. J. de Math. Pures et Appl, 1988, 67: 227-236.
[46] I. Daubechies. Orthonormal bases of compactly supported wavelets[J]. Commun. on Pure and Appl. Math., 1988, 4l: 909-996.
[47] S. Mallat. Multiresolution approximations and wavelet orthonormaI bases of L2(R)[J]. Trans. Amer. Math. Soc., 1989, 315: 69-87.
[48] S. Mallat. A theory for multiresolution signal decomposition: the wavelet representation[J]. IEEE Trans. PAMI, 1989, 11(7): 674-693.
[49] A. Cohen, I. Daubechies, J.C. Feauveau. Biorthogonal orthonormal bases of compactly supported wavelets[J]. Commun. on Pure and Appl. Math., 1992, 45: 485-560.
[50] R.R. Coifman Y. Meyer, M.V. Wickerhauser. Wavelet and signal processing, in Ruskai ed.:Wavelet and Their application[M]. Boston, US: Jones and Bartlett Publishers, 1992.
[51] W. Sweldens. The Lifting Scheme: A custom-design construction of biorthogonal wavelet[J]. Applied and Computational Harmonic Analysis, 1996, 3(2): 186-200.
[52] W. Sweldens. The Lifting Scheme: A construction of second generation wavelets[J]. SIAM J. Math. Anal., 1997, 29(2): 511-546.
[53] A.R. Calderbank, I. Daubechies, W. Sweldens. Wavelet transforms that map integers to integers[J]. Applied and Computational Harmonic Analysis, 1998, 5(3):332-369.
[54] J. Lebrun, M. Vetterli. Balanced multiwavelets theory and design[J]. IEEE Transacitons on Signal Processing, 1998, 46(4):1119-1125.
[55] T.N. Goodman, S.L. Lee. Wavelets of multiplicity[J]. Trans on Amer. Math. Soc, 1994, 342: 307-324.
[56] E.J. Candes, D.L. Donoho. Ridgelets: the key to high-dimensional intermittency?[J]. Phil. Trans. Roy. Soc. Lond. A., 1999, 357: 2495-2509.
[57] D.L. Donoho. Ridge functions and orthonormal ridgelets[J]. Journal of Approximation Theory, 2001, 111(2): 143-179.
[58] E.J. Candes, D.L. Donoho. Curvelets—A surprisingly effective nonadaptive representation for objects with edges, in A. Cohen, C. Rabut, and L. L. Schumaker (Eds), Curve and Surface Fitting: Saint-Malo 1999[M]. Nashville: Vanderbilt Univ. Press, 1999.
[59] J.L. Starck, E.J. Candes, D.L. Donoho. The curvelet transform for image denoising[J]. IEEE Transacitons on Signal Processing, 2002, 11(6): 670-684.
[60] D.L. Donoho. Wedgelets: Nearly-minimax estimation of edges[J]. Ann. Statist., 1999, 27: 859-897.
[61]黄得双,毛二可,韩月秋.小波变换应用于雷达信号处理的潜力和展望[J].北京理工大学学报, 1995, 15(2): 186-191.
[62]范中,田立生.利用子波变换检测瞬时信号[J].电子学报, 1996, 24(1): 78-82
[63]徐金梧,徐科.小波变换在滚动轴承故障诊断中的应用[J].机械工程学报, 1997, 9(2): 51-55.
[64]张中民,卢文祥,杨叔子,等.基于小波系数包络谱的滚动轴承故障诊断[J].振动工程学报, 1998, 11(1): 65-69.
[65]章珂,刘贵忠,邹大文,等.二进小波变换方法的地震信号分时分频去噪处理[J].地球物理学报, 1999,16(2): 94-99.
[66]陈庆虎,李柱.表面粗糙度提取的小波频谱法[J].机械工程学报, 1999, 35(3): 541-543.
[67] E.L. Pennec, S. Mallat. Sparse geometric image representations with bandelets[J]. IEEE Transacitons on Image Processing, 2005, 14(4): 423-438.
[68] G.A. Westenskow, D. Grote, F. Bieniosek, J.W. Kwan. A multi-beamlet injector for heavy ion fusion: Experiments and modeling[C]. Proceedings of PAC07, 2007, 1: 3777-3781.
[69] S. Mallat. Geometrical grouplets[J]. Appl. Comput. Harmon. Anal., to appear.
[70]杨福生.小波变换的工程分析与应用[M].北京:科学出版社, 1999.
[71] R.J. Duffin, A.C. Schaeffer. A class of nonharmonic Fourier Series[J]. Trans. Amer. Math. Soc., 1952, 36: 1561-1574.
[72] R.M. Young. An introduction to nonharmonic Fourier Series[M]. New York: Academic Press, 1980.
[73] I. Daubechies. The wavelet transform, time-frequency localization and signal analysis[J]. IEEE Trans. Information Theory, 1990, 36(5): 961-1005.
[74] Stephane Mallat著.信号处理的小波导引[M].杨力华,戴道清,黄文良,等译. 2版.北京:机械工业出版社, 2002.
[75] R.R. Coifman, M.V. Wickerhauser. Entropy based algorithm for best basis selection[J]. IEEE Trans. Information Theory, 1992, 38(2): 713-718.
[76] S.S. Chen, D.L. Donoho, M.A. Saunders. Atomic decomposition by basis pursuit[J]. SIAM REVIEW, 2001, 43(1): 129-159.
[77] S. Mallat, Z.F. Zhang. Matching pursuits with time-frequency dictionaries[J]. IEEE Trans. Signal Processing, 1993, 41(12): 3397-3415.
[78] M. Vetterli, C. Herley. Wavelets and filter banks: theory and design[J]. IEEE Trans. Acoust, Speech, Signal Processing, 1992, 40(9): 2207-2232.
[79] A.R. Calderbank, I. Daubechies, W. Sweldens. Wavelet transforms that map integers to integers[J]. Applied and Computational Harmonic Analysis, 1998, 5(3): 332-369.
[80] M.J. Shensa. The discrete wavelet transform: wedding theàtrous and Mallat algorithm[J]. IEEE Trans. Signal Processing, 1992, 40(10): 2464-2482.
[81]秦树人,汤宝平,徐铭陶,等.工程信号小波变换分析仪系统的研究[J].中国机械工程, 1999, 10(4): 443-446.
[82]秦树人.一项具国际先进水平的小波理论应用成果[J].中国机械工程, 1999, 10(9): 1008-1010.
[83] S.R. Qin, Z.K. Chen, B.P. Tang. Research of wavelet transform instrument system for signal analysis[J]. Chinese Journal of Mechanical Engineering, 2000, 13(2): 114-121.
[84]秦毅,秦树人,毛永芳.小波变换中经验模态分解的基波检测及其在机械系统中的应用[J].机械工程学报, 2008, 44(3): 135-142.
[85]杨建国.小波分析及其工程应用[M].北京:机械工业出版社, 2005.
[86] J.G. Yang, S.T. Park. An anti-aliasing algorithm for discrete wavelet transform[J]. MechanicalSystems and Signal processing, 2003, 17(5): 945-954.
[87]杜天军,陈光禹,雷勇.基于混叠补偿小波变换的电力系统谐波检测方法[J].中国电机工程学报, 2005, 25(3): 54-59.
[88] D.L. Jones, R.G. Baraniuk. Efficient approximation of continuous wavelet transform[J]. Electronic Letters, 1991, 27(9): 748-750.
[89] M. Unser, A. Aldroubi, S.J. Schiff. Fast implementation of the continuous wavelet transform with integer scales[J]. IEEE Trans. Signal Processing, 1994, 42(12): 3519-3523.
[90] O. Rioul, P. Duhamel. Fast algorithms for discrete and continuous wavelet transforms[J]. IEEE Trans. Information Theory, 1992, 38(2): 569-586.
[91]张彤,杨福生,唐庆玉.基于Mellin变换的连续小波变换快速算法[J].信号处理, 1996, 12(4): 342-349.
[92]唐炜,史忠科.时频域滤波及在飞机颤振试飞试验中的应用[J].振动与冲击, 2006, 25(4): 46-50.
[93] X.G. Xia. System identification using chirp signals and time-variant filters in the joint time-frequency Domain[J]. IEEE Trans. Signal Processing, 1997, 45(8): 2072-2084.
[94]梁霖,徐光华,侯成刚.基于奇异值分解的连续小波消噪方法[J].西安交通大学学报, 2004, 38(9): 46-50.
[95]车红昆,项占琴,程耀东.超声检测信号时频邻域自适应消噪技术[J].机械工程学报, 2007, 43(6): 226-231.
[96] S. Mallat, W.L. Hwang. Singularity detection and processing with wavelets[J]. IEEE Trans. Information Theory, 1992, 38(2): 617-643.
[97] Y.S Xu, J.B Weaver, M.J. Healy, J. Lu. Wavelet transform domain filters: a spatially selective noise filtration technique[J]. IEEE Trans. Image Processing, 1994, 3(6): 747-758.
[98]李仲宁,罗志增.基于小波变换的空域相关法在肌电信号中的应用[J].电子学报, 2007, 35(7): 1414-1418.
[99] D.L. Donoho, I.M. Johnstone. Ideal spatial adaptation via wavelet shrinkage[J]. Biometrika, 1994, 18: 425-455.
[100]D.L. Donoho, I.M. Johnstone. Adapting to unknown smoothness via wavelet shrinkage[J]. Journal of the American Statistical Association, 1995, 90: 1200-1224.
[101]D.L.Donoho. De-noising by soft-thrsholding[J]. IEEE Trans. Information Theory, 1995, 41(3): 613-627.
[102]祝海龙,郭天佑,屈梁生.基于二进小波变换和软阈值改进的信号消噪[J].自动化学报, 2004, 30(2): 199-206.
[103]N.P. Delprat, B. Escudie, P. Guillemain, et al. Asymptotic wavelet and Gabor analysis:extraction of instantaneous frequencies[J]. IEEE Trans. Information Theory, 1992, 38(2): 644-664.
[104]P. Guillemain, R. K. Martinet. Characterization of acoustic signals through continuous linear time-frequency representations[J]. Proc. IEEE, 1996, 84(2): 561-585.
[105]权建峰,邵森木,郭东敏.小波变换在无线电引信参数提取中的应用研究[J].探测与控制学报, 2005, 25(24): 122-127.
[106]张征平,任震,黄雯莹,等.基于小波脊线的电动机转子故障检测新方法[J].中国电机工程学报, 2003, 23(1): 97-101.
[107]任宜春,易伟建.钢筋混凝土梁的非线性振动识别研究[J].工程力学, 2006, 23(8): 90-95.
[108]牛发亮,黄进,杨家强.基于电磁转矩小波变换的感应电机转子断条故障诊断[J].中国电机工程学报, 2005, 25(24): 122-127.
[109]魏云冰,王万良,赵燕伟,等.基于小波脊线的刮水器电动机机械特性测试[J].机械工程学报, 2006, 42(6): 141-144.
[110]朱洪俊,王忠,秦树人.小波变换对瞬态信号特征信息的精确提取[J].机械工程学报, 2005, 41(12): 196-199.
[111]胡正磊,孙进平,袁运能,等.基于小波边缘提取和脊线跟踪技术的SAR图像河流检测算法[J].电子与信息学报, 2007, 29(3): 524-527.
[112]钟秉林,黄仁.机械故障诊断学[M]. 2版.北京:机械工业出版社, 1998.
[113]R.A. Carmona, W.L. Hwang, B. Torresani. Characterization of signals by the ridges of their wavelet transforms[J]. IEEE Trans. Signal Processing, 1997, 45(10): 2 586-2 590.
[114]R.A. Carmona, W.L. Hwang, B. Torresani. Multiridge detection and time-frequency reconstruction[J]. IEEE Trans. Signal Processing, 1999, 47(2): 480-492.
[115]N. ?zkurt, F.A. Savac. Determination of wavelet ridges of nonstationary signals by singular value decomposition[J]. IEEE Trans. Circuits and systems—II: Express Briefs, 2005, 52(8): 480-485.
[116]F. Auger, P. Flandrin. Improving the readability of time-frequency and time-scale representations by the reassignment method[J]. 1995, 43(5): 1068-1089.
[117]马辉,赵鑫,赵群超,等.时频分析在旋转机械故障诊断中的应用[J].振动与冲击, 2007, 26(3): 61-63.
[118]彭志科,何永勇,褚福磊.小波尺度谱在振动信号分析中的应用研究[J].机械工程学报, 2002, 38(3): 122-126.
[119]赵松年,熊小芸.子波变换与子波分析[M].北京:电子工业出版社, 1996.
[120]张贤达.矩阵分析与应用[M].北京:清华大学出版社, 2004.
[121]J.L. Starck, M.Elad, D.L. Donoho. Redundant multiscale transforms and their application formorphological component analysis[J]. Adv. Imag. Electron Phys., 2004, 132.
[122]J.M. Lewis and C.S. Burrus. Approximate continuous wavelet transform with an application to noise reduction[C]. Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), 1998, 3: 1533-1536.
[123]I.W. Selesnick. The double density DWT, in: A. Petrosian and F. G. Meyer (Eds), Wavelets in signal and image analysis: From Theory to Practice[M]. Norwell: Kluwer, 2001.
[124]A. Petukhov. Explicit construction of framelets[J]. Appl. Comput. Harmon. Anal., 2001, 11(2): 313-327.
[125]A. Petukhov. Symmetric framelets[J]. Constr. Approx., 2003, 19(2): 309-328.
[126]I. Daubechies, B. Han, A. Ron, and Z. Shen. Framelets: MRA-based constructions of wavelet frames[J]. Appl. Comput. Harmon. Anal., 2003, 14(1): 1-46.
[127]I. Daubechies, B. Han. Pairs of dual wavelet frames from any two refinable functions[J]. Constr. Approx., 2004 20 (3): 325-352.
[128]C.K. Chui, W. He. Compactly supported tight frames associated with refinable functions[J]. Appl. Comput. Harmon. Anal., 2000, 8(3): 293-319.
[129]C.K. Chui, W. He, J. St?cklerckler. Compactly supported tight and sibling frames with maximum vanishing moments[J]. Appl. Comput. Harmon. Anal., 2002, 13(3): 224-262.
[130]C.K. Chui, W. He, J. St?ckler, Q.Y. Sun, Compactly supported tight affine frames with integer dilations and maximum vanishing moments[J]. Adv. Comput. Math., 2003, 18(2): 159-187.
[131]C.K. Chui, W. He, J. St?cklerckler. Nonstationary tight wavelet frames, I: Bounded intervals[J]. Appl. Comput. Harmon. Anal., 2004, 17(2): 141-197.
[132]C.K. Chui, W. He, J. St?cklerckler. Nonstationary tight wavelet frames, II: unbounded intervals[J]. Appl. Comput. Harmon. Anal., 2005, 18(1): 25-66.
[133]B. Han. On dual wavelet tight frames[J]. Appl. Comput. Harmon. Anal., 1997, 4(4): 380-413.
[134]B. Han, Q. Mo. Multiwavelet frames from refinable function vectors[J]. Adv. Comput. Math. 2003, 18(2): 211-245.
[135]B. Han, Q. Mo. Splitting a matrix of Laurent polynomials with symmetry and its application to symmetric framelet filter banks[J]. SIAM J. Matrix Anal. Appl., 2004, 26(1): 97-124.
[136]I.W. Selesnick. Smooth wavelet tight frames with zero moments[J]. Appl. Comput. Harmon. Anal., 2001, 10(2): 163-181.
[137]Z.f. Shang, X.W. Zhou. Dual generators for weighted irregular wavelet frames and reconstruction error[J]. Appl. Comput. Harmon. Anal., 2007, 22(3): 356-367.
[138]B. Dong, Z.W. Shen. Pseudo-splines, wavelets and framelets[J]. Appl. Comput. Harmon. Anal., 2007, 22(1): 78-104.
[139]M. Charina, J. St?ckler. Tight wavelet frames for irregular multiresolution analysis[J]. Appl. Comput. Harmon. Anal., 2008, 25(1): 98-113.
[140]A. Ron, Z.W. Shen. Affine systems in L2( d): The analysis of the analysis operator[J]. J. Funct. Anal., 1997, 148(2): 408–447.
[141]A. Ron, Z.W. Shen. Affine systems in L2( d): II. Dual systems[J]. J. Fourier Anal. Appl., 1997, 3: 617–637.
[142]S.S. Goh, Z.Y. Lim, Z.W. Shen. Symmetric and antisymmetric tight wavelet frames[J]. Appl. Comput. Harmon. Anal., 2007, 20(3): 411-421.
[143]Q. Jiang. Parameterizations of masks for tight affine frames with two symmetric/antisymmetric generators[J]. Adv. Comput. Math., 2003, 18: 247–268.
[144]I.W. Selesnick, A.F. Abdelnour. Symmetric wavelet tight frames with two generators[J]. Appl. Comput. Harmon. Anal., 2004, 17(2): 211-225
[145]B. Han, Q. Mo. Symmetric MRA tight wavelet frames with three generators and high vanishing moments[J]. Appl. Comput. Harmon. Anal., 2005, 18(1): 67-93.
[146]A.F. Abdelnour, I.W. Selesnick. Symmetric nearly shift-invariant tight frame wavelets[J]. Appl. Comput. Harmon. Anal., 2005, 18(1): 67-93.
[147]P.P. Vaidyanathan, T.Q. Nguyen, Z. Doganata, and T. Saram?ki. Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices[J]. IEEE Trans. Acoust, Speech, Signal Process, 1989, 37(7): 1042-1056.
[148]N.G. Kingsbury. The dual-tree complex wavelet transform: A new technique for shift invariance and directional filters[J]. Proc. English IEEE DSP Workshop, 1998: 9-12.
[149]N.G. Kingsbury. Image processing with complex wavelets[J]. Philos. Trans. Roy. Soc. London Ser. A, 1999, 357: 2543-2560.
[150]罗鹏,高协平.基于双树复数小波变换的图像去噪方法[J].光子学报, 2008, 37(3): 604-608.
[151]李江涛,倪国强,王强.基于双树复数小波变换和双变量萎缩阈值图像降噪[J].光学技术, 2007, 33(5): 723-727.
[152]I.W. Selesnick. The double-density dual-tree discrete wavelet transform[J]. IEEE Trans. Signal Processing, 2004, 52(5): 1304-1314.
[153]I.W. Selesnick. Hilbert transform pairs of wavelet bases[J]. IEEE Signal Processing Lett., 2001, 8: 170-173.
[154]I.W. Selesnick. The design of approximate Hilbert transform pairs of wavelet Bases[J]. IEEE Trans. Signal Processing, 2002, 50(5): 1144-1152.
[155]李鹏,喻罡,冀晓燕,等.基于双密度双树小波变换的超声图像降噪[J].系统仿真学报,2007, 19(24): 5797-5801.
[156]B. Han. Dual multiwavelet frames with high balancing order and compact fast frame transform[J]. Appl. Comput. Harmon. Anal., to appear.
[157]I.W. Selesnick. A higher density discrete wavelet transform[J]. IEEE Trans. Signal Processing, 2006, 54(8): 3039-3048.
[158]O. Herrmann. On the approximation problem in nonrecursive digital filter design[J]. IEEE Trans. Circuit Theory, 1971, 18(3): 411-413.
[159]R.H. Chan, Z.W. Shen, T. Xia. A framelet algorithm for enhancing video stills[J]. Appl. Comput. Harmon. Anal., 2007, 23(2): 153-170.
[160]J.F. Cai, R.H. Chan, Z.W. Shen. A framelet-based image inpainting algorithm[J]. Appl. Comput. Harmon. Anal., 2008, 24(2): 131-149.
[161]C. Sagiv, N.A. Sochen, Y.Y. Zeevi. Two-dimensional affine frames for image analysis and synthesis[J]. Appl. Comput. Harmon. Anal., 2008, 25(1): 98-113.
[162]秦树人,汤宝平,钟佑明,等.智能控件化虚拟仪器系统——原理与实现[M].北京:科学出版社, 2004.
[163]秦树人.虚拟仪器[M].北京:中国计量出版社, 2003.
[164]尹爱军,王见,周传德.秦氏模型——基于智能虚拟控件的仪器[M].北京:科学出版社, 2007.
[165]秦树人,张思复,汤宝平.集成测试技术与虚拟仪器系统[J].中国机械工程, 1999, 10(1): 77-81.
[166]秦树人.虚拟仪器——测试仪器从硬件到软件[J].振动、测试与诊断. 2000, 20(1):1-6.
[167]Qin Shuren. Intelligent virtual controls——measuring instrument form whole to part[J]. Chinese Journal of Mechanical Engineering, 2002, 15(2): 131-135.
[168]Qin Shuren. Intelligent Virtual controls——new concept of virtual instrument[C]. Proceedings Of 2nd ISIST, 2002, 8: 75-79.
[169]秦树人,汤宝平.面向21世纪的绿色仪器[J].中国机械工程, 2000, 11(3): 275-278.
[170]汤宝平,谢亭亭,周传德,等.基于软件体系结构的秦氏模型智能虚拟控件集成框架的研究[J].机械工程学报, 39(4), 2003, 4: 83-86.
[171]汤宝平.秦氏模型智能虚拟控件的实现[J].中国机械工程, 2003, 14(14): 1217-1220.
[172]汤宝平,尹爱军,周传德,等.基于秦氏模型的虚拟仪器开发系统的研究[J].中国机械工程, 2004, 6(11): 1018-1021.
[173]尹爱军,秦树人,毛永芳.智能控件化虚拟仪器的模型化开发[J].重庆大学学报, 2006, 29(6): 7-9.
[174]尹爱军,毛永芳,秦树人.基于动态路由层次消息总线的虚拟仪器开发系统架构的研究[J].中国机械工程(增刊), 2006, 8: 310-313.
[175]周传德,汤宝平.基于秦氏模型的智能虚拟显示器的研究[J].仪器仪表学报, 2005, 20(2): 206-210.
[176]秦毅,秦树人,尹爱军.基于秦氏模型的可复用仪器模块的研究[J].中国机械工程, 2007, 18(6): 711-714.
[177]汤宝平.新一代虚拟仪器——智能控件化虚拟仪器系统的研究[D].重庆:重庆大学博士学位论文, 2003.
[178]尹爱军.秦氏模型虚拟仪器及VMIDS开发系统的研究[D].重庆:重庆大学博士学位论文, 2006.
[179]周传德.科学计算可视化理论及智能虚拟显示系统的研究[D].重庆:重庆大学博士学位论文, 2006.
[180]周传德,秦树人,尹爱军.科学可视化理论及智能虚拟显示系统[M].北京:科学出版社, 2007.
[181]周传德,尹爱军,汤宝平.秦氏模型智能控件化虚拟仪器系统及其本质特征[J].测控技术, 2005, 24(7): 53-56.
[182]丁康,李巍华,朱小勇.齿轮及齿轮箱故障诊断实用技术[M].北京:机械工业出版社, 2005.
[2]邹红星,周小波,李延达.时频分析:回溯与前瞻[J].电子学报, 2000, 28(9): 78-84.
[3]张贤达.现代信号处理[M]. 2版.北京:清华大学出版社, 2002.
[4]张贤达,保铮.非平稳信号分析与处理[M].北京:国防工业出版社, 1998.
[5]纪跃波.多分辨时频分析理论与多功能时频分析系统的研究[D].重庆:重庆大学博士学位论文, 2002.
[6] L. Cohen著.时频分析:理论与应用[M].白居宪译.西安:西安交通大学出版社, 1998.
[7] D. Gabor. Theory of communication[J]. J. IEE, 1946, 93: 429-457.
[8] E.P. Wigner. On the quantum correction for thermodynamic equilibrium[J]. Physical Review, 1932, 40: 749-759.
[9] J. Ville. Theorie et applications de la notion de dignal analytique[J]. Cables et Transmission, 1948, 2A: 61-74.
[10] L. Cohen. Generalized phase-space distribution functions[J]. J. Math. Phys., 1966, 7: 781-786.
[11] I.H. Choi, J.W. Williams. Improved time-frequency representation of multicomponent signals using exponential[J]. IEEE Trans. Acoust, Speech, Signal Processing, 1989, 37: 862-871.
[12] J. Jeong, J.W. Williams. Kernel design for reduced interference distributions[J]. IEEE Trans. Signal Processing, 1992, 40: 402-412.
[13] J.W. Williams, J. Jeong. New time-frequency distributions: theory and application[J]. In: Proc. IEEE ICASSP-89, 1989: 1243-1247.
[14] Y. Zhao, Y. Atlas, R. Marks. The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals[J]. IEEE Trans. Acoust., Speech, Signal Processing, 1990, 38: 1084-1091.
[15] F. Auger, P. Flandrin. Improving the readability of time-frequency and time-scale representations by the reassignment method[J]. IEEE Trans. Signal Processing, 1995, 43:1068-1089.
[16] L. Cohen T.E. Posch. Positive time-frequency distribution functions[J]. IEEE Trans. Acoust, Speech, Signal Processing, 1985, 33: 31-38.
[17] C. John, T. Daniel. Radon transformation of time-frequency distributions for analysis of multicomponent signals[J]. IEEE Trans. Signal Processing, 1994,42: 3166-3177.
[18] V. Namias. The fractional order Fourier Transform and its application to quantum mechanics[J].J. Inst. Math. Applicat., 1980, 25: 241-265.
[19] A. Grossmann, J. Morlet. Decomposition of hardy function into square integrable wavelet of constant shape[J]. SIAM J. of Math. Anal., 1984, 15(4): 723-736.
[20] C.K. Chui. An introduction to wavelets[M]. New York: Academic Press, 1992.
[21] I. Daubechies. Ten lectures on wavelets[M]. Philadelphia: SIAM, l992.
[22] N.E. Huang, Z. Shen, S.R. Long, et al. The empirical mode decomposition and the Hilbert Spectrum for nonlinear and non-stationary time series analysis[J]. Proc. R. Soc. Lond. A, 1998, 454:903-995.
[23]钟佑明.希尔伯特-黄变换局瞬信号分析理论的研究[D].重庆:重庆大学博士学位论文, 2002.
[24]钟佑明,秦树人,汤宝平.一种振动信号新变换法的研究[J].振动工程学报, 2002, 15(2): 233-238.
[25]钟佑明,秦树人.希尔伯特-黄变换的统一理论依据研究[J].振动与冲击, 2006, 25(3): 40-43.
[26]李天云,赵妍,李楠,等.基于HHT的电能质量检测新方法[J].中国电机工程学报, 2005, 25(17): 52-56.
[27]于德介,杨宇,程军圣.一种基于EMD和SVM的齿轮故障诊断方法[J].机械工程学报, 2005, 41(1): 140-144.
[28] D.J. Yu, J.S. Cheng, Y. Yang. Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings[J]. Mechanical Systems and Signal processing, 2005, 19(2): 259-270.
[29]徐冠雷,王孝通,徐孝刚,朱涛.基于限邻域经验模式分解的多波段图像融合[J].红外与毫米波学报, 2006, 25(3): 225-228.
[30]程军圣,于德介,杨宇.基于支持矢量回归机的Hilbert-Huang变换端点效应问题的处理方法[J].机械工程学报, 2006, 42(4): 23-31.
[31] Y. Qin, S.R. Qin, Y.F. Mao. Fast implemention of orthogonal empirical mode decomposition and its application into harmonic detection[J]. Chinese Journal of Mechanical Engineering, 2008, 21(2): 93-98.
[32]赵进平.异常事件对EMD方法的影响及其解决方法研究[J].青岛海洋大学学报, 2001, 31(6): 805-814.
[33] J.S. Cheng, D.J. Yu, Y. Yang. Research on the intrinsic mode function (IMF) criterion in EMD method[J]. Mechanical Systems and Signal processing, 2006, 20(4): 817-824.
[34] S.R. Qin, Y.M. Zhong. A new envelope algorithm of Hilbert-Huang transform[J]. Mechanical Systems and Signal processing, 2006, 20(8): 1941-1952.
[35] Q.H. Chen, N.E. Huang, S. Riemenschneider, Y.S. Xu. A B-spline approach for empirical mode decompositions[J]. Advances in Computational Mathematics, 2006, 24: 171-195.
[36] A. Potamianos, P. Maragos. A comparison of the energy operator and the Hilbert transform approach to signal and speech demodulation[J]. Signal Processing, 1994, 37(1): 95-120.
[37] P. Maragos, J.F. Kaiser, T.F. Quatieri. On amplitude and frequency demodulation using energy operator[J]. IEEE Transacitons on Signal Processing, 1993, 41(4): 1532-1550.
[38] A.C. Bovik, P. Maragos, T.F. Quatieri. AM–FM energy detection and separation in noise using multiband energy operators[J]. IEEE Transacitons on Signal Processing, 1993, 41(12): 3245-3265.
[39] B. Santhanam, P. Maragos. Multicomponent AM–FM demodulation via periodicity-based algebraic separation and energy-based demodulation[J]. IEEE Transacitons on Communications, 2000, 48(3): 473-490.
[40] F. Gianfelici, G. Biagetti, P. Crippa, et al. Multicomponent AM-FM representations: an asymptotically exact approach[J]. IEEE Transactions on Audio, Speech, and Language Processing, 2007, 15(3): 823-837.
[41] Y. Qin, S.R. Qin, Y.F. Mao. Research on iterated Hilbert transform and its application in mechanical fault diagnosis[J]. Mechanical Systems and Signal processing, 2008, 22(8): 1967-1980.
[42]李建平.小波分析与信号处理——理论、应用与软件实现[M].重庆:重庆出版社, 1997.
[43] Y. Meyer. Principe d’incertitude, bases hilbertiennes et algebras d’operateurs[C]. France:, Seminaire Bourbaki, 1986.
[44] G. Battle. A block spin construction of ondelettes, Part 1: Lemarie function[J]. Commun. Math. Phys., 1987, 110: 601-615.
[45] P.G. Lemarie. Ondelletes a localization exponentlelles[J]. J. de Math. Pures et Appl, 1988, 67: 227-236.
[46] I. Daubechies. Orthonormal bases of compactly supported wavelets[J]. Commun. on Pure and Appl. Math., 1988, 4l: 909-996.
[47] S. Mallat. Multiresolution approximations and wavelet orthonormaI bases of L2(R)[J]. Trans. Amer. Math. Soc., 1989, 315: 69-87.
[48] S. Mallat. A theory for multiresolution signal decomposition: the wavelet representation[J]. IEEE Trans. PAMI, 1989, 11(7): 674-693.
[49] A. Cohen, I. Daubechies, J.C. Feauveau. Biorthogonal orthonormal bases of compactly supported wavelets[J]. Commun. on Pure and Appl. Math., 1992, 45: 485-560.
[50] R.R. Coifman Y. Meyer, M.V. Wickerhauser. Wavelet and signal processing, in Ruskai ed.:Wavelet and Their application[M]. Boston, US: Jones and Bartlett Publishers, 1992.
[51] W. Sweldens. The Lifting Scheme: A custom-design construction of biorthogonal wavelet[J]. Applied and Computational Harmonic Analysis, 1996, 3(2): 186-200.
[52] W. Sweldens. The Lifting Scheme: A construction of second generation wavelets[J]. SIAM J. Math. Anal., 1997, 29(2): 511-546.
[53] A.R. Calderbank, I. Daubechies, W. Sweldens. Wavelet transforms that map integers to integers[J]. Applied and Computational Harmonic Analysis, 1998, 5(3):332-369.
[54] J. Lebrun, M. Vetterli. Balanced multiwavelets theory and design[J]. IEEE Transacitons on Signal Processing, 1998, 46(4):1119-1125.
[55] T.N. Goodman, S.L. Lee. Wavelets of multiplicity[J]. Trans on Amer. Math. Soc, 1994, 342: 307-324.
[56] E.J. Candes, D.L. Donoho. Ridgelets: the key to high-dimensional intermittency?[J]. Phil. Trans. Roy. Soc. Lond. A., 1999, 357: 2495-2509.
[57] D.L. Donoho. Ridge functions and orthonormal ridgelets[J]. Journal of Approximation Theory, 2001, 111(2): 143-179.
[58] E.J. Candes, D.L. Donoho. Curvelets—A surprisingly effective nonadaptive representation for objects with edges, in A. Cohen, C. Rabut, and L. L. Schumaker (Eds), Curve and Surface Fitting: Saint-Malo 1999[M]. Nashville: Vanderbilt Univ. Press, 1999.
[59] J.L. Starck, E.J. Candes, D.L. Donoho. The curvelet transform for image denoising[J]. IEEE Transacitons on Signal Processing, 2002, 11(6): 670-684.
[60] D.L. Donoho. Wedgelets: Nearly-minimax estimation of edges[J]. Ann. Statist., 1999, 27: 859-897.
[61]黄得双,毛二可,韩月秋.小波变换应用于雷达信号处理的潜力和展望[J].北京理工大学学报, 1995, 15(2): 186-191.
[62]范中,田立生.利用子波变换检测瞬时信号[J].电子学报, 1996, 24(1): 78-82
[63]徐金梧,徐科.小波变换在滚动轴承故障诊断中的应用[J].机械工程学报, 1997, 9(2): 51-55.
[64]张中民,卢文祥,杨叔子,等.基于小波系数包络谱的滚动轴承故障诊断[J].振动工程学报, 1998, 11(1): 65-69.
[65]章珂,刘贵忠,邹大文,等.二进小波变换方法的地震信号分时分频去噪处理[J].地球物理学报, 1999,16(2): 94-99.
[66]陈庆虎,李柱.表面粗糙度提取的小波频谱法[J].机械工程学报, 1999, 35(3): 541-543.
[67] E.L. Pennec, S. Mallat. Sparse geometric image representations with bandelets[J]. IEEE Transacitons on Image Processing, 2005, 14(4): 423-438.
[68] G.A. Westenskow, D. Grote, F. Bieniosek, J.W. Kwan. A multi-beamlet injector for heavy ion fusion: Experiments and modeling[C]. Proceedings of PAC07, 2007, 1: 3777-3781.
[69] S. Mallat. Geometrical grouplets[J]. Appl. Comput. Harmon. Anal., to appear.
[70]杨福生.小波变换的工程分析与应用[M].北京:科学出版社, 1999.
[71] R.J. Duffin, A.C. Schaeffer. A class of nonharmonic Fourier Series[J]. Trans. Amer. Math. Soc., 1952, 36: 1561-1574.
[72] R.M. Young. An introduction to nonharmonic Fourier Series[M]. New York: Academic Press, 1980.
[73] I. Daubechies. The wavelet transform, time-frequency localization and signal analysis[J]. IEEE Trans. Information Theory, 1990, 36(5): 961-1005.
[74] Stephane Mallat著.信号处理的小波导引[M].杨力华,戴道清,黄文良,等译. 2版.北京:机械工业出版社, 2002.
[75] R.R. Coifman, M.V. Wickerhauser. Entropy based algorithm for best basis selection[J]. IEEE Trans. Information Theory, 1992, 38(2): 713-718.
[76] S.S. Chen, D.L. Donoho, M.A. Saunders. Atomic decomposition by basis pursuit[J]. SIAM REVIEW, 2001, 43(1): 129-159.
[77] S. Mallat, Z.F. Zhang. Matching pursuits with time-frequency dictionaries[J]. IEEE Trans. Signal Processing, 1993, 41(12): 3397-3415.
[78] M. Vetterli, C. Herley. Wavelets and filter banks: theory and design[J]. IEEE Trans. Acoust, Speech, Signal Processing, 1992, 40(9): 2207-2232.
[79] A.R. Calderbank, I. Daubechies, W. Sweldens. Wavelet transforms that map integers to integers[J]. Applied and Computational Harmonic Analysis, 1998, 5(3): 332-369.
[80] M.J. Shensa. The discrete wavelet transform: wedding theàtrous and Mallat algorithm[J]. IEEE Trans. Signal Processing, 1992, 40(10): 2464-2482.
[81]秦树人,汤宝平,徐铭陶,等.工程信号小波变换分析仪系统的研究[J].中国机械工程, 1999, 10(4): 443-446.
[82]秦树人.一项具国际先进水平的小波理论应用成果[J].中国机械工程, 1999, 10(9): 1008-1010.
[83] S.R. Qin, Z.K. Chen, B.P. Tang. Research of wavelet transform instrument system for signal analysis[J]. Chinese Journal of Mechanical Engineering, 2000, 13(2): 114-121.
[84]秦毅,秦树人,毛永芳.小波变换中经验模态分解的基波检测及其在机械系统中的应用[J].机械工程学报, 2008, 44(3): 135-142.
[85]杨建国.小波分析及其工程应用[M].北京:机械工业出版社, 2005.
[86] J.G. Yang, S.T. Park. An anti-aliasing algorithm for discrete wavelet transform[J]. MechanicalSystems and Signal processing, 2003, 17(5): 945-954.
[87]杜天军,陈光禹,雷勇.基于混叠补偿小波变换的电力系统谐波检测方法[J].中国电机工程学报, 2005, 25(3): 54-59.
[88] D.L. Jones, R.G. Baraniuk. Efficient approximation of continuous wavelet transform[J]. Electronic Letters, 1991, 27(9): 748-750.
[89] M. Unser, A. Aldroubi, S.J. Schiff. Fast implementation of the continuous wavelet transform with integer scales[J]. IEEE Trans. Signal Processing, 1994, 42(12): 3519-3523.
[90] O. Rioul, P. Duhamel. Fast algorithms for discrete and continuous wavelet transforms[J]. IEEE Trans. Information Theory, 1992, 38(2): 569-586.
[91]张彤,杨福生,唐庆玉.基于Mellin变换的连续小波变换快速算法[J].信号处理, 1996, 12(4): 342-349.
[92]唐炜,史忠科.时频域滤波及在飞机颤振试飞试验中的应用[J].振动与冲击, 2006, 25(4): 46-50.
[93] X.G. Xia. System identification using chirp signals and time-variant filters in the joint time-frequency Domain[J]. IEEE Trans. Signal Processing, 1997, 45(8): 2072-2084.
[94]梁霖,徐光华,侯成刚.基于奇异值分解的连续小波消噪方法[J].西安交通大学学报, 2004, 38(9): 46-50.
[95]车红昆,项占琴,程耀东.超声检测信号时频邻域自适应消噪技术[J].机械工程学报, 2007, 43(6): 226-231.
[96] S. Mallat, W.L. Hwang. Singularity detection and processing with wavelets[J]. IEEE Trans. Information Theory, 1992, 38(2): 617-643.
[97] Y.S Xu, J.B Weaver, M.J. Healy, J. Lu. Wavelet transform domain filters: a spatially selective noise filtration technique[J]. IEEE Trans. Image Processing, 1994, 3(6): 747-758.
[98]李仲宁,罗志增.基于小波变换的空域相关法在肌电信号中的应用[J].电子学报, 2007, 35(7): 1414-1418.
[99] D.L. Donoho, I.M. Johnstone. Ideal spatial adaptation via wavelet shrinkage[J]. Biometrika, 1994, 18: 425-455.
[100]D.L. Donoho, I.M. Johnstone. Adapting to unknown smoothness via wavelet shrinkage[J]. Journal of the American Statistical Association, 1995, 90: 1200-1224.
[101]D.L.Donoho. De-noising by soft-thrsholding[J]. IEEE Trans. Information Theory, 1995, 41(3): 613-627.
[102]祝海龙,郭天佑,屈梁生.基于二进小波变换和软阈值改进的信号消噪[J].自动化学报, 2004, 30(2): 199-206.
[103]N.P. Delprat, B. Escudie, P. Guillemain, et al. Asymptotic wavelet and Gabor analysis:extraction of instantaneous frequencies[J]. IEEE Trans. Information Theory, 1992, 38(2): 644-664.
[104]P. Guillemain, R. K. Martinet. Characterization of acoustic signals through continuous linear time-frequency representations[J]. Proc. IEEE, 1996, 84(2): 561-585.
[105]权建峰,邵森木,郭东敏.小波变换在无线电引信参数提取中的应用研究[J].探测与控制学报, 2005, 25(24): 122-127.
[106]张征平,任震,黄雯莹,等.基于小波脊线的电动机转子故障检测新方法[J].中国电机工程学报, 2003, 23(1): 97-101.
[107]任宜春,易伟建.钢筋混凝土梁的非线性振动识别研究[J].工程力学, 2006, 23(8): 90-95.
[108]牛发亮,黄进,杨家强.基于电磁转矩小波变换的感应电机转子断条故障诊断[J].中国电机工程学报, 2005, 25(24): 122-127.
[109]魏云冰,王万良,赵燕伟,等.基于小波脊线的刮水器电动机机械特性测试[J].机械工程学报, 2006, 42(6): 141-144.
[110]朱洪俊,王忠,秦树人.小波变换对瞬态信号特征信息的精确提取[J].机械工程学报, 2005, 41(12): 196-199.
[111]胡正磊,孙进平,袁运能,等.基于小波边缘提取和脊线跟踪技术的SAR图像河流检测算法[J].电子与信息学报, 2007, 29(3): 524-527.
[112]钟秉林,黄仁.机械故障诊断学[M]. 2版.北京:机械工业出版社, 1998.
[113]R.A. Carmona, W.L. Hwang, B. Torresani. Characterization of signals by the ridges of their wavelet transforms[J]. IEEE Trans. Signal Processing, 1997, 45(10): 2 586-2 590.
[114]R.A. Carmona, W.L. Hwang, B. Torresani. Multiridge detection and time-frequency reconstruction[J]. IEEE Trans. Signal Processing, 1999, 47(2): 480-492.
[115]N. ?zkurt, F.A. Savac. Determination of wavelet ridges of nonstationary signals by singular value decomposition[J]. IEEE Trans. Circuits and systems—II: Express Briefs, 2005, 52(8): 480-485.
[116]F. Auger, P. Flandrin. Improving the readability of time-frequency and time-scale representations by the reassignment method[J]. 1995, 43(5): 1068-1089.
[117]马辉,赵鑫,赵群超,等.时频分析在旋转机械故障诊断中的应用[J].振动与冲击, 2007, 26(3): 61-63.
[118]彭志科,何永勇,褚福磊.小波尺度谱在振动信号分析中的应用研究[J].机械工程学报, 2002, 38(3): 122-126.
[119]赵松年,熊小芸.子波变换与子波分析[M].北京:电子工业出版社, 1996.
[120]张贤达.矩阵分析与应用[M].北京:清华大学出版社, 2004.
[121]J.L. Starck, M.Elad, D.L. Donoho. Redundant multiscale transforms and their application formorphological component analysis[J]. Adv. Imag. Electron Phys., 2004, 132.
[122]J.M. Lewis and C.S. Burrus. Approximate continuous wavelet transform with an application to noise reduction[C]. Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), 1998, 3: 1533-1536.
[123]I.W. Selesnick. The double density DWT, in: A. Petrosian and F. G. Meyer (Eds), Wavelets in signal and image analysis: From Theory to Practice[M]. Norwell: Kluwer, 2001.
[124]A. Petukhov. Explicit construction of framelets[J]. Appl. Comput. Harmon. Anal., 2001, 11(2): 313-327.
[125]A. Petukhov. Symmetric framelets[J]. Constr. Approx., 2003, 19(2): 309-328.
[126]I. Daubechies, B. Han, A. Ron, and Z. Shen. Framelets: MRA-based constructions of wavelet frames[J]. Appl. Comput. Harmon. Anal., 2003, 14(1): 1-46.
[127]I. Daubechies, B. Han. Pairs of dual wavelet frames from any two refinable functions[J]. Constr. Approx., 2004 20 (3): 325-352.
[128]C.K. Chui, W. He. Compactly supported tight frames associated with refinable functions[J]. Appl. Comput. Harmon. Anal., 2000, 8(3): 293-319.
[129]C.K. Chui, W. He, J. St?cklerckler. Compactly supported tight and sibling frames with maximum vanishing moments[J]. Appl. Comput. Harmon. Anal., 2002, 13(3): 224-262.
[130]C.K. Chui, W. He, J. St?ckler, Q.Y. Sun, Compactly supported tight affine frames with integer dilations and maximum vanishing moments[J]. Adv. Comput. Math., 2003, 18(2): 159-187.
[131]C.K. Chui, W. He, J. St?cklerckler. Nonstationary tight wavelet frames, I: Bounded intervals[J]. Appl. Comput. Harmon. Anal., 2004, 17(2): 141-197.
[132]C.K. Chui, W. He, J. St?cklerckler. Nonstationary tight wavelet frames, II: unbounded intervals[J]. Appl. Comput. Harmon. Anal., 2005, 18(1): 25-66.
[133]B. Han. On dual wavelet tight frames[J]. Appl. Comput. Harmon. Anal., 1997, 4(4): 380-413.
[134]B. Han, Q. Mo. Multiwavelet frames from refinable function vectors[J]. Adv. Comput. Math. 2003, 18(2): 211-245.
[135]B. Han, Q. Mo. Splitting a matrix of Laurent polynomials with symmetry and its application to symmetric framelet filter banks[J]. SIAM J. Matrix Anal. Appl., 2004, 26(1): 97-124.
[136]I.W. Selesnick. Smooth wavelet tight frames with zero moments[J]. Appl. Comput. Harmon. Anal., 2001, 10(2): 163-181.
[137]Z.f. Shang, X.W. Zhou. Dual generators for weighted irregular wavelet frames and reconstruction error[J]. Appl. Comput. Harmon. Anal., 2007, 22(3): 356-367.
[138]B. Dong, Z.W. Shen. Pseudo-splines, wavelets and framelets[J]. Appl. Comput. Harmon. Anal., 2007, 22(1): 78-104.
[139]M. Charina, J. St?ckler. Tight wavelet frames for irregular multiresolution analysis[J]. Appl. Comput. Harmon. Anal., 2008, 25(1): 98-113.
[140]A. Ron, Z.W. Shen. Affine systems in L2( d): The analysis of the analysis operator[J]. J. Funct. Anal., 1997, 148(2): 408–447.
[141]A. Ron, Z.W. Shen. Affine systems in L2( d): II. Dual systems[J]. J. Fourier Anal. Appl., 1997, 3: 617–637.
[142]S.S. Goh, Z.Y. Lim, Z.W. Shen. Symmetric and antisymmetric tight wavelet frames[J]. Appl. Comput. Harmon. Anal., 2007, 20(3): 411-421.
[143]Q. Jiang. Parameterizations of masks for tight affine frames with two symmetric/antisymmetric generators[J]. Adv. Comput. Math., 2003, 18: 247–268.
[144]I.W. Selesnick, A.F. Abdelnour. Symmetric wavelet tight frames with two generators[J]. Appl. Comput. Harmon. Anal., 2004, 17(2): 211-225
[145]B. Han, Q. Mo. Symmetric MRA tight wavelet frames with three generators and high vanishing moments[J]. Appl. Comput. Harmon. Anal., 2005, 18(1): 67-93.
[146]A.F. Abdelnour, I.W. Selesnick. Symmetric nearly shift-invariant tight frame wavelets[J]. Appl. Comput. Harmon. Anal., 2005, 18(1): 67-93.
[147]P.P. Vaidyanathan, T.Q. Nguyen, Z. Doganata, and T. Saram?ki. Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices[J]. IEEE Trans. Acoust, Speech, Signal Process, 1989, 37(7): 1042-1056.
[148]N.G. Kingsbury. The dual-tree complex wavelet transform: A new technique for shift invariance and directional filters[J]. Proc. English IEEE DSP Workshop, 1998: 9-12.
[149]N.G. Kingsbury. Image processing with complex wavelets[J]. Philos. Trans. Roy. Soc. London Ser. A, 1999, 357: 2543-2560.
[150]罗鹏,高协平.基于双树复数小波变换的图像去噪方法[J].光子学报, 2008, 37(3): 604-608.
[151]李江涛,倪国强,王强.基于双树复数小波变换和双变量萎缩阈值图像降噪[J].光学技术, 2007, 33(5): 723-727.
[152]I.W. Selesnick. The double-density dual-tree discrete wavelet transform[J]. IEEE Trans. Signal Processing, 2004, 52(5): 1304-1314.
[153]I.W. Selesnick. Hilbert transform pairs of wavelet bases[J]. IEEE Signal Processing Lett., 2001, 8: 170-173.
[154]I.W. Selesnick. The design of approximate Hilbert transform pairs of wavelet Bases[J]. IEEE Trans. Signal Processing, 2002, 50(5): 1144-1152.
[155]李鹏,喻罡,冀晓燕,等.基于双密度双树小波变换的超声图像降噪[J].系统仿真学报,2007, 19(24): 5797-5801.
[156]B. Han. Dual multiwavelet frames with high balancing order and compact fast frame transform[J]. Appl. Comput. Harmon. Anal., to appear.
[157]I.W. Selesnick. A higher density discrete wavelet transform[J]. IEEE Trans. Signal Processing, 2006, 54(8): 3039-3048.
[158]O. Herrmann. On the approximation problem in nonrecursive digital filter design[J]. IEEE Trans. Circuit Theory, 1971, 18(3): 411-413.
[159]R.H. Chan, Z.W. Shen, T. Xia. A framelet algorithm for enhancing video stills[J]. Appl. Comput. Harmon. Anal., 2007, 23(2): 153-170.
[160]J.F. Cai, R.H. Chan, Z.W. Shen. A framelet-based image inpainting algorithm[J]. Appl. Comput. Harmon. Anal., 2008, 24(2): 131-149.
[161]C. Sagiv, N.A. Sochen, Y.Y. Zeevi. Two-dimensional affine frames for image analysis and synthesis[J]. Appl. Comput. Harmon. Anal., 2008, 25(1): 98-113.
[162]秦树人,汤宝平,钟佑明,等.智能控件化虚拟仪器系统——原理与实现[M].北京:科学出版社, 2004.
[163]秦树人.虚拟仪器[M].北京:中国计量出版社, 2003.
[164]尹爱军,王见,周传德.秦氏模型——基于智能虚拟控件的仪器[M].北京:科学出版社, 2007.
[165]秦树人,张思复,汤宝平.集成测试技术与虚拟仪器系统[J].中国机械工程, 1999, 10(1): 77-81.
[166]秦树人.虚拟仪器——测试仪器从硬件到软件[J].振动、测试与诊断. 2000, 20(1):1-6.
[167]Qin Shuren. Intelligent virtual controls——measuring instrument form whole to part[J]. Chinese Journal of Mechanical Engineering, 2002, 15(2): 131-135.
[168]Qin Shuren. Intelligent Virtual controls——new concept of virtual instrument[C]. Proceedings Of 2nd ISIST, 2002, 8: 75-79.
[169]秦树人,汤宝平.面向21世纪的绿色仪器[J].中国机械工程, 2000, 11(3): 275-278.
[170]汤宝平,谢亭亭,周传德,等.基于软件体系结构的秦氏模型智能虚拟控件集成框架的研究[J].机械工程学报, 39(4), 2003, 4: 83-86.
[171]汤宝平.秦氏模型智能虚拟控件的实现[J].中国机械工程, 2003, 14(14): 1217-1220.
[172]汤宝平,尹爱军,周传德,等.基于秦氏模型的虚拟仪器开发系统的研究[J].中国机械工程, 2004, 6(11): 1018-1021.
[173]尹爱军,秦树人,毛永芳.智能控件化虚拟仪器的模型化开发[J].重庆大学学报, 2006, 29(6): 7-9.
[174]尹爱军,毛永芳,秦树人.基于动态路由层次消息总线的虚拟仪器开发系统架构的研究[J].中国机械工程(增刊), 2006, 8: 310-313.
[175]周传德,汤宝平.基于秦氏模型的智能虚拟显示器的研究[J].仪器仪表学报, 2005, 20(2): 206-210.
[176]秦毅,秦树人,尹爱军.基于秦氏模型的可复用仪器模块的研究[J].中国机械工程, 2007, 18(6): 711-714.
[177]汤宝平.新一代虚拟仪器——智能控件化虚拟仪器系统的研究[D].重庆:重庆大学博士学位论文, 2003.
[178]尹爱军.秦氏模型虚拟仪器及VMIDS开发系统的研究[D].重庆:重庆大学博士学位论文, 2006.
[179]周传德.科学计算可视化理论及智能虚拟显示系统的研究[D].重庆:重庆大学博士学位论文, 2006.
[180]周传德,秦树人,尹爱军.科学可视化理论及智能虚拟显示系统[M].北京:科学出版社, 2007.
[181]周传德,尹爱军,汤宝平.秦氏模型智能控件化虚拟仪器系统及其本质特征[J].测控技术, 2005, 24(7): 53-56.
[182]丁康,李巍华,朱小勇.齿轮及齿轮箱故障诊断实用技术[M].北京:机械工业出版社, 2005.