Nuclear pulse signal needs to be transformed to a suitable pulse shape to remove noise and improve energy resolution of a nuclear spectrometry system. In this paper, a new digital Gaussian shaping method is proposed.A...Nuclear pulse signal needs to be transformed to a suitable pulse shape to remove noise and improve energy resolution of a nuclear spectrometry system. In this paper, a new digital Gaussian shaping method is proposed.According to Sallen-Key analog Gaussian shaping filter circuits, the system function of Sallen-Key analog Gaussian shaping filter is deduced on the basis of Kirchhoff laws. The system function of the digital Gaussian shaping filter based on bilinear transformation is deduced too. The expression of unit impulse response of the digital Gaussian shaping filter is obtained by inverse z-transform. The response of digital Gaussian shaping filter is deduced from convolution sum of the unit impulse response and the digital nuclear pulse signal. The simulation and experimental results show that the digital nuclear pulse has been transformed to a pulse with a pseudo-Gaussian, which confirms the feasibility of the new digital Gaussian pulse shaping algorithm based on bilinear transformation.展开更多
A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper's formants in different frequency ba...A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper's formants in different frequency bands, the spectrum of the whispered speech will be processed in the separate partitions of this paper. On the basis of this spectrum, we will establish a conversion function able to usefully convert whispered speech to normal speech. Because of the whisper's non-linear offset in relation to normal speech, this paper introduces an expansion factor in the bilinear transform function making it correspond more closely to the actual conversion demands of whispered speech to normal speech. The introduction of this factor takes the non-linear move of the spectrum and the compression of the formant bandwidth into consideration, thus effectively reducing the spectrum distortion distance in the conversion. The experiment results show that the conversion presented in this paper effectively improves both the sound quality and the intelligibility of whispered speech.展开更多
In this paper, nonlocal symmetries defined by bilinear Baacklund transformation for bilinear potential Kd V(p Kd V)equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian for...In this paper, nonlocal symmetries defined by bilinear Baacklund transformation for bilinear potential Kd V(p Kd V)equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian form of Kd V(SKd V)equation, the nonlocal symmetry is localized and the Levi transformation is presented. Besides, based on three different types of nonlocal symmetries for potential Kd V equation, three sets of negative p Kd V hierarchies along with their bilinear forms are constructed. An impressive result is that the coefficients of the third type of(bilinear) negative p Kd V hierarchy(N 〉 0) are variable, which are obtained via introducing an arbitrary parameter by considering the translation invariance of the p Kd V equation.展开更多
Investigated in this paper is the generalized nonlinear Schrdinger equation with radial symmetry.Withthe help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear metho...Investigated in this paper is the generalized nonlinear Schrdinger equation with radial symmetry.Withthe help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method.Bcklund transformation in the bilinear form is presented, through which a new solution is constructed.Graphically, wehave found that the solitons are symmetric about x=0, while the soliton pulse width and amplitude will change alongwith the distance and time during the propagation.展开更多
In this paper, two types of the (2+1)-dimensional breaking soliton equations are investigated, whichdescribe the interactions of the Riemann waves with the long waves.With symbolic computation, the Hirota bilinearform...In this paper, two types of the (2+1)-dimensional breaking soliton equations are investigated, whichdescribe the interactions of the Riemann waves with the long waves.With symbolic computation, the Hirota bilinearforms and Bcklund transformations are derived for those two systems.Furthermore, multisoliton solutions in termsof the Wronskian determinant are constructed, which are verified through the direct substitution of the solutions intothe bilinear equations.Via the Wronskian technique, it is proved that the Bcklund transformations obtained are theones between the (N-1)-and N-soliton solutions.Propagations and interactions of the kink-/bell-shaped solitonsare presented.It is shown that the Riemann waves possess the solitonic properties, and maintain the amplitudes andvelocities in the collisions only with some phase shifts.展开更多
Generalized Casoratian condition and Casoratian solutions of the Toda lattice are given in terms of its bilinear Backlund transformation. By choosing suitable Casoratian entries and parameter in the bilinear Backlund ...Generalized Casoratian condition and Casoratian solutions of the Toda lattice are given in terms of its bilinear Backlund transformation. By choosing suitable Casoratian entries and parameter in the bilinear Backlund transformation, we can give transformations among many kinds of solutions.展开更多
In the paper we discuss the Wronskian solutions of modified Korteweg-de Vries equation (mKdV) via theBcklund transformation (BT) and a generalized Wronskian condition is given,which allows us to substitute an arbitrar...In the paper we discuss the Wronskian solutions of modified Korteweg-de Vries equation (mKdV) via theBcklund transformation (BT) and a generalized Wronskian condition is given,which allows us to substitute an arbitrarycoefficient matrix in the G_N(t) for the original diagonal one.展开更多
Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the s...Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.展开更多
基金Supported by National High Technology Research and Development Program of China(No.2012AA061803)Higher Education and Teaching Reform Project of Chendu University of Technology(No.13JGY25)
文摘Nuclear pulse signal needs to be transformed to a suitable pulse shape to remove noise and improve energy resolution of a nuclear spectrometry system. In this paper, a new digital Gaussian shaping method is proposed.According to Sallen-Key analog Gaussian shaping filter circuits, the system function of Sallen-Key analog Gaussian shaping filter is deduced on the basis of Kirchhoff laws. The system function of the digital Gaussian shaping filter based on bilinear transformation is deduced too. The expression of unit impulse response of the digital Gaussian shaping filter is obtained by inverse z-transform. The response of digital Gaussian shaping filter is deduced from convolution sum of the unit impulse response and the digital nuclear pulse signal. The simulation and experimental results show that the digital nuclear pulse has been transformed to a pulse with a pseudo-Gaussian, which confirms the feasibility of the new digital Gaussian pulse shaping algorithm based on bilinear transformation.
基金supported by the National Natural Science Foundation of China(61271359,61071215)Suzhou Science and Technology Development Plan(SYG201001)Key Joint Laboratory of Soochow University and JieMei Biomedical Engineering Instrument
文摘A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper's formants in different frequency bands, the spectrum of the whispered speech will be processed in the separate partitions of this paper. On the basis of this spectrum, we will establish a conversion function able to usefully convert whispered speech to normal speech. Because of the whisper's non-linear offset in relation to normal speech, this paper introduces an expansion factor in the bilinear transform function making it correspond more closely to the actual conversion demands of whispered speech to normal speech. The introduction of this factor takes the non-linear move of the spectrum and the compression of the formant bandwidth into consideration, thus effectively reducing the spectrum distortion distance in the conversion. The experiment results show that the conversion presented in this paper effectively improves both the sound quality and the intelligibility of whispered speech.
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ13A010014)the National Natural Science Foundation of China(Grant Nos.11326164,11401528,and 11275072)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120076110024)
文摘In this paper, nonlocal symmetries defined by bilinear Baacklund transformation for bilinear potential Kd V(p Kd V)equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian form of Kd V(SKd V)equation, the nonlocal symmetry is localized and the Levi transformation is presented. Besides, based on three different types of nonlocal symmetries for potential Kd V equation, three sets of negative p Kd V hierarchies along with their bilinear forms are constructed. An impressive result is that the coefficients of the third type of(bilinear) negative p Kd V hierarchy(N 〉 0) are variable, which are obtained via introducing an arbitrary parameter by considering the translation invariance of the p Kd V equation.
基金Supported by the National Natural Science Foundation of China under Grant No.60772023the Open Fund (No.BUAASKLSDE-09KF-04)+2 种基金Supported Project (No.SKLSDE-2010ZX-07) of the State Key Laboratory of Software Development Environment,Beijing University of Aeronautics and Astronauticsthe National Basic Research Program of China (973 Program) under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.200800130006,Chinese Ministry of Education
文摘Investigated in this paper is the generalized nonlinear Schrdinger equation with radial symmetry.Withthe help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method.Bcklund transformation in the bilinear form is presented, through which a new solution is constructed.Graphically, wehave found that the solitons are symmetric about x=0, while the soliton pulse width and amplitude will change alongwith the distance and time during the propagation.
基金Supported by the National Natural Science Foundation of China under Grant No.60772023 the Open Fund under Grant No.BUAASKLSDE-09KF-04l+2 种基金Supported Project under Grant No.SKLSDE-2010ZX-07 of the State Key Laboratory of Software Development Environment,Beijing University of Aeronautics and Astronauticsthe National Basic Research Program of China (973 Program) under Grant No.2005CB321901 the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.200800130006,Chinese Ministry of Education
文摘In this paper, two types of the (2+1)-dimensional breaking soliton equations are investigated, whichdescribe the interactions of the Riemann waves with the long waves.With symbolic computation, the Hirota bilinearforms and Bcklund transformations are derived for those two systems.Furthermore, multisoliton solutions in termsof the Wronskian determinant are constructed, which are verified through the direct substitution of the solutions intothe bilinear equations.Via the Wronskian technique, it is proved that the Bcklund transformations obtained are theones between the (N-1)-and N-soliton solutions.Propagations and interactions of the kink-/bell-shaped solitonsare presented.It is shown that the Riemann waves possess the solitonic properties, and maintain the amplitudes andvelocities in the collisions only with some phase shifts.
基金Supported by National Natural Science Foundation of China under Grant No. 10671121Shanghai Leading Academic Discipline Project under Grant No. J50101
文摘Generalized Casoratian condition and Casoratian solutions of the Toda lattice are given in terms of its bilinear Backlund transformation. By choosing suitable Casoratian entries and parameter in the bilinear Backlund transformation, we can give transformations among many kinds of solutions.
基金National Natural Science Foundation of China under Grant Nos.10371070 and 10671121the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers
文摘In the paper we discuss the Wronskian solutions of modified Korteweg-de Vries equation (mKdV) via theBcklund transformation (BT) and a generalized Wronskian condition is given,which allows us to substitute an arbitrarycoefficient matrix in the G_N(t) for the original diagonal one.
基金National Natural Science Foundation of China Under Grant No.50278090
文摘Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.