Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential eq...Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.展开更多
Due to the disturbances arising from the coherence of reflected waves and from echo noise,problems such as limitations,instability and poor accuracy exist with the current quantitative analysis methods.According to th...Due to the disturbances arising from the coherence of reflected waves and from echo noise,problems such as limitations,instability and poor accuracy exist with the current quantitative analysis methods.According to the intrinsic features of GPR signals and wavelet time–frequency analysis,an optimal wavelet basis named GPR3.3 wavelet is constructed via an improved biorthogonal wavelet construction method to quantitatively analyse the GPR signal.A new quantitative analysis method based on the biorthogonal wavelet(the QAGBW method)is proposed and applied in the analysis of analogue and measured signals.The results show that compared with the Bayesian frequency-domain blind deconvolution and with existing wavelet bases,the QAGBW method based on optimal wavelet can limit the disturbance from factors such as the coherence of reflected waves and echo noise,improve the quantitative analytical precision of the GPR signal,and match the minimum thickness for quantitative analysis with the vertical resolution of GPR detection.展开更多
This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employi...This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.展开更多
The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formul...The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform. For an arbitrary given square-integrable function f(t),g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform. The result shows that time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.展开更多
基金This project was supported by the National Natural Science Foundation of China (No. 19871080).
文摘Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.
基金Projects(51678071,51278071)supported by the National Natural Science Foundation of ChinaProjects(14KC06,CX2015BS02)supported by Changsha University of Science&Technology,China
文摘Due to the disturbances arising from the coherence of reflected waves and from echo noise,problems such as limitations,instability and poor accuracy exist with the current quantitative analysis methods.According to the intrinsic features of GPR signals and wavelet time–frequency analysis,an optimal wavelet basis named GPR3.3 wavelet is constructed via an improved biorthogonal wavelet construction method to quantitatively analyse the GPR signal.A new quantitative analysis method based on the biorthogonal wavelet(the QAGBW method)is proposed and applied in the analysis of analogue and measured signals.The results show that compared with the Bayesian frequency-domain blind deconvolution and with existing wavelet bases,the QAGBW method based on optimal wavelet can limit the disturbance from factors such as the coherence of reflected waves and echo noise,improve the quantitative analytical precision of the GPR signal,and match the minimum thickness for quantitative analysis with the vertical resolution of GPR detection.
基金supported by the National Natural Science Foundation of China (6057408860274014)
文摘This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.
文摘The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform. For an arbitrary given square-integrable function f(t),g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform. The result shows that time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.
