In this paper, it is described that the time-frequency resolution of geophysical signals is affected by the time window function attenuation coefficient and sampling interval and how such effects are eliminated effect...In this paper, it is described that the time-frequency resolution of geophysical signals is affected by the time window function attenuation coefficient and sampling interval and how such effects are eliminated effectively. Improving the signal resolution is the key to signal time-frequency analysis processing and has wide use in geophysical data processing and extraction of attribute parameters. In this paper, authors research the effects of the attenuation coefficient choice of the Gabor transform window function and sampling interval on signal resolution. Unsuitable parameters not only decrease the signal resolution on the frequency spectrum but also miss the signals. It is essential to first give the optimum window and range of parameters through time-frequency analysis simulation using the Gabor transform. In the paper, the suggestions about the range and choice of the optimum sampling interval and processing methods of general seismic signals are given.展开更多
Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributio...Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.展开更多
The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improv...The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.展开更多
Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-f...Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-forms,which leverage sparse coding(SC),have gained significant attention in the geosciences due to their ability to achieve high TF resolution.However,the iterative approaches typically employed in sparse TF transforms are computationally intensive,making them impractical for real seismic data analysis.To address this issue,we propose an interpretable convolutional sparse coding(CSC)network to achieve high TF resolution.The proposed model is generated based on the traditional short-time Fourier transform(STFT)transform and a modified UNet,named ULISTANet.In this design,we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm(LISTA)blocks,a specialized form of CSC.The LISTA block,which evolves from the traditional iterative shrinkage thresholding algorithm(ISTA),is optimized for extracting sparse features more effectively.Furthermore,we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet.Finally,the proposed method’s performance is subsequently validated using both synthetic and field data,demonstrating its potential for enhanced seismic data analysis.展开更多
This paper introduces the localized Radon transform (LRT) into time-frequency distributions and presents the localized Radon-Wigner transform (LRWT). The definition of LRWT and a fast algorithm is derived, the propert...This paper introduces the localized Radon transform (LRT) into time-frequency distributions and presents the localized Radon-Wigner transform (LRWT). The definition of LRWT and a fast algorithm is derived, the properties of LRWT and its relationship with Radon-Wigner transform, Wigner distribution (WD), ambiguity function (AF), and generalized-marginal time-frequency distributions are analyzed.展开更多
Some factors influencing the intelligibility of the enhanced whisper in the joint time-frequency domain are evaluated. Specifically, both the spectrum density and different regions of the enhanced spectrum are analyze...Some factors influencing the intelligibility of the enhanced whisper in the joint time-frequency domain are evaluated. Specifically, both the spectrum density and different regions of the enhanced spectrum are analyzed. Experimental results show that for a spectrum of some density, the joint time-frequency gain-modification based speech enhancement algorithm achieves significant improvement in intelligibility. Additionally, the spectrum region where the estimated spectrum is smaller than the clean spectrum, is the most important region contributing to intelligibility improvement for the enhanced whisper. The spectrum region where the estimated spectrum is larger than twice the size of the clean spectrum is detrimental to speech intelligibility perception within the whisper context.展开更多
The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and th...The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time-frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform （ST） and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time frequency spectrum. Second, using the secondary time frequency spectrum, we design a two- dimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time- fi＇equency-space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio （SNR）.展开更多
In this study,we report an analysis of cylinder head vibration signals at a steady engine speed using short-time Fourier transform(STFT).Three popular time-frequency analysis techniques,i.e.,STFT,analytic wavelet tran...In this study,we report an analysis of cylinder head vibration signals at a steady engine speed using short-time Fourier transform(STFT).Three popular time-frequency analysis techniques,i.e.,STFT,analytic wavelet transform(AWT) and S transform(ST),have been examined.AWT and ST are often applied in engine signal analyses.In particular,an AWT expression in terms of the quality factor Q and an analytical relationship between ST and AWT have been derived.The time-frequency resolution of a Gaussian function windowed STFT was studied via numerical simulation.Based on the simulation,the empirical limits for the lowest distinguishable frequency as well as the time and frequency resolutions were determined.These can provide insights for window width selection,spectrogram interpretation and artifact identification.Gaussian function windowed STFTs were applied to some cylinder head vibration signals.The spectrograms of the same signals from ST and AWT were also determined for comparison.The results indicate that the uniform resolution feature of STFT is not necessarily a disadvantage for time-frequency analysis of vibration signals when the engine is in stationary state because it can more accurately localize the frequency components excited by transient excitations without much loss of time resolution.展开更多
Radiometric normalization,as an essential step for multi-source and multi-temporal data processing,has received critical attention.Relative Radiometric Normalization(RRN)method has been primarily used for eliminating ...Radiometric normalization,as an essential step for multi-source and multi-temporal data processing,has received critical attention.Relative Radiometric Normalization(RRN)method has been primarily used for eliminating the radiometric inconsistency.The radiometric trans-forming relation between the subject image and the reference image is an essential aspect of RRN.Aimed at accurate radiometric transforming relation modeling,the learning-based nonlinear regression method,Support Vector machine Regression(SVR)is used for fitting the complicated radiometric transforming relation for the coarse-resolution data-referenced RRN.To evaluate the effectiveness of the proposed method,a series of experiments are performed,including two synthetic data experiments and one real data experiment.And the proposed method is compared with other methods that use linear regression,Artificial Neural Network(ANN)or Random Forest(RF)for radiometric transforming relation modeling.The results show that the proposed method performs well on fitting the radiometric transforming relation and could enhance the RRN performance.展开更多
The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in te...The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.展开更多
The Q-factor is an important physical parameter for characterizing the absorption and attenuation of seismic waves propagating in underground media,which is of great signifi cance for improving the resolution of seism...The Q-factor is an important physical parameter for characterizing the absorption and attenuation of seismic waves propagating in underground media,which is of great signifi cance for improving the resolution of seismic data,oil and gas detection,and reservoir description.In this paper,the local centroid frequency is defi ned using shaping regularization and used to estimate the Q values of the formation.We propose a continuous time-varying Q-estimation method in the time-frequency domain according to the local centroid frequency,namely,the local centroid frequency shift(LCFS)method.This method can reasonably reduce the calculation error caused by the low accuracy of the time picking of the target formation in the traditional methods.The theoretical and real seismic data processing results show that the time-varying Q values can be accurately estimated using the LCFS method.Compared with the traditional Q-estimation methods,this method does not need to extract the top and bottom interfaces of the target formation;it can also obtain relatively reasonable Q values when there is no eff ective frequency spectrum information.Simultaneously,a reasonable inverse Q fi ltering result can be obtained using the continuous time-varying Q values.展开更多
We present new connections among linear anomalous diffusion (AD), normal diffusion (ND) and the Central Limit Theorem (CLT). This is done by defining a point transformation to a new position variable, which we postula...We present new connections among linear anomalous diffusion (AD), normal diffusion (ND) and the Central Limit Theorem (CLT). This is done by defining a point transformation to a new position variable, which we postulate to be Cartesian, motivated by considerations from super-symmetric quantum mechanics. Canonically quantizing in the new position and momentum variables according to Dirac gives rise to generalized negative semi-definite and self-adjoint Laplacian operators. These lead to new generalized Fourier transformations and associated probability distributions, which are form invariant under the corresponding transform. The new Laplacians also lead us to generalized diffusion equations, which imply a connection to the CLT. We show that the derived diffusion equations capture all of the Fractal and Non-Fractal Anomalous Diffusion equations of O’Shaughnessy and Procaccia. However, we also obtain new equations that cannot (so far as we can tell) be expressed as examples of the O’Shaughnessy and Procaccia equations. The results show, in part, that experimentally measuring the diffusion scaling law can determine the point transformation (for monomial point transformations). We also show that AD in the original, physical position is actually ND when viewed in terms of displacements in an appropriately transformed position variable. We illustrate the ideas both analytically and with a detailed computational example for a non-trivial choice of point transformation. Finally, we summarize our results.展开更多
Early detection of sudden cardiac death may be used for surviving the life of cardiac patients. In this paper we have investigated an algorithm to detect and predict sudden cardiac death, by processing of heart rate v...Early detection of sudden cardiac death may be used for surviving the life of cardiac patients. In this paper we have investigated an algorithm to detect and predict sudden cardiac death, by processing of heart rate variability signal through the classical and time-frequency methods. At first, one minute of ECG signals, just before the cardiac death event are extracted and used to compute heart rate variability (HRV) signal. Five features in time domain and four features in frequency domain are extracted from the HRV signal and used as classical linear features. Then the Wigner Ville transform is applied to the HRV signal, and 11 extra features in the time-frequency (TF) domain are obtained. In order to improve the performance of classification, the principal component analysis (PCA) is applied to the obtained features vector. Finally a neural network classifier is applied to the reduced features. The obtained results show that the TF method can classify normal and SCD subjects, more efficiently than the classical methods. A MIT-BIH ECG database was used to evaluate the proposed method. The proposed method was implemented using MLP classifier and had 74.36% and 99.16% correct detection rate (accuracy) for classical features and TF method, respectively. Also, the accuracy of the KNN classifier were 73.87% and 96.04%.展开更多
We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by u...We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.展开更多
This paper proposes a new method for estimating the parameter of maneuvering targets based on sparse time-frequency transform in over-the-horizon radar（OTHR）. In this method, the sparse time-frequency distribution o...This paper proposes a new method for estimating the parameter of maneuvering targets based on sparse time-frequency transform in over-the-horizon radar（OTHR）. In this method, the sparse time-frequency distribution of the radar echo is obtained by solving a sparse optimization problem based on the short-time Fourier transform. Then Hough transform is employed to estimate the parameter of the targets. The proposed algorithm has the following advantages： Compared with the Wigner-Hough transform method, the computational complexity of the sparse optimization is low due to the application of fast Fourier transform（FFT）. And the computational cost of Hough transform is also greatly reduced because of the sparsity of the time-frequency distribution. Compared with the high order ambiguity function（HAF） method, the proposed method improves in terms of precision and robustness to noise. Simulation results show that compared with the HAF method, the required SNR and relative mean square error are 8 dB lower and 50 dB lower respectively in the proposed method. While processing the field experiment data, the execution time of Hough transform in the proposed method is only 4% of the Wigner-Hough transform method.展开更多
This paper investigates topological transformation during normal grain growth by carrying out a computer vertex simulation. Results show that topological correlation agrees with the models proposed by Blanc et al. and...This paper investigates topological transformation during normal grain growth by carrying out a computer vertex simulation. Results show that topological correlation agrees with the models proposed by Blanc et al. and Weaire. Topological transformation occurs more often on grains with some topological classes instead of equal probability on each boundary. This can be qualitatively explained by topological correlation.展开更多
A new time-frequency representation called Dopplerlet transform, which uses the dilated, translated and modulated windowed Doppler signals as its basis functions, is proposed, and the Fourier transform, short-time Fou...A new time-frequency representation called Dopplerlet transform, which uses the dilated, translated and modulated windowed Doppler signals as its basis functions, is proposed, and the Fourier transform, short-time Fourier transform (including Gabor transform), wavelet transform, and chirplet transform are formulated in one framework of Dopplerlet transform accordingly.It is proved that the matching pursuits based on Dopplerlet basis functions are convergent, and that the energy of residual signals yielded in the decomposition process decays exponentially. Simulation results show that the matching pursuits with Dopplerlet basis functions can characterize compactly a nonstationary signal.展开更多
The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is define...The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.展开更多
This paper presents an evaluation of time-frequency methods for the analysis of seismic signals.Background of the present work is to describe,how the frequency content of the signal is changing in time.The theoretical...This paper presents an evaluation of time-frequency methods for the analysis of seismic signals.Background of the present work is to describe,how the frequency content of the signal is changing in time.The theoretical basis of short time Fourier transform,Gabor transform,wavelet transform,S-transform,Wigner distribution,Wigner-Ville distribution,Pseudo Wigner-Ville distribution,Smoothed Pseudo Wigner-Ville distribution,Choi-William distribution,Born-Jordan Distribution and cone shape distribution are presented.The strengths and weaknesses of each technique are verified by applying them to a particular synthetic seismic signal and recorded real time earthquake data.展开更多
基金This work was funded by National Natural Science Foundation of China-（No. 40474044）.
文摘In this paper, it is described that the time-frequency resolution of geophysical signals is affected by the time window function attenuation coefficient and sampling interval and how such effects are eliminated effectively. Improving the signal resolution is the key to signal time-frequency analysis processing and has wide use in geophysical data processing and extraction of attribute parameters. In this paper, authors research the effects of the attenuation coefficient choice of the Gabor transform window function and sampling interval on signal resolution. Unsuitable parameters not only decrease the signal resolution on the frequency spectrum but also miss the signals. It is essential to first give the optimum window and range of parameters through time-frequency analysis simulation using the Gabor transform. In the paper, the suggestions about the range and choice of the optimum sampling interval and processing methods of general seismic signals are given.
基金This work was supported by the National Natural Science Foundation of China(91538201)the Taishan Scholar Project of Shandong Province(ts201511020)the project supported by Chinese National Key Laboratory of Science and Technology on Information System Security(6142111190404).
文摘Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.
基金Supported by the National Science Foundation of China(42055402)。
文摘The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.
基金supported by the National Natural Science Foundation of China under Grant 42474139the Key Research and Development Program of Shaanxi under Grant 2024GX-YBXM-067.
文摘Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-forms,which leverage sparse coding(SC),have gained significant attention in the geosciences due to their ability to achieve high TF resolution.However,the iterative approaches typically employed in sparse TF transforms are computationally intensive,making them impractical for real seismic data analysis.To address this issue,we propose an interpretable convolutional sparse coding(CSC)network to achieve high TF resolution.The proposed model is generated based on the traditional short-time Fourier transform(STFT)transform and a modified UNet,named ULISTANet.In this design,we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm(LISTA)blocks,a specialized form of CSC.The LISTA block,which evolves from the traditional iterative shrinkage thresholding algorithm(ISTA),is optimized for extracting sparse features more effectively.Furthermore,we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet.Finally,the proposed method’s performance is subsequently validated using both synthetic and field data,demonstrating its potential for enhanced seismic data analysis.
文摘This paper introduces the localized Radon transform (LRT) into time-frequency distributions and presents the localized Radon-Wigner transform (LRWT). The definition of LRWT and a fast algorithm is derived, the properties of LRWT and its relationship with Radon-Wigner transform, Wigner distribution (WD), ambiguity function (AF), and generalized-marginal time-frequency distributions are analyzed.
基金The National Natural Science Foundation of China(No.61301295,61273266,61301219,61201326,61003131)the Natural Science Foundation of Anhui Province(No.1308085QF100,1408085MF113)+2 种基金the Natural Science Foundation of Jiangsu Province(No.BK20130241)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.12KJB510021)the Doctoral Fund of Anhui University
文摘Some factors influencing the intelligibility of the enhanced whisper in the joint time-frequency domain are evaluated. Specifically, both the spectrum density and different regions of the enhanced spectrum are analyzed. Experimental results show that for a spectrum of some density, the joint time-frequency gain-modification based speech enhancement algorithm achieves significant improvement in intelligibility. Additionally, the spectrum region where the estimated spectrum is smaller than the clean spectrum, is the most important region contributing to intelligibility improvement for the enhanced whisper. The spectrum region where the estimated spectrum is larger than twice the size of the clean spectrum is detrimental to speech intelligibility perception within the whisper context.
基金financially supported by the National 973 Project(No.2014CB239006)the National Natural Science Foundation of China(No.41104069 and 41274124)the Fundamental Research Funds for Central Universities(No.R1401005A)
文摘The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time-frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform （ST） and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time frequency spectrum. Second, using the secondary time frequency spectrum, we design a two- dimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time- fi＇equency-space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio （SNR）.
基金Project (No. 2011BAE22B05) supported by the National Key Technologies Supporting Program of China during the 12th Five-Year Plan Period
文摘In this study,we report an analysis of cylinder head vibration signals at a steady engine speed using short-time Fourier transform(STFT).Three popular time-frequency analysis techniques,i.e.,STFT,analytic wavelet transform(AWT) and S transform(ST),have been examined.AWT and ST are often applied in engine signal analyses.In particular,an AWT expression in terms of the quality factor Q and an analytical relationship between ST and AWT have been derived.The time-frequency resolution of a Gaussian function windowed STFT was studied via numerical simulation.Based on the simulation,the empirical limits for the lowest distinguishable frequency as well as the time and frequency resolutions were determined.These can provide insights for window width selection,spectrogram interpretation and artifact identification.Gaussian function windowed STFTs were applied to some cylinder head vibration signals.The spectrograms of the same signals from ST and AWT were also determined for comparison.The results indicate that the uniform resolution feature of STFT is not necessarily a disadvantage for time-frequency analysis of vibration signals when the engine is in stationary state because it can more accurately localize the frequency components excited by transient excitations without much loss of time resolution.
基金This research was funded by the National Natural Science Fund of China[grant number 41701415]Science fund project of Wuhan Institute of Technology[grant number K201724]Science and Technology Development Funds Project of Department of Transportation of Hubei Province[grant number 201900001].
文摘Radiometric normalization,as an essential step for multi-source and multi-temporal data processing,has received critical attention.Relative Radiometric Normalization(RRN)method has been primarily used for eliminating the radiometric inconsistency.The radiometric trans-forming relation between the subject image and the reference image is an essential aspect of RRN.Aimed at accurate radiometric transforming relation modeling,the learning-based nonlinear regression method,Support Vector machine Regression(SVR)is used for fitting the complicated radiometric transforming relation for the coarse-resolution data-referenced RRN.To evaluate the effectiveness of the proposed method,a series of experiments are performed,including two synthetic data experiments and one real data experiment.And the proposed method is compared with other methods that use linear regression,Artificial Neural Network(ANN)or Random Forest(RF)for radiometric transforming relation modeling.The results show that the proposed method performs well on fitting the radiometric transforming relation and could enhance the RRN performance.
基金Supported by National Natural Science Foundation of China(No. 10372068).
文摘The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.
基金This work was supported by The National Key Research and Development Program(No.2016YFC0600505 and 2018YFC0603701)National Natural Science Foundation(No.41974134 and 41774127).
文摘The Q-factor is an important physical parameter for characterizing the absorption and attenuation of seismic waves propagating in underground media,which is of great signifi cance for improving the resolution of seismic data,oil and gas detection,and reservoir description.In this paper,the local centroid frequency is defi ned using shaping regularization and used to estimate the Q values of the formation.We propose a continuous time-varying Q-estimation method in the time-frequency domain according to the local centroid frequency,namely,the local centroid frequency shift(LCFS)method.This method can reasonably reduce the calculation error caused by the low accuracy of the time picking of the target formation in the traditional methods.The theoretical and real seismic data processing results show that the time-varying Q values can be accurately estimated using the LCFS method.Compared with the traditional Q-estimation methods,this method does not need to extract the top and bottom interfaces of the target formation;it can also obtain relatively reasonable Q values when there is no eff ective frequency spectrum information.Simultaneously,a reasonable inverse Q fi ltering result can be obtained using the continuous time-varying Q values.
文摘We present new connections among linear anomalous diffusion (AD), normal diffusion (ND) and the Central Limit Theorem (CLT). This is done by defining a point transformation to a new position variable, which we postulate to be Cartesian, motivated by considerations from super-symmetric quantum mechanics. Canonically quantizing in the new position and momentum variables according to Dirac gives rise to generalized negative semi-definite and self-adjoint Laplacian operators. These lead to new generalized Fourier transformations and associated probability distributions, which are form invariant under the corresponding transform. The new Laplacians also lead us to generalized diffusion equations, which imply a connection to the CLT. We show that the derived diffusion equations capture all of the Fractal and Non-Fractal Anomalous Diffusion equations of O’Shaughnessy and Procaccia. However, we also obtain new equations that cannot (so far as we can tell) be expressed as examples of the O’Shaughnessy and Procaccia equations. The results show, in part, that experimentally measuring the diffusion scaling law can determine the point transformation (for monomial point transformations). We also show that AD in the original, physical position is actually ND when viewed in terms of displacements in an appropriately transformed position variable. We illustrate the ideas both analytically and with a detailed computational example for a non-trivial choice of point transformation. Finally, we summarize our results.
文摘Early detection of sudden cardiac death may be used for surviving the life of cardiac patients. In this paper we have investigated an algorithm to detect and predict sudden cardiac death, by processing of heart rate variability signal through the classical and time-frequency methods. At first, one minute of ECG signals, just before the cardiac death event are extracted and used to compute heart rate variability (HRV) signal. Five features in time domain and four features in frequency domain are extracted from the HRV signal and used as classical linear features. Then the Wigner Ville transform is applied to the HRV signal, and 11 extra features in the time-frequency (TF) domain are obtained. In order to improve the performance of classification, the principal component analysis (PCA) is applied to the obtained features vector. Finally a neural network classifier is applied to the reduced features. The obtained results show that the TF method can classify normal and SCD subjects, more efficiently than the classical methods. A MIT-BIH ECG database was used to evaluate the proposed method. The proposed method was implemented using MLP classifier and had 74.36% and 99.16% correct detection rate (accuracy) for classical features and TF method, respectively. Also, the accuracy of the KNN classifier were 73.87% and 96.04%.
基金The project supported by the President Foundation of the Chinese Academy of Sciences and National Natural Science Foundation of China under Grant No. 10475056.
文摘We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.
基金supported by the National Natural Science Foundation of China(611011726137118461301262)
文摘This paper proposes a new method for estimating the parameter of maneuvering targets based on sparse time-frequency transform in over-the-horizon radar（OTHR）. In this method, the sparse time-frequency distribution of the radar echo is obtained by solving a sparse optimization problem based on the short-time Fourier transform. Then Hough transform is employed to estimate the parameter of the targets. The proposed algorithm has the following advantages： Compared with the Wigner-Hough transform method, the computational complexity of the sparse optimization is low due to the application of fast Fourier transform（FFT）. And the computational cost of Hough transform is also greatly reduced because of the sparsity of the time-frequency distribution. Compared with the high order ambiguity function（HAF） method, the proposed method improves in terms of precision and robustness to noise. Simulation results show that compared with the HAF method, the required SNR and relative mean square error are 8 dB lower and 50 dB lower respectively in the proposed method. While processing the field experiment data, the execution time of Hough transform in the proposed method is only 4% of the Wigner-Hough transform method.
基金We also thank the support from State Key Program for Basic Research of China(No.2003CB314702,No.2003CB314706)NSFC(No.10347125)+1 种基金the foundation of Doctoral Program of Ministrv of Education(No.20030286003)the foundation of Science and Technology of Southeast University(No.9206001270,No.9206001271)
文摘This paper investigates topological transformation during normal grain growth by carrying out a computer vertex simulation. Results show that topological correlation agrees with the models proposed by Blanc et al. and Weaire. Topological transformation occurs more often on grains with some topological classes instead of equal probability on each boundary. This can be qualitatively explained by topological correlation.
基金Supported by the National Natural Science Fundation of China(Grant No.69775009)
文摘A new time-frequency representation called Dopplerlet transform, which uses the dilated, translated and modulated windowed Doppler signals as its basis functions, is proposed, and the Fourier transform, short-time Fourier transform (including Gabor transform), wavelet transform, and chirplet transform are formulated in one framework of Dopplerlet transform accordingly.It is proved that the matching pursuits based on Dopplerlet basis functions are convergent, and that the energy of residual signals yielded in the decomposition process decays exponentially. Simulation results show that the matching pursuits with Dopplerlet basis functions can characterize compactly a nonstationary signal.
文摘The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.
文摘This paper presents an evaluation of time-frequency methods for the analysis of seismic signals.Background of the present work is to describe,how the frequency content of the signal is changing in time.The theoretical basis of short time Fourier transform,Gabor transform,wavelet transform,S-transform,Wigner distribution,Wigner-Ville distribution,Pseudo Wigner-Ville distribution,Smoothed Pseudo Wigner-Ville distribution,Choi-William distribution,Born-Jordan Distribution and cone shape distribution are presented.The strengths and weaknesses of each technique are verified by applying them to a particular synthetic seismic signal and recorded real time earthquake data.
