A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformatio...A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.展开更多
<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace sat...<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.展开更多
A phase-shift fiber Bragg grating (FBG) with sampling is proposed to generate a multi-channel bandpass filter in the background of multi-channel stopbands.The sampled moiré fiber gratings are analyzed by Fourier ...A phase-shift fiber Bragg grating (FBG) with sampling is proposed to generate a multi-channel bandpass filter in the background of multi-channel stopbands.The sampled moiré fiber gratings are analyzed by Fourier transform theory first,and then simulation and experiment are performed,the results show that transmission peaks are opened in every reflective channel,the spectrum shape of every channel is identical.It can be used to fabricate multi-wavelength distributed feedback (DFB) fiber laser.展开更多
A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better conv...A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.展开更多
In the process of fault detection and classification,the operation mode usually drifts over time,which brings great challenges to the algorithms.Because traditional machine learning based fault classification cannot d...In the process of fault detection and classification,the operation mode usually drifts over time,which brings great challenges to the algorithms.Because traditional machine learning based fault classification cannot dynamically update the trained model according to the probability distribution of the testing dataset,the accuracy of these traditional methods usually drops significantly in the case of covariate shift.In this paper,an importance-weighted transfer learning method is proposed for fault classification in the nonlinear multi-mode industrial process.It effectively alters the drift between the training and testing dataset.Firstly,the mutual information method is utilized to perform feature selection on the original data,and a number of characteristic parameters associated with fault classification are selected according to their mutual information.Then,the importance-weighted least-squares probabilistic classifier(IWLSPC)is utilized for binary fault detection and multi-fault classification in covariate shift.Finally,the Tennessee Eastman(TE)benchmark is carried out to confirm the effectiveness of the proposed method.The experimental result shows that the covariate shift adaptation based on importance-weight sampling is superior to the traditional machine learning fault classification algorithms.Moreover,IWLSPC can not only be used for binary fault classification,but also can be applied to the multi-classification target in the process of fault diagnosis.展开更多
Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a t...Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？展开更多
A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ ...A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.展开更多
To determine the feasibility and practicability of interrupt continuous wave (CW) approach proposed for real time simulating radar intermediate frequency(IF) video signal, theoretical analysis and computer simulation...To determine the feasibility and practicability of interrupt continuous wave (CW) approach proposed for real time simulating radar intermediate frequency(IF) video signal, theoretical analysis and computer simulation were used. Phases at two linked points between the end and beginning of adjoined frames are always consistent; the bias Doppler frequency for the time delay of A/D sampling start responds to that for target acceleration. No digital phase compensation is required at continuous points, and the interrupt CW approach has apparently practical values.展开更多
In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉x...In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.展开更多
We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform bu...We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between ∑a^m=1v（φ（ta））and L2[0, 2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on ∑a^m=1v（φ（ta））.展开更多
文摘A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.
文摘<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.
文摘A phase-shift fiber Bragg grating (FBG) with sampling is proposed to generate a multi-channel bandpass filter in the background of multi-channel stopbands.The sampled moiré fiber gratings are analyzed by Fourier transform theory first,and then simulation and experiment are performed,the results show that transmission peaks are opened in every reflective channel,the spectrum shape of every channel is identical.It can be used to fabricate multi-wavelength distributed feedback (DFB) fiber laser.
基金This work is supported in part by the National Natural Science Foundation of China （10771190, 10801136）, the Mathematical Tianyuan Foundation of China NSF （10526036）, China Postdoctoral Science Foundation （20060391063）, Natural Science Foundation of Guangdong Province （07300434）
文摘A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.
文摘In the process of fault detection and classification,the operation mode usually drifts over time,which brings great challenges to the algorithms.Because traditional machine learning based fault classification cannot dynamically update the trained model according to the probability distribution of the testing dataset,the accuracy of these traditional methods usually drops significantly in the case of covariate shift.In this paper,an importance-weighted transfer learning method is proposed for fault classification in the nonlinear multi-mode industrial process.It effectively alters the drift between the training and testing dataset.Firstly,the mutual information method is utilized to perform feature selection on the original data,and a number of characteristic parameters associated with fault classification are selected according to their mutual information.Then,the importance-weighted least-squares probabilistic classifier(IWLSPC)is utilized for binary fault detection and multi-fault classification in covariate shift.Finally,the Tennessee Eastman(TE)benchmark is carried out to confirm the effectiveness of the proposed method.The experimental result shows that the covariate shift adaptation based on importance-weight sampling is superior to the traditional machine learning fault classification algorithms.Moreover,IWLSPC can not only be used for binary fault classification,but also can be applied to the multi-classification target in the process of fault diagnosis.
文摘Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？
文摘A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.
文摘To determine the feasibility and practicability of interrupt continuous wave (CW) approach proposed for real time simulating radar intermediate frequency(IF) video signal, theoretical analysis and computer simulation were used. Phases at two linked points between the end and beginning of adjoined frames are always consistent; the bias Doppler frequency for the time delay of A/D sampling start responds to that for target acceleration. No digital phase compensation is required at continuous points, and the interrupt CW approach has apparently practical values.
文摘In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.
文摘We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between ∑a^m=1v（φ（ta））and L2[0, 2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on ∑a^m=1v（φ（ta））.
