The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. Thi...The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects： instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.展开更多
In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[...In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.展开更多
获得同时含有稳态频率和瞬态频率成分信号的高分辨率时频分布是时频分析的重点与难点,为了解决此类信号进行同步压缩短时傅里叶变换(synchro-squeezed short time Fourier transform,SSTFT)时窗长受限的问题,提出了基于小波包分解的自...获得同时含有稳态频率和瞬态频率成分信号的高分辨率时频分布是时频分析的重点与难点,为了解决此类信号进行同步压缩短时傅里叶变换(synchro-squeezed short time Fourier transform,SSTFT)时窗长受限的问题,提出了基于小波包分解的自适应同步压缩短时傅里叶变换(adaptive synchro-squeezed short time Fourier transform by wave packet decomposition,WPD-ASSTFT)方法。首先,借助小波包分解将信号分解为若干个子信号;之后,对不同的子信号进行自适应窗长选择,确定使子信号进行短时傅里叶变换(short time Fourier transform,STFT)的时频分布Renyi熵值最小时对应的窗长——最优窗长;然后,将各个子信号在最优窗长下进行SSTFT;最后,将所有子信号的时频分布相加得到原始信号的时频分布。通过小波包分解,将信号分解为不同频率范围的子信号,通过自适应窗长选择,使得SSTFT的时频图分辨率最佳。利用该方法对仿真信号和铁路轴箱加速度信号进行分析,结果表明:由WPD-ASSTFT得到的时频分布具有良好的分辨率。展开更多
This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)i...This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)is the n-th term of the Gram-Schmidt orthogonalization of the Szego kernels k_(a1),k_(an),or their multiple forms.Three schemes are presented.The first two schemes each directly obtain all the function values f(z).In the first one we use Nevanlinna’s inner and outer function factorization which merely requires the 1-intensity measurements equivalent to know the modulus|f(z)|.In the second scheme we do not use deep complex analysis,but require some 2-and 3-intensity measurements.The third scheme,as an application of AFD,gives sparse representation of f(z)converging quickly in the energy sense,depending on consecutively selected maximal n-intensity measurements|<f,E_(a1…an)>|.展开更多
基金supported by the UM Multi-Year Research Grant under Grant No.MYRG144(Y3-L2)-FST11-ZLM
文摘The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects： instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.
基金University of Macao Multi-Year Research Grant Ref.No MYRG2016-00053-FST and MYRG2018-00168-FSTthe Science and Technology Development Fund,Macao SAR FDCT/0123/2018/A3.
文摘In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.
文摘获得同时含有稳态频率和瞬态频率成分信号的高分辨率时频分布是时频分析的重点与难点,为了解决此类信号进行同步压缩短时傅里叶变换(synchro-squeezed short time Fourier transform,SSTFT)时窗长受限的问题,提出了基于小波包分解的自适应同步压缩短时傅里叶变换(adaptive synchro-squeezed short time Fourier transform by wave packet decomposition,WPD-ASSTFT)方法。首先,借助小波包分解将信号分解为若干个子信号;之后,对不同的子信号进行自适应窗长选择,确定使子信号进行短时傅里叶变换(short time Fourier transform,STFT)的时频分布Renyi熵值最小时对应的窗长——最优窗长;然后,将各个子信号在最优窗长下进行SSTFT;最后,将所有子信号的时频分布相加得到原始信号的时频分布。通过小波包分解,将信号分解为不同频率范围的子信号,通过自适应窗长选择,使得SSTFT的时频图分辨率最佳。利用该方法对仿真信号和铁路轴箱加速度信号进行分析,结果表明:由WPD-ASSTFT得到的时频分布具有良好的分辨率。
基金The Science and Technology Development Fund,Macao SAR(File no.0123/2018/A3)supported by the Natural Science Foundation of China(61961003,61561006,11501132)+2 种基金Natural Science Foundation of Guangxi(2016GXNSFAA380049)the talent project of the Education Department of the Guangxi Government for one thousand Young-Middle-Aged backbone teachersthe Natural Science Foundation of China(12071035)。
文摘This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)is the n-th term of the Gram-Schmidt orthogonalization of the Szego kernels k_(a1),k_(an),or their multiple forms.Three schemes are presented.The first two schemes each directly obtain all the function values f(z).In the first one we use Nevanlinna’s inner and outer function factorization which merely requires the 1-intensity measurements equivalent to know the modulus|f(z)|.In the second scheme we do not use deep complex analysis,but require some 2-and 3-intensity measurements.The third scheme,as an application of AFD,gives sparse representation of f(z)converging quickly in the energy sense,depending on consecutively selected maximal n-intensity measurements|<f,E_(a1…an)>|.
