This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates th...This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.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
Radon- Wigner变换是一种直线积分的投影变换 ,它对多分量 L FM信号提供了较好的时频局域性 ,从而有利于多分量 L FM信号的解释和分析 .通过时域解线调和频域解线调处理可以完整地在时频平面计算出 Radon变换 .对于多分量 L FM信号的分...Radon- Wigner变换是一种直线积分的投影变换 ,它对多分量 L FM信号提供了较好的时频局域性 ,从而有利于多分量 L FM信号的解释和分析 .通过时域解线调和频域解线调处理可以完整地在时频平面计算出 Radon变换 .对于多分量 L FM信号的分析好于 Wigner- Ville变换等常用的时频变换 .展开更多
针对已有Radon-Wigner变换(RWT)对线性调频连续波(linear frequency modulated continuous wave,LFMCW)雷达目标加速度估计计算复杂高、精度低的问题,提出了一种改进的RWT算法。该算法通过熵值法得到加速度的粗估计,对RWT结果求二阶原...针对已有Radon-Wigner变换(RWT)对线性调频连续波(linear frequency modulated continuous wave,LFMCW)雷达目标加速度估计计算复杂高、精度低的问题,提出了一种改进的RWT算法。该算法通过熵值法得到加速度的粗估计,对RWT结果求二阶原点矩减小搜索计算量,并且提出了RWT插值方法,将其应用到迭代RWT中用于提高加速度估计精度。实验结果表明,该算法在低信噪比的情况下可以准确检测出匀加速微弱目标,计算量较小且精度较高。展开更多
Based on the Radon transform and fractional Fourier transform we introduce the fractional Radon trans-formation (FRT). We identify the transform kernel for FRT. The FRT of Wigner operator is derived, which naturallyre...Based on the Radon transform and fractional Fourier transform we introduce the fractional Radon trans-formation (FRT). We identify the transform kernel for FRT. The FRT of Wigner operator is derived, which naturallyreduces to the projector of eigenvector of the rotated quadrature in the usual Radon transform case.展开更多
The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distributi...The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution-a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.
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.
文摘针对已有Radon-Wigner变换(RWT)对线性调频连续波(linear frequency modulated continuous wave,LFMCW)雷达目标加速度估计计算复杂高、精度低的问题,提出了一种改进的RWT算法。该算法通过熵值法得到加速度的粗估计,对RWT结果求二阶原点矩减小搜索计算量,并且提出了RWT插值方法,将其应用到迭代RWT中用于提高加速度估计精度。实验结果表明,该算法在低信噪比的情况下可以准确检测出匀加速微弱目标,计算量较小且精度较高。
文摘Based on the Radon transform and fractional Fourier transform we introduce the fractional Radon trans-formation (FRT). We identify the transform kernel for FRT. The FRT of Wigner operator is derived, which naturallyreduces to the projector of eigenvector of the rotated quadrature in the usual Radon transform case.
基金supported by National Natural Science Foundation of China (Grant No 10874174)the President Foundation of Chinese Academy of Sciences
文摘The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution-a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.
