Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator,...Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula （Huygens-Fresnel integration transformation describing optical diffraction）. The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz -- rz^＊ in the ｜Z〉g representation, while ｜z〉g in phase space is graphically denoted by an ellipse.展开更多
We propose the quadratic constrained formulas for the design of linear phase cosine modulated paraunitary filter banks given in references . Using these formulae, we can, directly, optimize the prototype filter coeff...We propose the quadratic constrained formulas for the design of linear phase cosine modulated paraunitary filter banks given in references . Using these formulae, we can, directly, optimize the prototype filter coefficients in a quadratic form. A design example is also given to demonstrate these formulae in this paper.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10874174 and 10675108)the President Foundation of the Chinese Academy of Sciencesthe Specilized Research Fund for the Doctorial Program of the Higher Education of China (Grant No.20070358009)
文摘Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula （Huygens-Fresnel integration transformation describing optical diffraction）. The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz -- rz^＊ in the ｜Z〉g representation, while ｜z〉g in phase space is graphically denoted by an ellipse.
文摘We propose the quadratic constrained formulas for the design of linear phase cosine modulated paraunitary filter banks given in references . Using these formulae, we can, directly, optimize the prototype filter coefficients in a quadratic form. A design example is also given to demonstrate these formulae in this paper.
