线性正则变换域Wigner-Ville分布的熵不确定性原理

Entropic Uncertainty Relations of the Wigner-Ville Distribution in Linear Canonical Transform Domain

  • 摘要: 针对线性正则变换相关的不确定性原理的研究问题,本文得到线性正则变换域Wigner-Ville分布的熵不确定性原理.根据线性正则变换的性质与特点,得到线性正则变换域的Pitt不等式,根据此不等式进一步得到了线性正则变换域Wigner-Ville分布的熵不确定关系式.所得到结果可以看作是经典熵不确性关系式在线性正则变换域的广义形式,为深入研究线性正则变换的理论及应用奠定良好的基础.

     

    Abstract: To investigate the uncertainty principle problems associated with the linear canonical transform, a new kind of entropic uncertainty relation for Wigner-Ville distribution associated with the linear canonical transform domain was derived. Firstly, the Pitt inequality in the linear canonical transform domain was generalized. And then the entropic uncertainty relation for Wigner-Ville distribution associated with the linear canonical transform domain was derived based on the Pitt inequality. The derived results can be taken as the generalization of the classical entropic uncertainty principle in the linear canonical transform domain, and lay the foundation for the theory and application investigation of linear canonical transform.

     

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