Heisenberg's uncertainty principles for the 2-D nonseparable linear canonical transforms
Heisenberg's uncertainty principles for the 2-D nonseparable linear canonical transforms
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DOI：
10.1016/j.sigpro.2012.11.023
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发表时间：
2013-05
期刊：
影响因子：
--
通讯作者：
Jian-Jiun Ding;S. Pei
中科院分区：
文献类型：
--
作者：
Jian-Jiun Ding;S. Pei
一维傅里叶变换（FT）、一维分数傅里叶变换（FRFT）和一维线性正则变换（LCT）的不确定性原理已经被导出。本文推广了前人的工作，导出了二维不可分线性正则变换（2-D NSLCT）的测不准原理，包括复输入、真实的输入和det（B）=0的情况，其中B是2-D NSLCT的参数子集.由于二维NSLCT是许多运算的推广，因此，利用所导出的不确定性原理，还可以找到许多二维运算的不确定性原理，如二维Fresnel变换、二维FT、二维FRFT、二维LCT、二维Gyrator变换等，而且，我们还发现，旋转、缩放、二维高斯函数的线性调频乘法可以使空间域和变换域的方差乘积最小。
The uncertainty principles of the 1-D Fourier transform (FT), the 1-D fractional Fourier transform (FRFT), and the 1-D linear canonical transform (LCT) have already been derived. In this paper, we extend the previous works and derive the uncertainty principles for the two-dimensional nonseparable linear canonical transform (2-D NSLCT), including the complex input case, the real input case, and the case where det(B)=0 where B is a parameter subset of the 2-D NSLCT. Since the 2-D NSLCT is a generalization of many operations, with the derived uncertainty principles, the uncertain principles of many 2-D operations, such as the 2-D Fresnel transform, the 2-D FT, the 2-D FRFT, the 2-D LCT, and the 2-D gyrator transform, can also be found. Moreover, we find that the rotation, scaling, and chirp multiplication of the 2-D Gaussian function can minimize the product of the variances in the space and the transform domains.