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Generalized entropic uncertainty principle on fractional Fourier transform

Guanlei Xu, Xiaotong Wang, Xiaogang Xu

Signal ProcessingMay 29, 200942 citations

Generalized Heisenberg uncertainty relations for complex-valued signals out of Hilbert transform associated with LCT

Guanlei Xu, Xiaogang Xu, Xiaotong Wang

OptikSep 24, 20207 citations

A generalized uncertainty principle of the fractional Fourier transforms

Yonggang Li, Yanan Zhang

International Conference on Optics, Electronics, and Communication Engineering (OECE)Nov 21, 20250 citations

Heisenberg’s uncertainty principle for N -dimensional fractional Fourier transform of complex-valued functions

Zhichao Zhang, Puyu Han, Yun Ping Sun +6 more

OptikApr 26, 20218 citations

Generalized uncertainty principles associated with Hilbert transform

Guanlei Xu, Xiaotong Wang, Wang Longtao +3 more

Signal Image and Video ProcessingSep 12, 201312 citations

Bi-dimensional Generalized Uncertainty Relations Associated with Hilbert Transform in LCT Domain

Guanlei Xu, Shao Limin, Xiaotong Wang +1 more

This paper discusses the Heisenberg’s uncertainty relations associated with two types of 2D LCT (linear canonical transform). These uncertainty bounds are related with the transform parameters of LCT. In addition, we show that the certainty bounds for the complex signals derived by LCT are different with that for the general complex signals in most cases. The special cases of these principles in traditional domains are provided as well. First, these new uncertainty relations enrich the ensemble of uncertainty principles. Second, these derived bounds yield new viewpoint of complex signals via 2D Hilbert transform.This paper discusses the Heisenberg’s uncertainty relations associated with two types of 2D LCT (linear canonical transform). These uncertainty bounds are related with the transform parameters of LCT. In addition, we show that the certainty bounds for the complex signals derived by LCT are different with that for the general complex signals in most cases. The special cases of these principles in traditional domains are provided as well. First, these new uncertainty relations enrich the ensemble of uncertainty principles. Second, these derived bounds yield new viewpoint of complex signals via 2D Hilbert transform.

DEStech Transactions on Engineering and Technology ResearchDec 21, 20161 citation

Generalized entropic uncertainty principles on the complex signals in terms of fractional Hilbert transform

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