Heisenberg’s uncertainty principle for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e71" altimg="si4.svg"><mml:mi>N</mml:mi></mml:math>-dimensional fractional Fourier transform of complex-valued functions

Zhang, Zhichao; Han, Pu-Yu; Sun, Yun; Wu, An-Yang; Shi, Xi-Ya; Qiang, Sheng-Zhou; Xia, Jiang; Ga, Wang; Liu, Lu-Bo

doi:10.1016/j.ijleo.2021.167052

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Cited by 5 publications

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“…When A = cos α sin α − sin α cos α , the above theorem can reduce the N-dimensional Heisenberg's inequality of the FRFT for complex function [8].…”

Section: Corollarymentioning

confidence: 96%

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Inequalities for the Windowed Linear Canonical Transform of Complex Functions

Gao

2023

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In this paper, we generalize the N-dimensional Heisenberg’s inequalities for the windowed linear canonical transform (WLCT) of a complex function. Firstly, the definition for N-dimensional WLCT of a complex function is given. In addition, the N-dimensional Heisenberg’s inequality for the linear canonical transform (LCT) is derived. It shows that the lower bound is related to the covariance and can be achieved by a complex chirp function with a Gaussian function. Finally, the N-dimensional Heisenberg’s inequality for the WLCT is exploited. In special cases, its corollary can be obtained.

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“…When A = cos α sin α − sin α cos α , the above theorem can reduce the N-dimensional Heisenberg's inequality of the FRFT for complex function [8].…”

Section: Corollarymentioning

confidence: 96%

“…Zhang [8] has generalized the N-dimensional Heisenberg's inequality of the FT for complex function. It can be restated as follows:…”

Section: Inequalities Associated With the Wlctmentioning

confidence: 99%