A sharper uncertainty inequality which exhibits a lower bound tighter than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained. The condition that reaches an equality relation of the uncertainty inequality is deduced. Example and simulations are carried out to illustrate that the newly derived uncertainty principle is truly sharper than the classical one. The new proposal's applications in time-frequency analysis, optical signal processing and physical optics propagation are also given.A sharper uncertainty inequality which exhibits a lower bound tighter than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained. The condition that reaches an equality relation of the uncertainty inequality is deduced. Example and simulations are carried out to illustrate that the newly derived uncertainty principle is truly sharper than the classical one. The new proposal's applications in time-frequency analysis, optical signal processing and physical optics propagation are also given.

IEEE Signal Processing LettersJan 1, 202126 citations

ON THE UNCERTAINTY PRINCIPLE

A. Gamba

Il Nuovo CimentoMay 31, 19500 citations

N -dimensional Heisenberg’s uncertainty principle for fractional Fourier transform

Zhichao Zhang

A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N -dimensional Heisenberg’s uncertainty principle is obtained, and extended from N -dimensional Fourier transform domain to two N -dimensional fractional Fourier transform domains. The conditions that reach the equality relation of the uncertainty inequalities are deduced. Example and simulation are performed to illustrate that the newly derived uncertainty principles are truly sharper than the existing ones in the literature. The new proposals’ applications in time-frequency analysis and optical system analysis are also given.A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N -dimensional Heisenberg’s uncertainty principle is obtained, and extended from N -dimensional Fourier transform domain to two N -dimensional fractional Fourier transform domains. The conditions that reach the equality relation of the uncertainty inequalities are deduced. Example and simulation are performed to illustrate that the newly derived uncertainty principles are truly sharper than the existing ones in the literature. The new proposals’ applications in time-frequency analysis and optical system analysis are also given.

arXiv:1906.05451Mar 9, 20201 citation

The New Uncertainty Principle

David Appell

Scientific AmericanJan 1, 200189 citations

Generalized Uncertainty Inequalities on Fisher Information Associated with LCT

Guanlei Xu, Xiaogang Xu, Xiaotong Wang

Uncertainty principle plays an important role in multiple fields such as physics, mathematics, signal processing, etc. The linear canonical transform (LCT) has been used widely in optics and information processing and so on. In this paper, a few novel uncertainty inequalities on Fisher information associated with linear canonical transform are deduced. These newly deduced uncertainty relations not only introduce new physical interpretation in signal processing, but also build the relations between the uncertainty lower bounds and the LCT transform parameters a, b, c and d for the first time, which give us the new ideas for the analysis and potential applications. In addition, these new uncertainty inequalities have sharper and tighter bounds which are the generalized versions of the traditional counterparts. Furthermore, some numeric examples are given to demonstrate the efficiency of these newly deduced uncertainty inequalities.Uncertainty principle plays an important role in multiple fields such as physics, mathematics, signal processing, etc. The linear canonical transform (LCT) has been used widely in optics and information processing and so on. In this paper, a few novel uncertainty inequalities on Fisher information associated with linear canonical transform are deduced. These newly deduced uncertainty relations not only introduce new physical interpretation in signal processing, but also build the relations between the uncertainty lower bounds and the LCT transform parameters a, b, c and d for the first time, which give us the new ideas for the analysis and potential applications. In addition, these new uncertainty inequalities have sharper and tighter bounds which are the generalized versions of the traditional counterparts. Furthermore, some numeric examples are given to demonstrate the efficiency of these newly deduced uncertainty inequalities.

Journal of Beijing Institute of TechnologySep 30, 20211 citation