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 Heisenberg's inequality and Bell's inequality

Masao Nagasawa

Kodai Mathematical JournalMar 1, 20121 citation

Inequalities in the Heisenberg and Schrödinger Uncertainty Relations

Wu Jiao, Yuan Li

数学进展Jul 3, 20190 citations

Fractional fourier transform: A variant of Heisenberg uncertainty principle, weighted uncertainty inequality and application

Mawardi Bahri

The focus of this article is to propose two different versions of the Heisenberg uncertainty principle related to the fractional Fourier transform (FrFT). The first version is directly derived using the basic connection between the traditional Fourier transform (FT) and the FrFT, and the second is derived by exploiting time differentiation property and Parseval’s formula for the FrFT. In addition, a weighted uncertainty inequality related to this transformation is investigated. As a simple illustration of the use of the obtained results, we design the fractional characteristic function. An inequality describing the relation between the probability density function and its fractional characteristic function is presented.The focus of this article is to propose two different versions of the Heisenberg uncertainty principle related to the fractional Fourier transform (FrFT). The first version is directly derived using the basic connection between the traditional Fourier transform (FT) and the FrFT, and the second is derived by exploiting time differentiation property and Parseval’s formula for the FrFT. In addition, a weighted uncertainty inequality related to this transformation is investigated. As a simple illustration of the use of the obtained results, we design the fractional characteristic function. An inequality describing the relation between the probability density function and its fractional characteristic function is presented.

An International Journal of Optimization and Control Theories & Applications (IJOCTA)Jul 6, 20260 citations

Generalisations of Heisenberg's inequality

Michael Cowling, John Price

Lecture notes in mathematicsJan 1, 198397 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