Uncertainty principles and fourier analysis

Yonggang Li, Yanan Zhang

Steeve Zozor, M. Portesi, Christophe Vignat

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.

Deng Feng-ru

Starting from the definition of Fourier transform,uncertainty principle in quantum mechanics is educed by the short term Fourier transform for the time variable signal.And the necessity of the relation between them is explained in this article,and an Ap- plication example about uncertainty principle in the wavelet analysis is given.

E. U. Condon