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

Abstract

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 and optical system analysis are also given. MSC 2010: 28A10, 42A38, 42B10, 81V80

The N-Dimensional Uncertainty Principle for the Free Metaplectic Transformation

“…are parameter matrices of the FMT. In Reference [13], he extends the classical N-dimensional Heisenberg's uncertainty principle to the fractional Fourier transform (FRFT). To the best of our knowledge, there are no other results published about UPs associated with the FMT.…”