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 analysis and optical system
analysis are also given.