  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.
