Abstract
The two-sided quaternion Fourier transform was introduced for the analysis of 2D linear time-invariant partial-differential systems. It has been shown to be a powerful tool in image processing. In this paper, several uncertainty inequalities for the two-sided quaternion Fourier transform are given with optimal constants, including the Pitt's inequality, logarithmic uncertainty inequality, Hausdorff–Young inequality, Hirschman's entropy inequality, generalized Heisenberg inequality, local uncertainty principle and qualitative uncertainty principle.
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