Abstract
The quaternion Fourier transform (QFT) and its properties are reviewed in this paper. Under the polar coordinate form for quaternion-valued signals, we strengthen the stronger uncertainty principles in terms of covariance for quaternion-valued signals based on the right-sided quaternion Fourier transform in both the directional and the spatial cases. We also obtain the conditions that give rise to the equal relations of two uncertainty principles. Examples are given to verify the results.
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