The Uncertainty Principles of Quaternion Fractional Fourier Transform

May 24, 2026 · Grace Period · + Add venue

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Authors Ke Cui, Haipan Shi, Xiaomin Tang arXiv ID 2605.25104 Category math.CV Cross-listed cs.IT Citations 0
Abstract
In this paper, we mainly establish the uncertainty principle (UP) for a function and its quaternion Fractional Fourier transform (QFrFT), as well as the UP for two QFrFTs. Using the polar representation of quaternion-valued signals, we give the UP for QFrFT in both the spatial and directional domains, providing a more precise condition for equality, example is given to verify the results. Furthermore, we extend the time-frequency UP to a frequency-frequency setting.
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