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arXiv · 2605.25104

The Uncertainty Principles of Quaternion Fractional Fourier Transform

Ke Cui·Haipan Shi·Xiaomin Tang
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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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Ke Cui, Haipan Shi, Xiaomin Tang. 2026-05-24. The Uncertainty Principles of Quaternion Fractional Fourier Transform. https://arxiv.org/abs/2605.25104

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