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.
| Subjects: | Complex Variables (math.CV); Information Theory (cs.IT) |
| Cite as: | arXiv:2605.25104 [math.CV] |
| (or arXiv:2605.25104v1 [math.CV] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25104 arXiv-issued DOI via DataCite (pending registration) |
From: Haipan Shi [view email]
[v1]
Sun, 24 May 2026 14:44:44 UTC (15 KB)
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