The Uncertainty Principles of Quaternion Fractional Fourier Transform
This is an incremental theoretical contribution for researchers working on quaternion signal processing and harmonic analysis.
The paper establishes uncertainty principles for the quaternion fractional Fourier transform, providing conditions for equality and extending the time-frequency uncertainty principle to a frequency-frequency setting.
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.