Abstract
The Hilbert transform is an important tool in image processing and optics. The Hilbert transform can be generalized to a fractional Hilbert transform. The generalization is driven by optics and image processing. We will generalize the fractional Hilbert transform into 2 dimensions by rotating the Hilbert transform in \({\mathbb{R}^{3}}\). The definition of the Hilbert transform as well as of the rotations will be done by quaternions.
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Dedicated to Klaus Gürlebeck on his 60-th Birthday
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Bernstein, S. A Fractional Hilbert Transform for 2D Signals. Adv. Appl. Clifford Algebras 24, 921–930 (2014). https://doi.org/10.1007/s00006-014-0489-6
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DOI: https://doi.org/10.1007/s00006-014-0489-6