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arXiv · 1507.05035

Fractional Riesz-Hilbert transforms and fractional monogenic signals

Swanhild Bernstein
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Abstract

The fractional Hilbert transforms plays an important role in optics and signal processing. In particular the analytic signal proposed by Gabor has as a key component the Hilbert transform. The higher dimensional Hilbert transform is the Riesz-Hilbert transform which was used by Felsberg and Sommer to construct the monogenic signal. We will construct fractional and quaternionic fractional Riesz-Hilbert transforms based on a eigenvalue decomposition. We will prove properties of these transformations such as shift and scale invariance, orthogonality and the semigroup property. Based on the fractional/quaternionic fractional Riesz-Hilbert transform we construct (quaternionic) fractional monogenic signals. These signals are rotated and modulated monogenic signals.

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Swanhild Bernstein. 2015-06-10. Fractional Riesz-Hilbert transforms and fractional monogenic signals. https://arxiv.org/abs/1507.05035

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