by Swanhild Bernstein (Submitted top arxiv on 10 Jun 2015)
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.
Subjects: Functional Analysis (math.FA)
MSC classes: 44A15, 30G35, 94A12, 94A08
Cite as: arXiv:1507.05035 [math.FA], (or arXiv:1507.05035v1 [math.FA] for this version)
Source: Email from S. Bernstein, 2015/07/22 21:48, swanhild.bernstein_AT_math.tu-freiberg.de, http://arxiv.org/pdf/1507.05035v1