Anzeige
Erschienen in:
2014 | OriginalPaper | Buchkapitel
Computing the Hilbert Transform in Wavelet Bases on Adaptive Grids
verfasst von : Frank Martin, Elias Wegert
Erschienen in: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation
Verlag: Springer Basel
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We propose an algorithm for the efficient numerical computation of the periodic Hilbert transform. The function to be transformed is represented in a basis of spline wavelets in Sobolev spaces. The underlying grids have a hierarchical structure which is locally refined during computation according to the behavior of the involved functions. Under appropriate assumptions, we prove that the algorithm can deliver a result with prescribed accuracy. Several test examples illustrate how the method works in practice.