The Mathematical Institute, University of Oxford, Eprints Archive

Computing the Hilbert transform and its inverse

Olver, Sheehan (2009) Computing the Hilbert transform and its inverse. Technical Report. Unspecified. (Submitted)

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We construct a new method for approximating Hilbert transforms and their inverse throughout the complex plane. Both problems can be formulated as Riemann-Hilbert problems via Plemelj's lemma. Using this framework, we re-derive existing approaches for computing Hilbert transforms over the real line and unit interval, with the added benefit that we can compute the Hilbert transform in the complex plane. We then demonstrate the power of this approach by generalizing to the half line. Combining two half lines, we can compute the Hilbert transform of a more general class of functions on the real line than is possible with existing methods.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Partial differential equations
H - N > Integral equations
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:865
Deposited By: Lotti Ekert
Deposited On:17 Dec 2009 08:04
Last Modified:29 May 2015 18:33

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