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Computing the Hilbert transform and its inverse

Abstract:

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 t...

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Publisher:
Unspecified
Publication date:
2009-11-01
UUID:
uuid:adcd2c51-7f30-4fc8-af02-0e1cf5529f21
Local pid:
oai:eprints.maths.ox.ac.uk:865
Deposit date:
2011-05-20

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