Numerical evaluation of the Hilbert transform by the Fast Fourier Transform (FFT) technique

Hsi‐Ping ‐P Liu, Dan D. Kosloff

Research output: Contribution to journalArticlepeer-review

Abstract

Summary. Three Fast Fourier Transform numerical methods for computing the Hilbert transform have been evaluated for their accuracy by numerical examples. All three methods employ the property that the Hdbert transform is a convolution. The first method uses the result that the Fourier transform of 1/πx is — isgn(ω). The second method is based on a discrete Hilbert transform introduced by Saito. The third method, introduced in this research note, uses linear interpolation to transform the Hilbert transform integral into a discrete convolution. The last method is shown by numerical examples from fault dislocation models to be more accurate than the other two methods when the Hilbert transform integral has high‐frequency components.

Original languageEnglish
Pages (from-to)791-799
Number of pages9
JournalGeophysical Journal of the Royal Astronomical Society
Volume67
Issue number3
DOIs
StatePublished - Dec 1981
Externally publishedYes

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