Fractional Hilbert transform

Adolf W. Lohmann; David Mendlovic; Zeev Zalevsky

doi:10.1364/OL.21.000281

Fractional Hilbert transform

Adolf W. Lohmann^*
, David Mendlovic
, Zeev Zalevsky

^*Corresponding author for this work

School of Electrical Engineering

Weizmann Institute of Science
Friedrich-Alexander University Erlangen-Nürnberg
Tel Aviv University

Research output: Contribution to journal › Article › peer-review

208 Scopus citations

Abstract

We have generalized the Hilbert transform by defining the fractional Hilbert transform (FHT) operation. In the first stage, two different approaches for defining the FHT are suggested. One is based on modifying only the spatial filter, and the other proposes using the fractional Fourier plane for filtering. In the second stage, the two definitions are combined into a fractional Hilbert transform, which is characterized by two parameters. Computer simulations are presented.

Original language	English
Pages (from-to)	281-283
Number of pages	3
Journal	Optics Letters
Volume	21
Issue number	4
DOIs	https://doi.org/10.1364/OL.21.000281
State	Published - 15 Feb 1996

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10.1364/OL.21.000281

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title = "Fractional Hilbert transform",

abstract = "We have generalized the Hilbert transform by defining the fractional Hilbert transform (FHT) operation. In the first stage, two different approaches for defining the FHT are suggested. One is based on modifying only the spatial filter, and the other proposes using the fractional Fourier plane for filtering. In the second stage, the two definitions are combined into a fractional Hilbert transform, which is characterized by two parameters. Computer simulations are presented.",

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year = "1996",

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AB - We have generalized the Hilbert transform by defining the fractional Hilbert transform (FHT) operation. In the first stage, two different approaches for defining the FHT are suggested. One is based on modifying only the spatial filter, and the other proposes using the fractional Fourier plane for filtering. In the second stage, the two definitions are combined into a fractional Hilbert transform, which is characterized by two parameters. Computer simulations are presented.

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Fractional Hilbert transform

Abstract

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