Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform

T. Alieva, M.J. Bastiaans

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)

Abstract

The ambiguity function and Cohen's class of bilinear phase-space distributions are represented in a quasi-polar coordinate system instead of in a Cartesian system. Relationships between these distributions and the fractional Fourier transform are derived; in particular, derivatives of the ambiguity function are related to moments of the fractional power spectra. A simplification is achieved for the description of underspread signals, for optical beam characterization, and for the generation of signal-adaptive phase-space distributions.
Original languageEnglish
Pages (from-to)2324-2329
Number of pages6
JournalJournal of the Optical Society of America A, Optics, Image Science and Vision
Volume17
Issue number12
DOIs
Publication statusPublished - 2000

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polar coordinates
Fourier transforms
ambiguity
Power spectrum
Derivatives
simplification
power spectra
moments

Cite this

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Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform. / Alieva, T.; Bastiaans, M.J.

In: Journal of the Optical Society of America A, Optics, Image Science and Vision, Vol. 17, No. 12, 2000, p. 2324-2329.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Alieva, T.

AU - Bastiaans, M.J.

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AB - The ambiguity function and Cohen's class of bilinear phase-space distributions are represented in a quasi-polar coordinate system instead of in a Cartesian system. Relationships between these distributions and the fractional Fourier transform are derived; in particular, derivatives of the ambiguity function are related to moments of the fractional power spectra. A simplification is achieved for the description of underspread signals, for optical beam characterization, and for the generation of signal-adaptive phase-space distributions.

U2 - 10.1364/JOSAA.17.002324

DO - 10.1364/JOSAA.17.002324

M3 - Article

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JO - Journal of the Optical Society of America A, Optics, Image Science and Vision

JF - Journal of the Optical Society of America A, Optics, Image Science and Vision

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