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

JOSA A, Vol. 17, Issue 12, pp. 2324-2329 (2000)

http://dx.doi.org/10.1364/JOSAA.17.002324

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### 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.

© 2000 Optical Society of America

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(200.0200) Optics in computing : Optics in computing

**History**

Original Manuscript: May 11, 2000

Revised Manuscript: September 11, 2000

Manuscript Accepted: September 11, 2000

Published: December 1, 2000

**Citation**

Tatiana Alieva and Martin J. Bastiaans, "Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform," J. Opt. Soc. Am. A **17**, 2324-2329 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-12-2324

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