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
Original Manuscript: May 11, 2000
Revised Manuscript: September 11, 2000
Manuscript Accepted: September 11, 2000
Published: December 1, 2000
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)