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

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. (C) 2000 Optical Society of America [S0740-3232(00)04012-6] OCIS codes: 070.0070, 200.0200.