T. Alieva et Mj. Bastiaans, Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform, J OPT SOC A, 17(12), 2000, pp. 2324-2329
The ambiguity function and Cohen's class of bilinear phase-space distributi
ons are represented in a quasi-polar coordinate system instead of in a Cart
esian 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 simplifi
cation is achieved for the description of underspread signals, for optical
beam characterization, and for the generation of signal-adaptive phase-spac
e distributions. (C) 2000 Optical Society of America [S0740-3232(00)04012-6
] OCIS codes: 070.0070, 200.0200.