Linear canonical ambiguity function and linear canonical transform moments

A new phase-space distribution, linear canonical ambiguity function (LCAF), is proposed based on the linear canonical transform (LCT). The properties and physical meaning of the LCAF are given. The LCT moments are introduced and the relationships between the LCAF and the LCT moments are also derived. As an application, simple expressions for the center of gravity of the LCT power spectra and the effective width of the first-order optical system diffracted beam are derived. Compared with the conventional ambiguity function, the LCAF has three additional freedoms, i.e., the parameters characterizing a LCT, which make the LCAF more attractive for the analysis of optical signals.