Scaled ambiguity function and scaled Wigner distribution for LCT signals

Abstract

In this article, a new version of ambiguity function (AF) and Wigner distribution (WD) based on the linear canonical transform (LCT) and the fractional instantaneous auto-correlation are proposed which are coined as scaled ambiguity function and scaled Wigner distribution (SAFL/SWDL). We initiate our investigation by establishing the fundamental relationship between the SAFL and SWDL. Then, the main properties including the conjugate-symmetry, shifting, scaling, marginal and Moyal’s formulae of SAFL and SWDL are investigated in detail. Finally, the applications of the newly defined transforms are performed to show the advantage of the theory.