k-Ambiguity function in the framework of offset linear canonical transform

Abstract

A new version of ambiguity function (AF) associated with the offset linear canonical transform (OLCT) is considered in this paper. This new version of AF coined as the [Formula: see text]-AF associated with the OLCT ([Formula: see text]-AFOL) is defined based on the OLCT and the fractional instantaneous auto-correlation. A natural magnification effect characterized by the extra degrees of freedom of the OLCT and by a factor [Formula: see text] on the frequency axis enables the [Formula: see text]-AFOL to have flexibility to be used in cross-term reduction. Firstly, we defined the [Formula: see text]-AF associated with the OLCT ([Formula: see text]-AFOL), and establish its relationship with the [Formula: see text]-Wigner distribution in OLCT domain. Later on, we define the basic properties including the scaling, conjugate-symmetry, shifting, marginal and Moyal’s formulae of [Formula: see text]-AFOL in depth. The results show that [Formula: see text]-AFOL can be viewed as one of the generalizations of the classical AF which has elegance, simplicity and flexibility in the frequency marginal property. The novelty of our paper lies in applications part, where we have shown how the proposed transform is used for the detection of single-component and bi-component linear frequency-modulated (LFM) signals.