Scaled Ambiguity Function Associated with Quadratic-Phase Fourier Transform

Quadratic-phase Fourier transform (QPFT) as a general integral transform has been considered into Wigner distribution (WD) and Ambiguity function (AF) to show more powerful ability for non-stationary signal processing. In this article, a new version of ambiguity function (AF) coined as scaled ambiguity function associated with the Quadratic-phase Fourier transform (QPFT) is proposed. This new version of AF is defined based on the QPFT and the fractional instantaneous auto-correlation. Firstly, we define the scaled ambiguity function associated with the QPFT (SAFQ). Then, the main properties including the conjugate-symmetry, shifting, scaling, marginal and Moyal’s formulae of SAFQ are investigated in detail, the results show that SAFQ can be viewed as the generalization of the classical AF. Finally, the newly defined SAFQ is used for the detection of linear-frequency-modulated (LFM) signals.