Unified Wigner–Ville distribution and ambiguity function in the linear canonical transform domain

Abstract

In this paper, we propose a novel integral transform by combining the generalized Wigner–Ville distribution (WDL) with the linear canonical transform (LCT). The new integral transform unifies the WDL and the generalized ambiguity function (AFL), and then can be considered as a generalization of the classical Wigner–Ville distribution (WVD) and ambiguity function (AF). Some useful properties of the new integral transform are derived, including conjugation symmetry property, conjugation invariance of LCT, marginal properties, shifting properties, anti-derivative property and Moyal formula. The relationships between the new integral transform and other common time–frequency analysis tools are discussed, such as the LCT, the short-time Fourier transform (STFT) and the short-time linear canonical transform (STLCT). The applications of the newly defined integral transform in the detection of one-component and bi-component linear frequency-modulated (LFM) signals embedded in white Gaussian noise are investigated. The comparisons of the detection performance of the new integral transform with that of the WDL and AFL are also performed to show the preponderance of the proposed techniques. The simulation results indicate that the new integral transform achieves better detection performance than the WDL and AFL.