New Wigner distribution and ambiguity function based on the generalized translation in the linear canonical transform domain

• A new kind of WD and AF based on generalized translation in LCT domain is proposed.
• Some important and useful properties of LWD and LAF are derived.
• LWD and LAF are used to estimate parameters of LFM signals.
• Compare LWD with LCWD and WDL, and LAF with LCAF and AFL in detection of LFM signals.
• LWD and LAF achieve better detection performance under low SNR.

The Wigner distribution (WD) and ambiguity function (AF) associated with the linear canonical transform (LCT), such as the linear canonical WD (LCWD), the linear canonical AF (LCAF), the generalized WD (WDL) and the generalized AF (AFL), have been shown to be very useful in non-stationary signal processing. Although the LCWD, LCAF, WDL and AFL can apply to the detection of linear frequency-modulated (LFM) signal, which is an important non-stationary signal and was widely applied in radar and sonar systems, both of them exhibit poor detection performance under low signal-to-noise ratio (SNR). In this paper, a new kind of WD and AF is derived based on the generalized translation in the LCT domain. Some essential properties and the applications of the newly defined WD and AF in the detection of the parameters of LFM signals are investigated. The results show that the new WD and AF applied to the parameters estimation for LFM signals are very useful and effective and achieve better detection performance than the LCWD and LCAF, respectively, as well as the WDL and AFL, respectively. Simulations are also given to verify the correctness and effectiveness of the proposed methods.