New Integral Transforms for Generalizing the Wigner Distribution and Ambiguity Function

The Wigner distribution (WD) and ambiguity function (AF) associated with the linear canonical transform (LCT) play a major role in non-stationary signal processing. Many novel time-frequency analysis tools for it exist, such as the linear canonical WD (LCWD), the linear canonical AF (LCAF), the WD in the LCT domain (WDL) and the AF in the LCT domain (AFL). The purpose of this letter is to introduce new integral transforms that can be regarded as the generalization of LCWD, LCAF, WDL, and AFL. Moreover, the newly defined integral transforms are shown to be useful and effective in filter design in the LCT domain for the separation of multi-component signals and detection of linear frequency-modulated (LFM) signals. The results show that the new integral transforms achieve better detection performance than LCWD, LCAF, WDL, and AFL. Simulations are also performed to verify the rationality and effectiveness of the derived methods.