Extending the scaling Wigner distribution in the realm of linear canonical domains

This paper studies a new distribution associated with the linear canonical transform (LCT), which is general to the scaled Wigner distribution (SWD) and abbreviated as SWDLC. Furthermore, some basic properties of the proposed distributions, such as shift property, conjugation symmetry property, marginal property, Moyal formula, anti-derivative property, and relationship with the short-time Fourier transform (STFT), are also presented in detail. The proposed new distribution has more advantages in the number of parameters than some known distributions. Besides, it shows not only flexibility but also superiority over SWD, especially in a cross-term reduction in the instantaneous frequency estimation of bi-component linear frequency modulation (LFM) signals. Furthermore, the parameter conditions for better angle and distance resolutions are lucidly demonstrated. In addition, numerical simulations clearly also show the superiority of the new distribution.