New time--frequency distribution based on the polynomial Wigner--Ville distribution and L class of Wigner--Ville distribution

A new kind of time-frequency distribution based on the polynomial Wigner-Ville distribution (PWVD) and L class of Wigner-Ville distribution (LWVD) is presented in this study, and it is named as LPWVD. The LPWVD can be implemented based on the convolution of LWVD in frequency domain. Compared with the PWVD, the LPWVD is cross-term free for multi-component signals, and the time-frequency convergence is higher than the PWVD. The asymptotic statistical performance of LPWVD for estimating the instantaneous frequency (IF) of a polynomial phase signal (PPS) is studied. The simulated results demonstrate the validity of the LPWVD.