Realization of the polynomial Wigner-Ville distribution (PWVD) based on the convolution in frequency domain

The Polynomial Wigner-Ville Distribution (PWVD) is a time-frequency signal analysis tool for representing Polynomial Phase Signal (PPS). An algorithm for implementation of the PWVD based on the convolution in frequency domain according to the structure of the PWVD is presented in this paper. By decomposing the PWVD into a series of convolutions of WVD or LWVD, the cross-terms can be reduced just because the WVD or LWVD can be calculated by the STFT, which is a linear transform. At the same time, the PWVD have a high time frequency convergence. The discrete implementation method and the corresponding computation complexity are analyzed and the effectiveness of the method is illustrated with numerical examples.