Generalized polynomial wigner spectrogram for high-resolution time-frequency analysis

Abstract

A good time-frequency (TF) analysis method should have the advantages of high clarity and no cross term. However, there is always a trade-off between the two goals. In this paper, we propose a new TF analysis method, which is called the generalized polynomial Wigner spectrogram (GPWS). It combines the generalized spectrogram (GS) and the polynomial Wigner-Ville distribution (PWVD). The PWVD has a good performance for analyzing the instantaneous frequency of a high order exponential function. However, it has the cross term problem in the multiple component case. By contrast, the GS can avoid the cross term problem, but its clarity is not enough. The proposed GPWS can combine the advantages of the PWVD and the GS. It can achieve the goals of high clarity, no cross term, and less computation time simultaneously. We also perform simulations to show that the proposed GPWS has better resolution than other TF analysis methods.