Use of the cross polynomial Wigner-Ville distribution for instantaneous frequency estimation of non-linear FM signals

The polynomial Wigner-Ville distribution (PWVD) was previously proposed as a method for time-frequency analysis of polynomial FM signals. Due to its highly non-linear nature, the PWVD performs poorly in the presence of noise with moderate to low signal-to-noise ratio (SNR). The present paper defines the cross polynomial Wigner-Ville distribution (X-PWVD), as a linear transform of the observed signal and investigates its use for the instantaneous frequency (IF) estimation of non-stationary signals. By using the X-PWVD in a simple iterative algorithm, such as the one previously proposed for the cross Wigner-Ville distribution (X-WVD), an efficient IF estimator is constructed for polynomial (quadratic and cubic) FM signals at relatively low SNRs. This IF estimation algorithm also converges faster than the one given in Boashash and O´Shea (1993), for equivalent signals