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.<
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