A performance analysis of polynomial FM signals

The polynomial Wigner-Ville distribution was designed as an optimal tool for characterising the spectral contents of a signal whose phase is a polynomial of a certain order. In this contribution, the peak of the polynomial Wigner-Ville distribution is used to estimate the instantaneous frequency of a polynomial phase signal. A general expression for the asymptotic variance is derived for the estimator, and a statistical comparison with a parametric method for estimating the instantaneous frequency, using the high-order ambiguity function, is established.