Local polynomial approximation of the instantaneous frequency: Asymptotic accuracy

The local polynomial approximation of the time-varying phase is used in order to estimate the instantaneous frequency and its derivatives for a case of a complex harmonic signal. The considered estimators are high-order generalization of the short-time Fourier transform and the Wigner-Ville distribution. The asymptotic variance and bias of the estimates are obtained in order to evaluate the accuracy and the tracking ability of the algorithms. The comparative study of the algorithms is presented.