Local polynomial periodogram for time-varying frequency estimation

The local polynomial time-frequency transform (LPTFT) and the local polynomial time-frequency periodogram (LPP) are proposed in order to estimate a rapidly time-varying frequency Omega(t) of a harmonic signal. The LPTFT gives a time-frequency energy distribution over the t - (Omega(t), d Omega(t)/dt, ..., d(m-1)Omega(t)/Pt-m-1) space, where m is the degree of the LPTFT. The LPTFT enables one to estimate both the time-varying frequency and its derivatives. The technique is based on the fitting of a local polynomial approximation of the frequency which implements a high-order nonparametric regression. The a priori information about bounds for the frequency and its derivatives can be incorporated to improve the accuracy of the estimation. The estimator is shown to be strongly consistent and Gaussian for a polynomial frequency. The asymptotic MSE of the estimators of d(s) Omega(t)/dt(s), s = 0, 1, 2,..., m(-1), are obtained for the case of a frequency with bounded m-derivative. Simulation results are presented.