Periodogram with varying and data-driven window length

The short-time Fourier transform and the corresponding periodogram give biased estimates of the instantaneous frequency (IF) if the IF in question is a nonlinear function of time. In the case of noisy signals, the optimal choice of the window length, based on asymptotic formulae for the variance and bias, can resolve the bias—variance trade-off usual for nonparametric estimation. However, the practical value of such optimal estimator is not significant since the optimal window length depends on the unknown smoothness of the IF. The main goal of this paper is to develop an adaptive, periodogram-based IF estimator with a time-varying and data-driven window length which is able to provide the accuracy close to the one that could be achieved if the smoothness of the IF were known in advance. The developed algorithm uses only the estimates of the IF and the formula for the variance of these estimates. Simulation shows good accuracy ability of the adaptive algorithm. ( 1998 Elsevier Science B.V. All rights reserved.