Chirp Rate and Instantaneous Frequency Estimation: Application to Recursive Vertical Synchrosqueezing

This letter introduces new chirp rate and instantaneous frequency estimators designed for frequency-modulated signals. These estimators are first investigated from a deterministic point of view, then compared together in terms of statistical efficiency. They are also used to design new recursive versions of the vertically synchrosqueezed short-time Fourier transform, using a previously published method (D. Fourer, F. Auger, and P. Flandrin, “Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT,” in
Proc. IEEE Int. Conf. Acoust., Speech Signal Process.
, Mar. 2016, pp. 4880–4884). This study paves the way to the real-time computation of a time-frequency representation, which is both invertible and sharply localized in frequency.