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

Abstract

International audienceThis 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. This study paves the way to the real-time computation of a time-frequency representation which is both invertible and sharply localized in frequency

The ASTRES toolbox for mode extraction of non-stationary multicomponent signals

“…An efficient recursive implementation (suitable for real-time computation), is proposed in [10], [12]. It uses a specific causal (one-sided) analysis window which can be expressed as h k (t)=…”

“…Thus, both classical and Levenberg-Marquardt reassigned Stockwellograms are obtained through Eqs. (12) and (13), by replacing F …”

“…Vertical synchrosqueezing uses an improved estimation of the instantaneous frequency (instead of the classical reassignment operator), thanks to the chirp rate estimationα x (t,ω) = Im(q x (t,ω)) (see [12] for a further investigation). The improved frequency estimator can be computed aŝ…”

“…For amplitude modulated signals, it is shown in [12] that (27) is biased, and can be improved using a slightly different estimator expressed as (when |q x (t,ω)| < ∞)…”

“…1), designed for automatic signal mode extraction, can be viewed as an extension of the previously proposed Time-Frequency ToolBox (TFTB) 1 . It contains implementations of some recent contributions related to reassignment, synchrosqueezing [10], [11], [6], [12], EMD [13], [14], and SSA [9] methods. This paper is organized as follows.…”