Analysis of Reassignment Operators Used in Synchrosqueezing Transforms: With an Application to Instantaneous Frequency Estimation

In this paper, our goal is to investigate the behavior of reassignment operators used in synchrosqueezing transforms to reassign the time-frequency representation of multicomponent signals made of the superposition of amplitude and frequency modulated modes. Indeed, while these operators are particularly efficient on specific types of modes, their quality worsens drastically when the modes depart from the ideal case they are designed for. In particular, when these interfere in the time-frequency plane or when some noise is present, we show the limits to the use of these reassignment operators for the estimation of the instantaneous frequency of the modes by studying their behavior in the vicinity of spectrogram ridges, and then propose a novel approach to circumvent these limitations.