We analyze the stability properties of the Synchrosqueezing transform, a time-frequency signal analysis method that can identify and extract oscillatory components with time-varying frequency and amplitude. We show that Synchrosqueezing is robust to bounded perturbations of the signal and to Gaussian white noise. These results justify its applicability to noisy or nonuniformly sampled data that...

This paper provides a general overview of Time-Frequency reassignment and synchrosqueezing techniques applied to multicomponent signals, covering the theoretical background and applications. We explain how synchrosqueezing can be viewed as a special case of reassignment enabling mode reconstruction and place emphasis on the interest of using such time-frequency distributions throughout with ill...

The synchrosqueezing method aims at decomposing 1D functions as superpositions of a small number of “Intrinsic Modes”, supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its reconstruction properties, the synchrosqueezing transform provides a powerful representation of multicomponent signals in the time-frequency plane, together with a re...

This paper provides a general overview of Time-Frequency reassignment and synchrosqueezing techniques applied to multicomponent signals in terms of the theoretical background and applications. Our goal is first to show how synchrosqueezing can be viewed as a special case of reassignment with the advantage of enabling mode reconstruction, under the assumption of small frequency modulation for th...

We consider in this article the analysis of multicomponent signals, defined as superpositions of modulated waves also called modes. More precisely, we focus on the analysis of a variant of the second-order synchrosqueezing transform, which was introduced recently, to deal with modes containing strong frequency modulation. Before going into this analysis, we revisit the case where the modes are ...

The Synchrosqueezing transform is a time-frequency analysis method that can decompose complex signals into time-varying oscillatory components. It is a form of time-frequency reassignment that is both sparse and invertible, allowing for the recovery of the signal. This article presents an overview of the theory and stability properties of Synchrosqueezing, as well as applications of the techniq...

The modulated oscillation model provides physically meaningful representations of timevarying harmonic processes, and has been instrumental in the development of modern time-frequency algorithms, such as the synchrosqueezing transform. We here extend this concept to multivariate signals, in order to identify oscillations common to multiple data channels. This is achieved by introducing a multiv...

Despite the population of the noninvasive, economic, comfortable, and easy-to-install photoplethysmography (PPG) sensor, a mathematically rigorous and stable algorithm to simultaneously extract the fundamental physiological information, including the instantaneous heart rate (IHR) and the instantaneous respiratory rate (IRR), from the single-channel PPG signal is lacking. A novel signal process...

We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu, andWu [Appl. Comput. Harmonic Anal., 30 (2010), pp. 243–261] and consider a variant of Synchrosqueezing, based on the short-time Fourier transform, to precisely define the instantaneous frequencies of a multicomponent AM-FM signal. W...