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 illustrative examples.

This paper considers the analysis of multicomponent signals, defined as superpositions of real or complex modulated waves. It introduces two new post-transformations for the short-time Fourier transform, that achieve a compact time-frequency representation while allowing for the separation and the reconstruction of the modes. These two new transformations thus provide the benefits of both the synchrosqueezing transform (which allows for reconstruction) and the reassignment method (which achieves a compact time-frequency representation). Numerical experiments on real and synthetic signals demonstrate the efficiency of these new transformations, and illustrate their differences.

The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are extensively used to analyze and process multicomponent signals, i.e. superpositions of modulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relation inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the CWT, it provides a sharp, concentrated representation, while remaining invertible. This technique received a renewed interest with the recent publication of an approximation result related to the application of the synchrosqueezing to multicomponent signals. In the current paper, we adapt the formulation of the synchrosqueezing to the STFT and state a similar theoretical result to that obtained in the CWT framework. The emphasis is put on the differences with the CWT-based synchrosqueezing with numerical experiments illustrating our statements.

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 assumed to be with weak frequency modulation as in the seminal paper of Daubechies et al. [8], to show that the constraint on the compactness of the analysis window in the Fourier domain can be alleviated. We also explain why the hypotheses made on the modes making up the multicomponent signal must be different when one considers either wavelet or short-time Fourier transform-based synchrosqueezing. The rest of the paper is devoted to the theoretical analysis of the variant of the second order synchrosqueezing transform [16] and numerical simulations illustrate the performance of the latter.

No abstract

International audienceEmpirical Mode Decomposition (EMD) is a relatively new method for adaptive multiscale signal representation. As it allows to adaptively analyze nonlinear and non-stationary signals, it is widely used in signal processing. Yet, as the standard EMD method lacks a solid mathematical background, many alternative constructions have been proposed to define similar decompositions in a more comprehensive way. This paper is in line with this idea, as it defines a new decomposition that lies on direct constrained optimization. We show that this new approach gives satisfactory results for narrow-band signals and preserves the essential characteristics of the original EM

No abstract

The paper deals with the problem of representing nonstationary signals jointly in time and frequency. We use the framework of reassignment methods, that achieve sharp and compact representations. More precisely, we introduce an enhanced version of the synchrosqueezed wavelet transform, which is shown to be more general than the standard synchrosqueezing, while remaining invertible. Numerical experiments measure the improvement brought about by using our new technique on synthetic data, while an analysis of the gravitational wave signal recently observed through the LIGO interferometer applies the method on a real dataset.