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.

In this letter, we describe a new method for bidimensional empirical mode decomposition (EMD). This decomposition is based on Delaunay triangulation and on piecewise cubic polynomial interpolation. Particular attention is devoted to boundary conditions that are crucial for the feasibility of the bidimensional EMD. The study of the behavior of the decomposition on a different kind of image shows its efficiency in terms of computational cost, and the decomposition of Gaussian white noises leads to bidimensional selective filter banks.Index Terms-Delaunay triangulation, empirical mode decomposition (EMD).