The second-order wavelet synchrosqueezing transform

The paper deals with the problem of representing non-stationary 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.