Synchrosqueezing of Multicomponent Signals

This report refers to work completed during my research internship at LJK Laboratory, Grenoble, from February until June 2014, under direction of M. Sylvain MEIGNEN, in fulfilment of the requirements for the degree of Master 2 of Philosophy in the IM2AG-UJF-Grenoble. Many practical signals can be modelized as a superposition of AM-FM modes. Such signals are usually called multi- component signals because they have several modes. One of the most significant issue of time-frequency (TF) analysis of such signals is the uncertainty principle, which stipulates that one cannot localize a signal with an arbitrary precision both in time and frequency. To cope with this limitation, reassignment methods aiming at sharpening the TF representations were introduced. A recent method called SynchroSqueezing Transforms (SST) has a similar purpose with the additional advantage of enabling the reconstruction of the different modes making up the signal. Unfortunately, SST is not adapted to signals having significant frequency modulation. To deal with this issue, an extension of SST called Vertical SST of order 2 (VSST) has been introduced.