MAKING SYNCHROSQUEEZING LOCALLY ADAPTIVE IN THE TIME-FREQUENCY PLANE

In this work, we explore the problem of making synchrosqueezing transform adaptive. Existing methods use a fixed order $N$ that assumes all the modes in the multicomponent signal have phases that behave as polynomials of order $N$. In this work, we introduce a new criterion to locally choose the best order of synchrosqueezing transform that retrieves the best representation for a multicomponent signal. We study its performance in terms of concentration and error with respect to ideal representation on both synthetic and real signals.